Decimal Arithmetic: – Adding, subtracting, multiplying, and dividing decimals.

DECIMAL ARITHMETIC Adding, subtracting, multiplying, and dividing decimals Grade 7 Mathematics: Decimal Arithmetic Subtopic Navigator Introduction Addition of Decimals Subtraction of Decimals Multiplication of Decimals Division of Decimals Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Understand and apply rules of decimal addition, subtraction, multiplication, and division. Solve multi-step problems involving decimals with accuracy. Apply decimal arithmetic in real-life problem-solving situations. Develop confidence in handling intermediate and difficult decimal-based questions. Lesson Introduction Decimals are an essential part of mathematics that represent numbers between whole numbers. They are widely used in money, measurements, and scientific calculations. Mastering decimal arithmetic—addition, subtraction, multiplication, and division—is a foundational skill in Grade 7. In this lesson, we will explore step-by-step strategies for performing these operations accurately. Addition of Decimals When adding decimals, the most important step is to line up the decimal points before adding. Zeros may be added to equalize decimal places where necessary. Example 1: Find [latex]245.67 + 13.8[/latex]. Solution: Line up decimal points: [latex]begin{aligned} &245.67 \ + & 13.80 \ hline &259.47 end{aligned}[/latex] Answer: [latex]259.47[/latex]. Example 2: Add [latex]76.234 + 18.7 + 9.856[/latex]. Solution: Align decimals: [latex]begin{aligned} &76.234 \ +&18.700 \ +&9.856 \ hline &104.790 end{aligned}[/latex] Answer: [latex]104.79[/latex]. Example 3: Find the sum of [latex]523.9 + 47.085 + 0.74[/latex]. Solution: [latex]begin{aligned} &523.900 \ +&47.085 \ +&0.740 \ hline &571.725 end{aligned}[/latex] Answer: [latex]571.725[/latex]. Exercises (Addition) Compute [latex]234.75 + 98.456 + 17.2[/latex]. Evaluate [latex]145.67 + 203.8 + 9.333[/latex]. Subtraction of Decimals Subtraction of decimals requires aligning decimal points just like addition. If necessary, add trailing zeros for equal decimal places before subtracting. Example 4: Find [latex]215.63 - 87.452[/latex]. Solution: [latex]begin{aligned} &215.630 \ -&87.452 \ hline &128.178 end{aligned}[/latex] Answer: [latex]128.178[/latex]. Example 5: Subtract [latex]700.4 - 289.765[/latex]. Solution: [latex]begin{aligned} &700.400 \ -&289.765 \ hline &410.635 end{aligned}[/latex] Answer: [latex]410.635[/latex]. Example 6: Find [latex]1200.85 - 999.999[/latex]. Solution: [latex]begin{aligned} &1200.850 \ -&999.999 \ hline &200.851 end{aligned}[/latex] Answer: [latex]200.851[/latex]. Exercises (Subtraction) Subtract [latex]546.27 - 289.456[/latex]. Find [latex]1000.05 - 899.876[/latex]. Multiplication of Decimals When multiplying decimals, ignore the decimal points at first. After multiplying, count the total number of decimal places in the factors, then place the decimal point in the product accordingly. Example 7: Multiply [latex]3.47 times 5.6[/latex]. Solution: Ignore decimals: [latex]347 times 56 = 19432[/latex]. Total decimal places: 2 + 1 = 3. So, [latex]19.432[/latex]. Answer: [latex]19.432[/latex]. Example 8: Multiply [latex]12.45 times 0.32[/latex]. Solution: Ignore decimals: [latex]1245 times 32 = 39840[/latex]. Decimal places: 2 + 2 = 4. Result: [latex]3.9840 = 3.984[/latex]. Answer: [latex]3.984[/latex]. Example 9: Multiply [latex]0.075 times 0.6[/latex]. Solution: [latex]75 times 6 = 450[/latex]. Decimal places: 3 + 1 = 4. Result: [latex]0.0450 = 0.045[/latex]. Answer: [latex]0.045[/latex]. Exercises (Multiplication) Find [latex]8.34 times 0.27[/latex]. Evaluate [latex]15.6 times 0.048[/latex]. Division of Decimals In decimal division, shift the decimal point of the divisor to make it a whole number. Apply the same shift to the dividend, then divide as with whole numbers. Example 10: Compute [latex]45.6 div 0.12[/latex]. Solution: Multiply divisor and dividend by 100: [latex]4560 div 12[/latex]. Result: [latex]380[/latex]. Answer: [latex]380[/latex]. Example 11: Divide [latex]72.45 div 0.15[/latex]. Solution: Shift by 100: [latex]7245 div 15 = 483[/latex]. Answer: [latex]483[/latex]. Example 12: Evaluate [latex]5.25 div 0.0075[/latex]. Solution: Shift by 10000: [latex]52500 div 75 = 700[/latex]. Answer: [latex]700[/latex]. Exercises (Division) Compute [latex]84.96 div 0.24[/latex]. Evaluate [latex]6.72 div 0.008[/latex]. Applications and Mixed Problems Example 13: A rope measures [latex]45.75[/latex] m. It is cut into 15 equal parts. What is the length of each part? Solution: [latex]45.75 div 15 = 3.05[/latex]. Answer: [latex]3.05 , m[/latex]. Example 14: A trader bought [latex]36.45[/latex] kg of rice and repackaged it into bags of [latex]2.7[/latex] kg each. How many bags did she fill? Solution: [latex]36.45 div 2.7 = 13.5[/latex]. Since bags must be whole, she filled 13 full bags and had half a bag left. Answer: 13 full bags and half bag. Example 15: A school prints 125 exam booklets, each costing [latex]18.75[/latex] dollars. Find the total expenditure. Solution: [latex]125 times 18.75 = 2343.75[/latex]. Answer: [latex]$2343.75[/latex]. Exercises (Applications) A car uses [latex]8.75[/latex] liters of fuel per 100 km. How much fuel is needed for [latex]425[/latex] km? The price of 3.6 kg of meat is [latex]$43.20[/latex]. What is the price per kg? Cumulative Exercises Find the sum: [latex]456.78 + 129.56 + 78.004[/latex]. Subtract: [latex]1000.25 - 876.345[/latex]. Multiply: [latex]15.24 times 0.36[/latex]. Divide: [latex]92.16 div 0.24[/latex]. A machine produces [latex]12.5[/latex] liters of oil per hour. How much will it produce in [latex]8.4[/latex] hours? The sum of three decimals is [latex]256.485[/latex]. If two numbers are [latex]123.45[/latex] and [latex]87.96[/latex], find the third. Find [latex]3.75 times 0.048[/latex]. Evaluate [latex]5.6 div 0.007[/latex]. A trader bought 24 items at [latex]$3.85[/latex] each. How much did he spend? A rope of length [latex]78.54[/latex] m is cut into pieces of [latex]2.3[/latex] m each. How many full pieces are obtained? Conclusion/Recap In this lesson, we explored decimal arithmetic, including addition, subtraction, multiplication, and division. We emphasized aligning decimals for addition and subtraction, counting decimal places in multiplication, and shifting decimals in division. These skills are vital in everyday problem-solving situations like money, measurements, and scientific work. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c