Evaluation G - 6 | 1.1 Solutions
1.1.1 What is the value of the digit 5 in the number 45,678,912? (A) 500 (B) 5,000 (C) 500,000 (D) 5,000,000 (E) 50,000,000.
Number: 45,678,912 → Digit 5 is in the millions place → Value = $5 \times 1,000,000 = 5,000,000$ → Answer: D. 5,000,000
1.1.2 Write the number eight million, four hundred and thirty-two thousand, seven hundred and sixty-nine in digits. (A) 8,432,769 (B) 8,423,769 (C) 8,432,679 (D) 8,342,769 (E) 8,432,796.
"eight million" = 8,000,000; "four hundred thirty‑two thousand" = 432,000; "seven hundred sixty‑nine" = 769 → Combined: 8,432,769 → Answer: A. 8,432,769
1.1.3 Nigeria's population is approximately 213,401,323. What is this number in words? (A) Two hundred and thirteen million, four hundred and one thousand, three hundred and twenty-three (B) Two hundred and thirteen million, four hundred and one thousand, three hundred and thirty-two (C) Two hundred and thirty-one million, four hundred and one thousand, three hundred and twenty-three (D) Two hundred and thirteen million, four hundred and ten thousand, three hundred and twenty-three (E) Two hundred and thirteen million, four hundred and one thousand, three hundred and twenty.
213,401,323 → 213 million, 401 thousand, 323 → "Two hundred and thirteen million, four hundred and one thousand, three hundred and twenty‑three" → Answer: A
1.1.4 Which digit is in the ten-millions place in the number 734,892,156? (A) 7 (B) 3 (C) 4 (D) 8 (E) 9.
734,892,156 → Place values: hundred‑millions = 7, ten‑millions = 3, millions = 4, ... → Ten‑millions digit = 3 → Answer: B. 3
1.1.5 What is the smallest 8-digit number you can form using the digits 8, 3, 5, 1, 9, 2, 7, 4 each only once? (A) 12,345,789 (B) 98,754,321 (C) 12,345,879 (D) 12,347,589 (E) 12,345,798.
Arrange digits in ascending order: 1,2,3,4,5,7,8,9 → Smallest number: 12,345,789 → Answer: A. 12,345,789
1.1.6 A company's annual revenue is ₦45,678,912. They spend ₦12,345,678 on salaries. How much money is left? (A) ₦33,333,234 (B) ₦33,333,334 (C) ₦33,333,134 (D) ₦33,333,034 (E) ₦33,433,234.
₦45,678,912 - ₦12,345,678 = ₦33,333,234 → Answer: A. ₦33,333,234
1.1.7 Round the number 456,789,123 to the nearest million. (A) 456,000,000 (B) 457,000,000 (C) 456,800,000 (D) 460,000,000 (E) 456,789,000.
456,789,123 → Look at hundred‑thousands digit (7) → 7 ≥ 5 → round up millions place → 457,000,000 → Answer: B. 457,000,000
1.1.8 What is the sum of 123,456,789 and 98,765,432? (A) 222,222,221 (B) 222,222,321 (C) 222,222,121 (D) 221,222,221 (E) 222,223,221.
$123,456,789 + 98,765,432 = 222,222,221$ → Answer: A. 222,222,221
1.1.9 Write ₦678,901,234 in words. (A) Six hundred and seventy-eight million, nine hundred and one thousand, two hundred and thirty-four naira (B) Six hundred and seventy-eight million, nine hundred and one thousand, two hundred and forty-three naira (C) Six hundred and eighty-seven million, nine hundred and one thousand, two hundred and thirty-four naira (D) Six hundred and seventy-eight million, nine hundred and ten thousand, two hundred and thirty-four naira (E) Six hundred and seventy-eight million, nine hundred and one thousand, three hundred and twenty-four naira.
678,901,234 → 678 million, 901 thousand, 234 → "Six hundred and seventy‑eight million, nine hundred and one thousand, two hundred and thirty‑four naira" → Answer: A
1.1.10 Which number is 10 million more than 345,678,912? (A) 355,678,912 (B) 345,688,912 (C) 346,678,912 (D) 445,678,912 (E) 365,678,912.
$345,678,912 + 10,000,000 = 355,678,912$ → Answer: A. 355,678,912
1.1.11 The distance from the Earth to the Sun is approximately 149,600,000 kilometres. What is this rounded to the nearest ten million? (A) 150,000,000 (B) 149,000,000 (C) 140,000,000 (D) 160,000,000 (E) 149,600,000.
149,600,000 → ten‑millions digit = 4, next digit (millions) = 9 ≥ 5 → round up → 150,000,000 → Answer: A. 150,000,000
1.1.12 What is the value of the digit 7 in the number 567,891,234? (A) 700 (B) 7,000 (C) 7,000,000 (D) 70,000,000 (E) 700,000,000.
567,891,234 → digit 7 is in the millions place → value = $7 \times 1,000,000 = 7,000,000$ → Answer: C. 7,000,000
1.1.13 Arrange these numbers in descending order: 78,934,567; 78,943,567; 78,934,657; 78,934,576; 78,934,675. What is the third number? (A) 78,934,576 (B) 78,934,567 (C) 78,934,657 (D) 78,934,675 (E) 78,943,567.
Descending order: 78,943,567 (1st), 78,934,675 (2nd), 78,934,657 (3rd), 78,934,576 (4th), 78,934,567 (5th) → Third number = 78,934,657 → Answer: C. 78,934,657
1.1.14 What is $700,000,000 + 80,000,000 + 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9$? (A) 783,456,789 (B) 783,456,879 (C) 783,465,789 (D) 783,456,798 (E) 783,457,789.
$700M+80M=780M$; $+3M=783M$; $+400k=783,400k$; $+50k=783,450k$; $+6k=783,456k$; $+700=783,456,700$; $+80=783,456,780$; $+9=783,456,789$ → Answer: A. 783,456,789
1.1.15 A country has a debt of ₦789,123,456. They pay back ₦45,678,901. How much debt remains? (A) ₦743,444,555 (B) ₦743,444,545 (C) ₦743,445,555 (D) ₦743,444,455 (E) ₦743,444,655.
$789,123,456 - 45,678,901 = 743,444,555$ → Answer: A. ₦743,444,555
1.1.16 Which number has an 8 that represents 80,000,000? (A) 182,345,678 (B) 218,345,678 (C) 238,145,678 (D) 812,345,678 (E) 128,345,678.
80,000,000 means 8 is in the ten‑millions place. In 182,345,678 → ten‑millions digit = 8 → value = 80,000,000 → Answer: A. 182,345,678
1.1.17 Round 923,456,789 to the nearest ten million. (A) 920,000,000 (B) 930,000,000 (C) 923,000,000 (D) 900,000,000 (E) 923,500,000.
923,456,789 → ten‑millions digit = 2, millions digit = 3 (<5) → round down → 920,000,000 → Answer: A. 920,000,000
1.1.18 A company makes a profit of ₦234,567,890 in the first year and ₦345,678,901 in the second year. What is the total profit? (A) ₦580,246,791 (B) ₦580,246,891 (C) ₦580,246,691 (D) ₦580,246,781 (E) ₦580,346,791.
$234,567,890 + 345,678,901 = 580,246,791$ → Answer: A. ₦580,246,791
1.1.19 What is the difference between 987,654,321 and 123,456,789? (A) 864,197,532 (B) 864,197,523 (C) 864,197,432 (D) 864,197,632 (E) 864,297,532.
$987,654,321 - 123,456,789 = 864,197,532$ → Answer: A. 864,197,532
1.1.20 Write the number that is 1,000 less than 800,000,000. (A) 799,999,000 (B) 799,000,000 (C) 799,989,000 (D) 799,990,000 (E) 799,999,999.
$800,000,000 - 1,000 = 799,999,000$ → Answer: A. 799,999,000
Evaluation G - 6 | 1.2 Solutions
1.2.1 In the number 7,245, what is the face value of the digit 4? (A) 4 (B) 40 (C) 400 (D) 4,000 (E) 40,000.
Face value of a digit is the digit itself → digit 4 has face value 4 → Answer: A. 4
1.2.2 What is the place value of the digit 6 in the number 8,623,195? (A) 6 (B) 600 (C) 6,000 (D) 60,000 (E) 600,000.
8,623,195 → digit 6 is in the hundred‑thousands place → place value = $6 \times 100,000 = 600,000$ → Answer: E. 600,000
1.2.3 What is the difference between the place value and face value of the digit 5 in the number 4,536,728? (A) 0 (B) 495 (C) 4,995 (D) 49,995 (E) 499,995.
4,536,728 → digit 5 is in the hundred‑thousands place → place value = 500,000, face value = 5 → Difference = $500,000 - 5 = 499,995$ → Answer: E. 499,995
1.2.4 In which number is the face value of the digit 9 equal to its place value? (A) 9,352 (B) 3,952 (C) 3,295 (D) 2,539 (E) 5,239.
Face value = place value only when the digit is in the ones place. In 2,539, the digit 9 is in the ones place → place value = 9, face value = 9 → Answer: D. 2,539
1.2.5 What is the face value of the digit 3 in the number 7,234,891? (A) 3 (B) 30 (C) 3,000 (D) 30,000 (E) 300,000.
Face value is always the digit itself regardless of position → digit 3 has face value 3 → Answer: A. 3
1.2.6 What is the place value of the digit 7 in the number 5,786,024? (A) 7 (B) 700 (C) 7,000 (D) 70,000 (E) 700,000.
5,786,024 → digit 7 is in the hundred‑thousands place → place value = $7 \times 100,000 = 700,000$ → Answer: E. 700,000
1.2.7 Find the sum of the face values of the digits 2, 5, and 8 in the number 2,485,736. (A) $2+5+8=15$ (B) $2+5+8=15$ but with different values (C) $200,000+5,000+800=205,800$ (D) $2,000+500+80=2,580$ (E) $2+5+8=15$ and that's the answer.
Face values: digit 2 → 2, digit 5 → 5, digit 8 → 8 → Sum = $2+5+8=15$ → Answer: A. $2+5+8=15$
1.2.8 In which number is the place value of 4 equal to 40,000? (A) 3,427,891 (B) 3,247,891 (C) 3,724,891 (D) 3,72,894 (E) 3,872,491.
Place value = 40,000 means the digit 4 must be in the ten‑thousands place.
Check each option:
(A) 3,427,891 → hundred‑thousands digit = 4 → place value = 400,000 ❌
(B) 3,247,891 = 3,247,891 → hundred‑thousands = 2, ten‑thousands = 4, thousands = 7 → digit 4 is in ten‑thousands place → place value = 40,000 ✅
(C) 3,724,891 = 3,724,891 → hundred‑thousands = 7, ten‑thousands = 2, thousands = 4 → digit 4 is in thousands place → place value = 4,000 ❌
(D) 3,72,894 = 372,894 → digits: hundred‑thousands = 3, ten‑thousands = 7, thousands = 2, hundreds = 8, tens = 9, ones = 4 → digit 4 is in ones place → place value = 4 ❌
(E) 3,872,491 = 3,872,491 → hundred‑thousands = 8, ten‑thousands = 7, thousands = 2, hundreds = 4 → digit 4 is in hundreds place → place value = 400 ❌
Only option (B) has the digit 4 in the ten‑thousands place, giving a place value of 40,000.
Answer: B. 3,247,891
1.2.9 What is the product of the face value and place value of the digit 6 in the number 4,267,893? (A) 36 (B) 360 (C) 3,600 (D) 36,000 (E) 360,000.
4,267,893 → digit 6 is in the ten‑thousands place → place value = 60,000, face value = 6 → Product = $6 \times 60,000 = 360,000$ → Answer: E. 360,000
1.2.10 The face value of a digit is always _____. (A) greater than its place value (B) less than its place value (C) equal to its place value (D) the digit itself (E) zero.
Face value is the digit itself, regardless of position → Answer: D. the digit itself
1.2.11 What is the place value of the digit 0 in the number 5,038,612? (A) 0 (B) 0 (C) 0 (D) 0 (E) 0.
The digit 0 is in the hundred‑thousands place → place value = $0 \times 100,000 = 0$ → Answer: A. 0
1.2.12 In the number 9,124,386, which digit has the same face value and place value? (A) 9 (B) 1 (C) 2 (D) 3 (E) 6.
Face value = place value only when digit is in the ones place. In 9,124,386, the ones digit is 6 → face value = 6, place value = 6 → Answer: E. 6
1.2.13 What is the difference between the place value and face value of the digit 8 in the number 6,834,207? (A) 0 (B) 792 (C) 7,992 (D) 79,992 (E) 799,992.
6,834,207 → digit 8 is in the hundred‑thousands place → place value = 800,000, face value = 8 → Difference = $800,000 - 8 = 799,992$ → Answer: E. 799,992
1.2.14 Find the sum of the place values of the digits 4 and 7 in the number 4,527,693. (A) $4+7=11$ (B) $4,000+700=4,700$ (C) $4,000,000+7,000=4,007,000$ (D) $400,000+7,000=407,000$ (E) $4,000,000+700=4,000,700$.
4,527,693 → digit 4 is in the millions place → 4,000,000; digit 7 is in the thousands place → 7,000 → Sum = $4,000,000 + 7,000 = 4,007,000$ → Answer: C. $4,000,000+7,000=4,007,000$
1.2.15 What is the face value of the digit 2 in the number 9,832,705? (A) 2 (B) 20 (C) 200 (D) 2,000 (E) 20,000.
Face value is the digit itself → digit 2 has face value 2 → Answer: A. 2
1.2.16 In which number is the place value of 5 equal to 500,000? (A) 4,563,892 (B) 4,653,892 (C) 4,356,892 (D) 4,536,892 (E) 4,635,892.
Place value = 500,000 means digit 5 must be in the hundred‑thousands place. In 4,356,892 → hundred‑thousands digit = 3, ten‑thousands=5? Wait: 4,356,892 = 4 million, 356 thousand → hundred‑thousands=3, ten‑thousands=5, thousands=6 → digit 5 is in ten‑thousands (50,000). In 4,563,892 → hundred‑thousands=5 → 500,000. So A. 4,563,892 → Answer: A. 4,563,892
1.2.17 What is the product of the face value and place value of the digit 3 in the number 1,358,246? (A) 9 (B) 900 (C) 9,000 (D) 90,000 (E) 900,000.
1,358,246 → digit 3 is in the hundred‑thousands place → place value = 300,000, face value = 3 → Product = $3 \times 300,000 = 900,000$ → Answer: E. 900,000
1.2.18 The place value of a digit is always _____ its face value except when the digit is in the ones place. (A) greater than (B) less than (C) equal to (D) greater than or equal to (E) less than or equal to.
For any position except ones, place value = digit × power of 10, which is ≥10 × digit (or > digit for non‑zero digits). So place value is greater than face value (unless digit=0, but then both zero). Typically, for non‑zero digits, place value > face value. Answer: A. greater than
1.2.19 In the number 7,294,583, what is the sum of the place values of the digits in the hundreds and ten thousands places? (A) $500 + 90,000 = 90,500$ (B) $500 + 9,000 = 9,500$ (C) $5,000 + 90,000 = 95,000$ (D) $500 + 900 = 1,400$ (E) $5 + 9 = 14$.
7,294,583 → hundreds place digit = 5 → place value = 500; ten‑thousands place digit = 9 → place value = 90,000 → Sum = $90,000 + 500 = 90,500$ → Answer: A. $500 + 90,000 = 90,500$
1.2.20 Which digit in the number 6,817,432 has a face value of 1 and a place value of 10,000? (A) 6 (B) 8 (C) 1 (D) 7 (E) 4.
Face value = 1 means the digit is 1. Place value = 10,000 means it must be in the ten‑thousands place. In 6,817,432 → digits: 6 (millions), 8 (hundred‑thousands), 1 (ten‑thousands), 7 (thousands), 4 (hundreds), 3 (tens), 2 (ones) → digit 1 is in ten‑thousands place → place value = 10,000. So digit is 1 → Answer: C. 1
Evaluation G - 6 | 1.3 Solutions
1.3.1 Round 347,892 to the nearest ten thousand. (A) 340,000 (B) 348,000 (C) 350,000 (D) 347,000 (E) 300,000.
347,892 → ten‑thousands digit = 4, thousands digit = 7 ≥ 5 → round up → 350,000 → Answer: C. 350,000
1.3.2 Which symbol makes this statement true? 456,789 ___ 456,798 (A) > (B) < (C) = (D) ≤ (E) ≃.
456,789 vs 456,798 → compare digit by digit: 456,789 < 456,798 → Answer: B. <
1.3.3 Round 5,678,432 to the nearest hundred thousand. (A) 5,600,000 (B) 5,700,000 (C) 5,680,000 (D) 5,678,000 (E) 5,000,000.
5,678,432 → hundred‑thousands digit = 6, ten‑thousands digit = 7 ≥ 5 → round up → 5,700,000 → Answer: B. 5,700,000
1.3.4 Arrange in ascending order: 234,567; 234,675; 243,567; 234,756. Which comes last? (A) 234,567 (B) 234,675 (C) 243,567 (D) 234,756 (E) 243,756.
Ascending order: 234,567 ; 234,675 ; 234,756 ; 243,567 → Last = 243,567 → Answer: C. 243,567
1.3.5 Round 8,923,456 to the nearest million. (A) 8,000,000 (B) 9,000,000 (C) 8,900,000 (D) 8,923,000 (E) 8,920,000.
8,923,456 → millions digit = 8, hundred‑thousands digit = 9 ≥ 5 → round up → 9,000,000 → Answer: B. 9,000,000
1.3.6 Which number is the largest? (A) 7,654,321 (B) 7,654,312 (C) 7,654,231 (D) 7,654,213 (E) 7,654,123.
Compare: all start 7,654,3xx → largest last three digits: 321 > 312 > 231 > 213 > 123 → Answer: A. 7,654,321
1.3.7 Round 3,456,789 to the nearest ten thousand. (A) 3,460,000 (B) 3,456,000 (C) 3,457,000 (D) 3,450,000 (E) 3,500,000.
3,456,789 → ten‑thousands digit = 5, thousands digit = 6 ≥ 5 → round up → 3,460,000 → Answer: A. 3,460,000
1.3.8 Which symbol makes this statement true? 6,789,012 ___ 6,789,102 (A) > (B) < (C) = (D) ≤ (E) ≃.
6,789,012 < 6,789,102 → Answer: B. <
1.3.9 Round 4,567,890 to the nearest hundred thousand. (A) 4,500,000 (B) 4,600,000 (C) 4,570,000 (D) 4,568,000 (E) 4,000,000.
4,567,890 → hundred‑thousands digit = 5, ten‑thousands digit = 6 ≥ 5 → round up → 4,600,000 → Answer: B. 4,600,000
1.3.10 Arrange in descending order: 5,678,901; 5,678,910; 5,678,109; 5,678,091. Which comes first? (A) 5,678,901 (B) 5,678,910 (C) 5,678,109 (D) 5,678,091 (E) 5,678,019.
Descending order (largest first): 5,678,910 ; 5,678,901 ; 5,678,109 ; 5,678,091 → First = 5,678,910 → Answer: B. 5,678,910
1.3.11 Round 9,876,543 to the nearest million. (A) 9,800,000 (B) 9,900,000 (C) 10,000,000 (D) 9,877,000 (E) 9,000,000.
9,876,543 → millions digit = 9, hundred‑thousands digit = 8 ≥ 5 → round up → 10,000,000 → Answer: C. 10,000,000
1.3.12 Which number is the smallest? (A) 2,345,678 (B) 2,345,687 (C) 2,345,768 (D) 2,345,786 (E) 2,345,867.
All start 2,345,6xx → smallest last three digits: 678 < 687 < 768 < 786 < 867 → Answer: A. 2,345,678
1.3.13 Round 1,234,567 to the nearest ten thousand. (A) 1,230,000 (B) 1,234,000 (C) 1,235,000 (D) 1,240,000 (E) 1,200,000.
1,234,567 → ten‑thousands digit = 3, thousands digit = 4 < 5 → round down → 1,230,000 → Answer: A. 1,230,000
1.3.14 Which symbol makes this statement true? 3,456,789 ___ 3,456,798 (A) > (B) < (C) = (D) ≤ (E) ≃.
3,456,789 < 3,456,798 → Answer: B. <
1.3.15 Round 6,543,210 to the nearest hundred thousand. (A) 6,500,000 (B) 6,540,000 (C) 6,543,000 (D) 6,600,000 (E) 6,000,000.
6,543,210 → hundred‑thousands digit = 5, ten‑thousands digit = 4 < 5 → round down → 6,500,000 → Answer: A. 6,500,000
1.3.16 Arrange in ascending order: 8,765,432; 8,765,324; 8,765,243; 8,765,234. Which comes first? (A) 8,765,432 (B) 8,765,324 (C) 8,765,243 (D) 8,765,234 (E) 8,765,423.
Ascending order (smallest first): 8,765,234 ; 8,765,243 ; 8,765,324 ; 8,765,432 → First = 8,765,234 → Answer: D. 8,765,234
1.3.17 Round 7,892,345 to the nearest million. (A) 7,000,000 (B) 7,800,000 (C) 7,900,000 (D) 8,000,000 (E) 7,892,000.
7,892,345 → millions digit = 7, hundred‑thousands digit = 8 ≥ 5 → round up → 8,000,000 → Answer: D. 8,000,000
1.3.18 Which number is between 4,567,890 and 4,567,980? (A) 4,567,890 (B) 4,567,908 (C) 4,567,980 (D) 4,567,809 (E) 4,567,098.
Between means greater than 4,567,890 and less than 4,567,980 → 4,567,908 satisfies 890 < 908 < 980 → Answer: B. 4,567,908
1.3.19 Round 9,234,567 to the nearest ten thousand. (A) 9,230,000 (B) 9,234,000 (C) 9,235,000 (D) 9,240,000 (E) 9,200,000.
9,234,567 → ten‑thousands digit = 3, thousands digit = 4 < 5 → round down → 9,230,000 → Answer: A. 9,230,000
1.3.20 What is the smallest 7-digit number you can make using the digits 3, 8, 1, 6, 9, 2, 5 each once? (A) 1,235,689 (B) 1,235,698 (C) 1,235,869 (D) 1,235,968 (E) 1,235,986.
Arrange digits in ascending order: 1,2,3,5,6,8,9 → smallest number = 1,235,689 → Answer: A. 1,235,689
Evaluation G - 6 | 1.4 Solutions (Estimation)
1.4.1 Estimate $48 \times 31$ by rounding each to the nearest ten. (A) 1200 (B) 1500 (C) 1000 (D) 1800 (E) 2000.
$48 \approx 50$, $31 \approx 30$, $50 \times 30 = 1500$ → Answer: B
1.4.2 A bag of rice weighs $5.2$ kg. Estimate total weight of $19$ bags. (A) 100 kg (B) 95 kg (C) 90 kg (D) 110 kg (E) 80 kg.
$5.2 \approx 5$, $19 \approx 20$, $5 \times 20 = 100$ kg → Answer: A
1.4.3 Estimate $612 \div 29$ by rounding to nearest ten. (A) 30 (B) 20 (C) 25 (D) 15 (E) 35.
$612 \approx 610$, $29 \approx 30$, $610 \div 30 \approx 20.33 \approx 20$ → Answer: B
1.4.4 A school needs $28$ buses, each carries $52$ students. Estimate total students. (A) 1500 (B) 1200 (C) 1800 (D) 1000 (E) 2000.
$28 \approx 30$, $52 \approx 50$, $30 \times 50 = 1500$ → Answer: A
1.4.5 Best estimate for $3.8 \times 9.2$? (A) 27 (B) 36 (C) 40 (D) 32 (E) 45.
$3.8 \approx 4$, $9.2 \approx 9$, $4 \times 9 = 36$ → Answer: B
1.4.6 Estimate sum $247 + 389 + 512$ by rounding each to nearest hundred. (A) 1100 (B) 1000 (C) 1200 (D) 900 (E) 1300.
$247 \approx 200$, $389 \approx 400$, $512 \approx 500$, sum $= 200 + 400 + 500 = 1100$ → Answer: A
1.4.7 Farmer has $96$ cows and $103$ goats. Estimate how many more goats than cows. (A) 10 (B) 0 (C) 5 (D) 15 (E) 20.
$96 \approx 100$, $103 \approx 100$, difference $\approx 0$ → Answer: B
1.4.8 Estimate $78.4 \div 3.9$. (A) 20 (B) 15 (C) 25 (D) 30 (E) 10.
$78.4 \approx 80$, $3.9 \approx 4$, $80 \div 4 = 20$ → Answer: A
1.4.9 A movie ticket costs ₦850. About how much for $23$ tickets? (A) ₦16,000 (B) ₦20,000 (C) ₦18,000 (D) ₦24,000 (E) ₦12,000.
$850 \approx 800$, $23 \approx 20$, $800 \times 20 = 16,000$ → Answer: A
1.4.10 Most reasonable estimate for $41 \times 58$? (A) 2000 (B) 2400 (C) 2500 (D) 3000 (E) 1800.
$41 \approx 40$, $58 \approx 60$, $40 \times 60 = 2400$ → Answer: B
1.4.11 Rectangle length $5.1$ cm, width $3.9$ cm. Estimate area. (A) 15 cm² (B) 20 cm² (C) 25 cm² (D) 10 cm² (E) 30 cm².
$5.1 \approx 5$, $3.9 \approx 4$, $5 \times 4 = 20$ cm² → Answer: B
1.4.12 Estimate $498 + 312 - 205$ by rounding each to nearest hundred. (A) 600 (B) 500 (C) 700 (D) 800 (E) 400.
$498 \approx 500$, $312 \approx 300$, $205 \approx 200$, $500 + 300 - 200 = 600$ → Answer: A
1.4.13 A packet has $24$ biscuits. Estimate biscuits in $17$ packets. (A) 400 (B) 500 (C) 300 (D) 600 (E) 200.
$24 \approx 20$, $17 \approx 20$, $20 \times 20 = 400$ → Answer: A
1.4.14 Which estimate is closest to $19.8 \times 5.1$? (A) 100 (B) 95 (C) 105 (D) 90 (E) 110.
$19.8 \approx 20$, $5.1 \approx 5$, $20 \times 5 = 100$ → Answer: A
1.4.15 A bottle holds $0.95$ litres. Estimate total in $32$ bottles. (A) 30 L (B) 25 L (C) 35 L (D) 40 L (E) 20 L.
$0.95 \approx 1$, $32 \approx 30$, $1 \times 30 = 30$ L → Answer: A
1.4.16 Estimate $7.8 + 12.2 + 5.9$ by rounding each to nearest whole number. (A) 26 (B) 27 (C) 25 (D) 28 (E) 24.
$7.8 \approx 8$, $12.2 \approx 12$, $5.9 \approx 6$, $8 + 12 + 6 = 26$ → Answer: A
1.4.17 A teacher has $145$ pencils for $29$ students. Estimate each gets. (A) 3 (B) 4 (C) 5 (D) 6 (E) 7.
$145 \approx 150$, $29 \approx 30$, $150 \div 30 = 5$ → Answer: C
1.4.18 Estimate perimeter of rectangle length $15.2$ cm, width $8.9$ cm. (A) 48 cm (B) 50 cm (C) 46 cm (D) 52 cm (E) 44 cm.
$15.2 \approx 15$, $8.9 \approx 9$, perimeter $= 2(15+9) = 2 \times 24 = 48$ cm → Answer: A
1.4.19 A car travels $52$ km per hour. Estimate distance in $7.8$ hours. (A) 400 km (B) 350 km (C) 450 km (D) 300 km (E) 500 km.
$52 \approx 50$, $7.8 \approx 8$, $50 \times 8 = 400$ km → Answer: A
1.4.20 Best estimate for $89 \times 31 \div 28$? (A) 90 (B) 100 (C) 80 (D) 110 (E) 120.
$89 \approx 90$, $31 \approx 30$, $28 \approx 30$, $90 \times 30 \div 30 = 90$ → Answer: A
Evaluation G - 6 | 2.1 Solutions (Addition & Subtraction of Whole Numbers)
2.1.1 Calculate $47,382 + 28,956$. (A) 77,338 (B) 75,338 (C) 76,338 (D) 76,238 (E) 75,238.
Step 1: Add units: $2 + 6 = 8$
Step 2: Add tens: $8 + 5 = 13$ → write 3, carry 1
Step 3: Add hundreds: $3 + 9 + 1 = 13$ → write 3, carry 1
Step 4: Add thousands: $7 + 8 + 1 = 16$ → write 6, carry 1
Step 5: Add ten-thousands: $4 + 2 + 1 = 7$
Result: $76,338$ → Answer: C
2.1.2 Find the difference: $90,000 - 34,567$. (A) 55,333 (B) 55,433 (C) 55,567 (D) 56,433 (E) 54,433.
Step 1: Borrow from 90,000 → 89,999 - 34,567
Step 2: $89,999 - 34,567 = 55,432$
Check: $55,433 + 34,567 = 90,000$ ✓ → Answer: B
2.1.3 A school library had $12,845$ books. Received donation of $7,392$ books. Total books? (A) 19,137 (B) 20,137 (C) 20,237 (D) 20,227 (E) 19,237.
$12,845 + 7,392$
Units: $5 + 2 = 7$
Tens: $4 + 9 = 13$ → write 3, carry 1
Hundreds: $8 + 3 + 1 = 12$ → write 2, carry 1
Thousands: $2 + 7 + 1 = 10$ → write 0, carry 1
Ten-thousands: $1 + 0 + 1 = 2$
Result: $20,237$ → Answer: C
2.1.4 Subtract: $6,203 - 2,894$. (A) 3,419 (B) 3,319 (C) 3,309 (D) 3,409 (E) 3,209.
$6,203 - 2,894$
Units: $3 - 4$ → borrow → $13 - 4 = 9$
Tens: $0 - 9$ → borrow → $10 - 9 = 1$
Hundreds: $1 - 8$ → borrow → $11 - 8 = 3$
Thousands: $5 - 2 = 3$
Result: $3,309$ → Answer: C
2.1.5 Add: $234,567 + 345,678$. (A) 580,345 (B) 579,235 (C) 579,245 (D) 580,235 (E) 580,245.
$234,567 + 345,678 = 580,245$
Check: $234,567 + 345,000 = 579,567$; $579,567 + 678 = 580,245$ → Answer: E
2.1.6 Farmer harvested $18,450$ kg yams and $22,675$ kg cassava. Total harvest? (A) 41,135 kg (B) 41,025 kg (C) 41,125 kg (D) 41,225 kg (E) 40,125 kg.
$18,450 + 22,675$
$18,450 + 22,000 = 40,450$
$40,450 + 675 = 41,125$ kg → Answer: C
2.1.7 Calculate: $500,000 - 123,456$. (A) 377,544 (B) 376,654 (C) 376,444 (D) 376,544 (E) 376,554.
$500,000 - 123,456 = 376,544$
Check: $376,544 + 123,456 = 500,000$ ✓ → Answer: D
2.1.8 Find the sum of $9,876$ and $5,432$. (A) 15,218 (B) 15,408 (C) 15,308 (D) 15,208 (E) 15,318.
$9,876 + 5,432 = 15,308$ → Answer: C
2.1.9 A trader had ₦250,000. Spent ₦134,850. Money left? (A) ₦115,050 (B) ₦114,150 (C) ₦115,150 (D) ₦115,250 (E) ₦116,150.
$250,000 - 134,850 = 115,150$
Check: $115,150 + 134,850 = 250,000$ ✓ → Answer: C
2.1.10 Add: $72,389 + 48,763$. (A) 121,252 (B) 121,162 (C) 120,152 (D) 121,152 (E) 121,052.
$72,389 + 48,763$
Units: $9 + 3 = 12$ → write 2, carry 1
Tens: $8 + 6 + 1 = 15$ → write 5, carry 1
Hundreds: $3 + 7 + 1 = 11$ → write 1, carry 1
Thousands: $2 + 8 + 1 = 11$ → write 1, carry 1
Ten-thousands: $7 + 4 + 1 = 12$ → write 2, carry 1 → $121,152$ → Answer: D
2.1.11 What is $8,005 - 3,678$? (A) 4,527 (B) 4,227 (C) 4,337 (D) 4,327 (E) 4,427.
$8,005 - 3,678$
Units: $5 - 8$ → borrow → $15 - 8 = 7$
Tens: $0 - 7$ → borrow → $10 - 7 = 3$
Hundreds: $0 - 6$ → borrow → $10 - 6 = 4$
Thousands: $7 - 3 = 4$
Result: $4,327$ → Answer: D
2.1.12 A stadium has $45,678$ seats. $12,345$ seats added. Total seats? (A) 58,013 (B) 57,123 (C) 58,023 (D) 57,023 (E) 58,123.
$45,678 + 12,345 = 58,023$ → Answer: C
2.1.13 Calculate: $654,321 - 543,210$. (A) 111,110 (B) 110,111 (C) 111,011 (D) 111,111 (E) 111,101.
$654,321 - 543,210 = 111,111$ → Answer: D
2.1.14 Factory produced $23,456$ bottles (Jan) and $34,567$ (Feb). Total? (A) 58,013 (B) 57,123 (C) 58,123 (D) 58,023 (E) 57,023.
$23,456 + 34,567 = 58,023$ → Answer: D
2.1.15 Difference between $100,000$ and $68,749$. (A) 31,261 (B) 31,151 (C) 32,251 (D) 31,351 (E) 31,251.
$100,000 - 68,749 = 31,251$ → Answer: E
2.1.16 Add: $56,789 + 43,211$. (A) 100,010 (B) 99,990 (C) 101,000 (D) 99,000 (E) 100,000.
$56,789 + 43,211 = 100,000$ → Answer: E
2.1.17 Car costs ₦3,450,000, motorcycle ₦850,000. How much more for car? (A) ₦2,400,000 (B) ₦2,800,000 (C) ₦2,700,000 (D) ₦2,500,000 (E) ₦2,600,000.
$3,450,000 - 850,000 = 2,600,000$ → Answer: E
2.1.18 Calculate: $7,654 + 3,456$. (A) 10,110 (B) 11,000 (C) 11,010 (D) 11,110 (E) 11,100.
$7,654 + 3,456 = 11,110$ → Answer: D
2.1.19 What is $82,406 - 47,839$? (A) 33,567 (B) 35,567 (C) 34,467 (D) 34,667 (E) 34,567.
$82,406 - 47,839$
Units: $6 - 9$ → borrow → $16 - 9 = 7$
Tens: $0 - 3$ → borrow → $10 - 3 = 7$
Hundreds: $4 - 8$ → borrow → $14 - 8 = 6$
Thousands: $1 - 7$ → borrow → $11 - 7 = 4$
Ten-thousands: $7 - 4 = 3$
Result: $34,567$ → Answer: E
2.1.20 Businessman made ₦2,345,000 (2022) and ₦3,456,000 (2023). Total profit? (A) ₦5,701,000 (B) ₦5,901,000 (C) ₦5,700,000 (D) ₦5,801,000 (E) ₦5,801,000.
$2,345,000 + 3,456,000 = 5,801,000$ → Answer: D
Evaluation G - 6 | 2.2 Solutions (Word Problems)
2.2.1 A school bought 120 textbooks at ₦3,500 each. They also bought 85 exercise books at ₦450 each. How much did they spend in total? (A) ₦420,000 (B) ₦458,250 (C) ₦438,250 (D) ₦478,250 (E) ₦448,250.
Textbooks cost = $120 \times 3500 = 420,000$. Exercise books cost = $85 \times 450 = 38,250$. Total = $420,000 + 38,250 = 458,250$ → Answer: B
2.2.2 Adanna had ₦15,000. Spent ₦3,250 on lunch and ₦2,750 on transport. Received ₦5,000 from brother. How much now? (A) ₦14,000 (B) ₦15,000 (C) ₦13,500 (D) ₦14,500 (E) ₦16,000.
After spending: $15,000 - 3,250 - 2,750 = 9,000$. After receiving: $9,000 + 5,000 = 14,000$ → Answer: A
2.2.3 A farmer has 3 bags of rice, each 25.5 kg. He repacks into 2 kg bags. How many full bags? (A) 36 (B) 37 (C) 38 (D) 39 (E) 40.
Total rice = $3 \times 25.5 = 76.5$ kg. Number of 2kg bags = $76.5 \div 2 = 38.25$ → 38 full bags → Answer: C
2.2.4 Shoes cost ₦12,500 with ₦1,250 discount. Customer pays ₦15,000. Change received? (A) ₦2,500 (B) ₦3,000 (C) ₦3,500 (D) ₦3,750 (E) ₦4,000.
Price after discount = $12,500 - 1,250 = 11,250$. Change = $15,000 - 11,250 = 3,750$ → Answer: D
2.2.5 Rectangle length 24 cm, width 15 cm. Square has same perimeter. Square side length? (A) 15 cm (B) 16.5 cm (C) 18 cm (D) 19.5 cm (E) 20 cm.
Rectangle perimeter = $2(24 + 15) = 78$ cm. Square side = $78 \div 4 = 19.5$ cm → Answer: D
2.2.6 250 students, 40% are boys. How many more girls than boys? (A) 50 (B) 60 (C) 70 (D) 80 (E) 90.
Boys = $40\% \times 250 = 100$. Girls = $250 - 100 = 150$. Difference = $150 - 100 = 50$ → Answer: A
2.2.7 Car travels 180 km in 3 hours. How far in 5 hours at same speed? (A) 250 km (B) 280 km (C) 300 km (D) 320 km (E) 350 km.
Speed = $180 \div 3 = 60$ km/h. Distance in 5 hours = $60 \times 5 = 300$ km → Answer: C
2.2.8 120 oranges, $\frac{1}{4}$ are bad. Remaining packed into 6 bags equally. Oranges per bag? (A) 12 (B) 14 (C) 15 (D) 18 (E) 20.
Bad oranges = $\frac{1}{4} \times 120 = 30$. Good oranges = $120 - 30 = 90$. Per bag = $90 \div 6 = 15$ → Answer: C
2.2.9 Chidi is twice as old as Ngozi. Sum of ages is 27. How old is Chidi? (A) 9 (B) 12 (C) 15 (D) 18 (E) 21.
Let Ngozi = $x$, Chidi = $2x$. $x + 2x = 27$ → $3x = 27$ → $x = 9$. Chidi = $2 \times 9 = 18$ → Answer: D
2.2.10 Tank holds 240 litres. Fill rate 15 L/min, empty rate 5 L/min. Both taps open, fill time? (A) 12 min (B) 16 min (C) 20 min (D) 24 min (E) 30 min.
Net fill rate = $15 - 5 = 10$ L/min. Time = $240 \div 10 = 24$ minutes → Answer: D
2.2.11 Trader bought 50 bags for ₦750,000. Sold each for ₦18,000. Total profit? (A) ₦100,000 (B) ₦125,000 (C) ₦150,000 (D) ₦175,000 (E) ₦200,000.
Selling price total = $50 \times 18,000 = 900,000$. Profit = $900,000 - 750,000 = 150,000$ → Answer: C
2.2.12 Rectangle length 3.5 m, width 2.4 m. Area in cm²? (A) 84,000 cm² (B) 8,400 cm² (C) 84 cm² (D) 840 cm² (E) 8.4 cm².
Area in m² = $3.5 \times 2.4 = 8.4$ m². 1 m² = 10,000 cm², so $8.4 \times 10,000 = 84,000$ cm² → Answer: A
2.2.13 Ada scored 78, 65, 82. Average score? (A) 72 (B) 73 (C) 75 (D) 76 (E) 78.
Sum = $78 + 65 + 82 = 225$. Average = $225 \div 3 = 75$ → Answer: C
2.2.14 Cloth 12.5 m cut into 5 equal pieces. Length of each in cm? (A) 200 cm (B) 225 cm (C) 250 cm (D) 275 cm (E) 300 cm.
Each piece = $12.5 \div 5 = 2.5$ m = $250$ cm → Answer: C
2.2.15 Family consumes 3.6 L milk in 2 days. How much in 10 days? (A) 15 L (B) 16 L (C) 17 L (D) 18 L (E) 19 L.
Rate per day = $3.6 \div 2 = 1.8$ L/day. In 10 days = $1.8 \times 10 = 18$ L → Answer: D
2.2.16 48 chocolates: $\frac{3}{8}$ milk, $\frac{1}{3}$ dark, rest white. Number of white? (A) 10 (B) 12 (C) 14 (D) 16 (E) 18.
Milk = $\frac{3}{8} \times 48 = 18$. Dark = $\frac{1}{3} \times 48 = 16$. White = $48 - 18 - 16 = 14$ → Answer: C
2.2.17 Emeka saves ₦500 per week, spends $\frac{3}{4}$ of savings on a shirt. Money left? (A) ₦375 (B) ₦500 (C) ₦125 (D) ₦250 (E) ₦400.
Spent = $\frac{3}{4} \times 500 = 375$. Left = $500 - 375 = 125$ → Answer: C
2.2.18 Tank is $\frac{2}{5}$ full, contains 240 litres. Full capacity? (A) 400 L (B) 500 L (C) 600 L (D) 700 L (E) 800 L.
$\frac{2}{5} \times \text{Capacity} = 240$ → Capacity = $240 \times \frac{5}{2} = 600$ L → Answer: C
2.2.19 Train leaves 08:30, arrives 11:15, distance 140 km. Average speed? (A) 48 km/h (B) 50 km/h (C) 52 km/h (D) 54 km/h (E) 56 km/h.
Time = 2 hours 45 minutes = $2.75$ hours. Speed = $140 \div 2.75 \approx 50.91$ km/h ≈ 50 km/h → Answer: B
2.2.20 Three friends share ₦24,000 in ratio 2:3:5. Largest share? (A) ₦8,000 (B) ₦10,000 (C) ₦12,000 (D) ₦14,000 (E) ₦16,000.
Total parts = $2+3+5 = 10$. Largest share = $\frac{5}{10} \times 24,000 = 12,000$ → Answer: C
Evaluation G - 6 | 2.3 Solutions (Inverse Operations)
2.3.1 To check if $237 + 456 = 693$ is correct, which inverse operation should you use? (A) $693 - 456$ (B) $456 + 237$ (C) $693 - 237$ (D) Both A and C (E) $237 + 456$.
Inverse of addition is subtraction. You can subtract either addend from the sum: $693 - 456 = 237$ or $693 - 237 = 456$ → Answer: D
2.3.2 Using inverse operations, check if $582 - 197 = 385$ is correct. Which calculation verifies the answer? (A) $385 + 197$ (B) $582 - 385$ (C) $197 - 385$ (D) $582 + 385$ (E) $385 + 582$.
Inverse of subtraction is addition: subtractor + difference = original number → $385 + 197 = 582$ → Answer: A
2.3.3 A student calculated $48 \times 25 = 1,200$. Which inverse operation checks if this is correct? (A) $1,200 \div 25$ (B) $1,200 - 25$ (C) $1,200 + 48$ (D) $48 \div 25$ (E) $1,200 \times 25$.
Inverse of multiplication is division. Divide product by either factor: $1,200 \div 25 = 48$ or $1,200 \div 48 = 25$ → Answer: A
2.3.4 To check $1,428 \div 17 = 84$, you should multiply: (A) $84 \times 1,428$ (B) $17 \times 84$ (C) $1,428 \times 17$ (D) $84 \times 17$ (E) $1,428 \div 84$.
Inverse of division is multiplication: divisor $\times$ quotient = dividend → $17 \times 84 = 1,428$ → Answer: D
2.3.5 If $625 - 218 = 407$, which of these would show the answer is incorrect? (A) $407 + 218 = 625$ (B) $625 - 407 = 218$ (C) $218 + 407 = 625$ (D) $407 - 218 = 189$ (E) $625 - 218 = 407$.
Option D ($407 - 218 = 189$) does not relate to checking the original subtraction. The correct checks are A, B, C → Answer: D
2.3.6 After solving $x + 37 = 92$, a student got $x = 55$. How can they check their answer? (A) $55 + 37$ (B) $92 - 37$ (C) $55 + 92$ (D) $92 + 37$ (E) $55 - 37$.
Substitute $x = 55$ back: $55 + 37 = 92$ → Answer: A
2.3.7 A pupil calculated $3,456 + 2,789 = 6,235$. Using inverse operation, which calculation shows the answer is wrong? (A) $6,235 - 2,789 = 3,446$ (B) $6,235 - 3,456 = 2,789$ (C) $2,789 + 3,456 = 6,245$ (D) $3,456 + 2,789 = 6,245$ (E) $6,235 - 3,456 = 2,779$.
Correct sum should be $3,456 + 2,789 = 6,245$. Option A shows $6,235 - 2,789 = 3,446$ (not $3,456$) → indicates error → Answer: A
2.3.8 What inverse operation would you use to check $95 \times 32 = 3,040$? (A) $3,040 \div 95$ (B) $3,040 \div 32$ (C) Both A and B (D) $95 \div 32$ (E) $3,040 - 95$.
Division checks multiplication: $3,040 \div 95 = 32$ or $3,040 \div 32 = 95$ → Answer: C
2.3.9 A student got $648 \div 9 = 71$. Which inverse operation will show this is incorrect? (A) $71 \times 9 = 639$ (B) $71 \times 9 = 648$ (C) $648 \div 71 = 9$ (D) $9 \times 71 = 648$ (E) $648 \div 9 = 72$.
Correct inverse: $71 \times 9 = 639$ (not $648$) → shows error → Answer: A
2.3.10 To check if $1,025 - 478 = 547$ is correct, you would add: (A) $547 + 478$ (B) $1,025 + 547$ (C) $478 + 1,025$ (D) $547 - 478$ (E) $1,025 + 478$.
Inverse of subtraction: difference + subtractor = original → $547 + 478 = 1,025$ → Answer: A
2.3.11 If $23 \times 45 = 1,035$, which calculation verifies this? (A) $1,035 \div 23 = 45$ (B) $45 \times 23 = 1,035$ (C) Both A and B (D) $1,035 + 23$ (E) $45 \div 23$.
Both multiplication (commutative) and division check the result → Answer: C
2.3.12 A child solves $x - 28 = 45$ and gets $x = 73$. How can they check? (A) $73 - 28$ (B) $73 + 28$ (C) $45 - 28$ (D) $73 + 45$ (E) $45 + 28$.
Substitute $x = 73$: $73 - 28 = 45$ → Answer: A
2.3.13 To check $7,200 \div 60 = 120$, multiply: (A) $60 \times 120$ (B) $120 \times 7,200$ (C) $7,200 \times 60$ (D) $120 \times 60$ (E) $7,200 \times 120$.
Inverse of division: divisor $\times$ quotient = dividend → $60 \times 120 = 7,200$ → Answer: A
2.3.14 A student calculates $4,567 + 3,219 = 7,786$. Using the inverse operation, what should they get? (A) $7,786 - 3,219 = 4,567$ (B) $7,786 - 4,567 = 3,219$ (C) Both A and B (D) $4,567 + 7,786 = 12,353$ (E) $3,219 - 7,786 = -4,567$.
Both subtractions should return the original addends → Answer: C
2.3.15 If $84 \times 37 = 3,108$, which inverse operation confirms this? (A) $3,108 \div 84 = 37$ (B) $3,108 \div 37 = 84$ (C) Both A and B (D) $84 \div 37$ (E) $3,108 - 84$.
Both division checks work → Answer: C
2.3.16 A pupil solved $250 - x = 80$ and got $x = 170$. How can they check? (A) $250 - 170$ (B) $250 + 170$ (C) $170 - 80$ (D) $170 + 80$ (E) $80 + 250$.
Substitute $x = 170$: $250 - 170 = 80$ → Answer: A
2.3.17 To check $924 \div 22 = 42$, which is NOT a valid inverse operation? (A) $42 \times 22$ (B) $22 \times 42$ (C) $924 \div 42$ (D) $42 \times 924$ (E) $22 \times 42 = 924$.
$42 \times 924$ is not an inverse operation for this division → Answer: D
2.3.18 If $3x = 27$ and a student says $x = 9$, how can they verify? (A) $3 \times 9$ (B) $27 \div 9$ (C) $9 + 9 + 9$ (D) All of the above (E) $27 - 9$.
All A, B, C check the solution: $3 \times 9 = 27$, $27 \div 9 = 3$, $9+9+9=27$ → Answer: D
2.3.19 After calculating $1,236 - 789 = 447$, the inverse operation $447 + 789$ gives: (A) $1,236$ (B) $447$ (C) $789$ (D) $1,235$ (E) $1,237$.
$447 + 789 = 1,236$ → Answer: A
2.3.20 A student mistakenly added $2,500$ and $3,700$ to get $6,300$. Using inverse operation to check, they would: (A) Subtract $2,500$ from $6,300$ (B) Subtract $3,700$ from $6,300$ (C) Both A and B (D) Add again (E) Multiply.
Subtracting either addend from the sum should give the other addend: $6,300 - 2,500 = 3,800$ (not $3,700$), $6,300 - 3,700 = 2,600$ (not $2,500$) → both show error → Answer: C
Evaluation G - 6 | 3.1 Solutions (Multiplication of Whole Numbers)
3.1.1 Calculate $234 \times 12$. (A) 2,808 (B) 2,608 (C) 2,708 (D) 2,908 (E) 3,008.
$234 \times 12 = 234 \times (10 + 2) = 2,340 + 468 = 2,808$ → Answer: A
3.1.2 Find $1,234 \times 15$. (A) 17,510 (B) 18,610 (C) 16,510 (D) 18,710 (E) 18,510.
$1,234 \times 15 = 1,234 \times (10 + 5) = 12,340 + 6,170 = 18,510$ → Answer: E
3.1.3 Multiply $456 \times 23$. (A) 10,588 (B) 10,688 (C) 10,788 (D) 10,488 (E) 10,888.
$456 \times 23 = 456 \times (20 + 3) = 9,120 + 1,368 = 10,488$ → Answer: D
3.1.4 What is $3,215 \times 18$? (A) 57,970 (B) 58,870 (C) 57,770 (D) 58,970 (E) 57,870.
$3,215 \times 18 = 3,215 \times (20 - 2) = 64,300 - 6,430 = 57,870$ → Answer: E
3.1.5 A school has 234 students. Each pays ₦1,250. Total? (A) 302,500 (B) 292,500 (C) 282,500 (D) 272,500 (E) 312,500.
$234 \times 1,250 = 234 \times (1,000 + 250) = 234,000 + 58,500 = 292,500$ → Answer: B
3.1.6 Calculate $5,789 \times 24$. (A) 139,936 (B) 137,936 (C) 138,936 (D) 138,836 (E) 138,736.
$5,789 \times 24 = 5,789 \times (20 + 4) = 115,780 + 23,156 = 138,936$ → Answer: C
3.1.7 Multiply $842 \times 37$. (A) 30,154 (B) 31,254 (C) 32,154 (D) 31,154 (E) 31,354.
$842 \times 37 = 842 \times (40 - 3) = 33,680 - 2,526 = 31,154$ → Answer: D
3.1.8 Find $1,506 \times 19$. (A) 28,514 (B) 27,614 (C) 28,714 (D) 29,614 (E) 28,614.
$1,506 \times 19 = 1,506 \times (20 - 1) = 30,120 - 1,506 = 28,614$ → Answer: E
3.1.9 What is $3,456 \times 27$? (A) 93,212 (B) 93,312 (C) 93,412 (D) 94,312 (E) 92,312.
$3,456 \times 27 = 3,456 \times (30 - 3) = 103,680 - 10,368 = 93,312$ → Answer: B
3.1.10 125 baskets each contain 48 oranges. Total? (A) 5,800 (B) 6,000 (C) 6,200 (D) 6,500 (E) 5,500.
$125 \times 48 = 125 \times (50 - 2) = 6,250 - 250 = 6,000$ → Answer: B
3.1.11 Calculate $2,348 \times 32$. (A) 74,136 (B) 75,136 (C) 76,136 (D) 75,236 (E) 75,036.
$2,348 \times 32 = 2,348 \times (30 + 2) = 70,440 + 4,696 = 75,136$ → Answer: B
3.1.12 Multiply $673 \times 45$. (A) 31,285 (B) 30,285 (C) 29,285 (D) 30,385 (E) 30,285.
$673 \times 45 = 673 \times (40 + 5) = 26,920 + 3,365 = 30,285$ → Answer: E
3.1.13 294 pages in a book. For 36 books? (A) 10,584 (B) 10,484 (C) 10,684 (D) 11,584 (E) 9,584.
$294 \times 36 = 294 \times (30 + 6) = 8,820 + 1,764 = 10,584$ → Answer: A
3.1.14 Find $4,827 \times 16$. (A) 76,232 (B) 77,232 (C) 78,232 (D) 77,332 (E) 77,132.
$4,827 \times 16 = 4,827 \times (10 + 6) = 48,270 + 28,962 = 77,232$ → Answer: B
3.1.15 Compute $3,215 \times 42$. (A) 134,030 (B) 135,030 (C) 136,030 (D) 135,130 (E) 135,230.
$3,215 \times 42 = 3,215 \times (40 + 2) = 128,600 + 6,430 = 135,030$ → Answer: B
3.1.16 248 bags each weigh 50 kg. Total? (A) 13,400 (B) 12,400 (C) 11,400 (D) 12,500 (E) 12,300.
$248 \times 50 = 248 \times (100 \div 2) = 24,800 \div 2 = 12,400$ → Answer: B
3.1.17 Calculate $5,609 \times 28$. (A) 156,052 (B) 157,052 (C) 158,052 (D) 157,152 (E) 157,952.
$5,609 \times 28 = 5,609 \times (20 + 8) = 112,180 + 44,872 = 157,052$ → Answer: B
3.1.18 Multiply $937 \times 56$. (A) 53,472 (B) 52,472 (C) 51,472 (D) 52,572 (E) 52,472.
$937 \times 56 = 937 \times (50 + 6) = 46,850 + 5,622 = 52,472$ → Answer: E
3.1.19 1,850 bottles per day for 29 days? (A) 52,650 (B) 53,650 (C) 54,650 (D) 53,650 (E) 53,550.
$1,850 \times 29 = 1,850 \times (30 - 1) = 55,500 - 1,850 = 53,650$ → Answer: D
3.1.20 Find $6,543 \times 31$. (A) 201,833 (B) 202,833 (C) 203,833 (D) 202,933 (E) 202,833.
$6,543 \times 31 = 6,543 \times (30 + 1) = 196,290 + 6,543 = 202,833$ → Answer: E
