Mon ey. Grade 7 Mathematics: Money - Understanding and Performing Operations Subtopic Navigator Understanding Money and Currency Addition and Subtraction with Money Multiplication with Money Division with Money Percentages with Money Discounts and Sales Tax Profit and Loss Calculations Simple Interest Calculations Budgeting and Financial Planning Cumulative Exercises Conclusion Lesson Objectives Perform addition, subtraction, multiplication, and division with money values Calculate percentages, discounts, and sales tax on monetary amounts Solve profit and loss problems involving cost price and selling price Calculate simple interest on investments and loans Create and analyze budgets and financial plans Apply money operations to real-world financial scenarios Understanding Money and Currency Money is a medium of exchange that allows us to value goods and services numerically. Understanding how to perform operations with money is essential for everyday financial transactions, budgeting, and making informed economic decisions. The basic unit of currency we'll use is the naira (₦), with kobo as the subunit (100 kobo = 1 naira). Addition /Subtraction with Money When adding and subtracting money, we must align decimal points carefully to ensure accurate calculations. Money values are typically expressed with two decimal places representing the subunit (kobo). Example 1: Complex Money Addition Calculate the total cost: ₦2,345.75 + ₦1,567.89 + ₦3,456.25 Solution: Align by decimal point: ₦2,345.75 ₦1,567.89 ₦3,456.25 ------------ ₦7,369.89 Verification: 75 + 89 + 25 = 189 kobo = ₦1.89 345 + 567 + 456 = 1,368 naira Total: 1,368 + 1.89 = ₦1,369.89 (plus thousands: 2,000 + 1,000 + 3,000 = 6,000) Complete total: ₦6,000 + ₦1,369.89 = ₦7,369.89 Example 2: Money Subtraction with Borrowing If you have ₦5,000 and spend ₦3,456.78, how much money remains? Solution: Write ₦5,000 as ₦5,000.00 ₦5,000.00 -₦3,456.78 ------------ ₦1,543.22 Step-by-step borrowing: Borrow 1 from thousands: 5,000 becomes 4,999 + 1.00 Subtract kobo: 100 - 78 = 22 kobo Subtract units: 9 - 6 = 3 naira Subtract tens: 9 - 5 = 4 tens (40 naira) Subtract hundreds: 9 - 4 = 5 hundreds (500 naira) Subtract thousands: 4 - 3 = 1 thousand (1,000 naira) Total: ₦1,000 + ₦500 + ₦40 + ₦3 + ₦0.22 = ₦1,543.22 Addition and Subtraction Problems Calculate: ₦4,567.89 + ₦3,456.78 + ₦2,345.67 If you have ₦8,000 and spend ₦5,678.90, how much remains? Find the total: ₦12,345.67 - ₦4,567.89 + ₦3,456.78 A person receives ₦15,000, spends ₦8,456.75, and then receives ₦3,500 more. What is the final balance? What is the difference between ₦10,000.50 and ₦7,456.89? Multiplication with Money When multiplying money by a whole number, we multiply as with decimals and ensure the result has two decimal places. When multiplying money by a decimal (like for discounts or tax), we must round appropriately to the nearest kobo. Example 1: Multiplying Money by Whole Numbers If one book costs ₦1,245.75, what is the cost of 24 books? Solution: Method 1: Direct Multiplication ₦1,245.75 × 24 = ₦1,245.75 × 20 + ₦1,245.75 × 4 = ₦24,915.00 + ₦4,983.00 = ₦29,898.00 Method 2: Standard Multiplication 1,245.75 × 24 -------- 4,983.00 (1,245.75 × 4) 24,915.00 (1,245.75 × 20) -------- ₦29,898.00 Example 2: Multiplying Money by Decimals Calculate 7.5% of ₦45,678.90 Solution: 7.5% = 0.075 ₦45,678.90 × 0.075 First: ₦45,678.90 × 0.07 = ₦3,197.523 ≈ ₦3,197.52 Then: ₦45,678.90 × 0.005 = ₦228.3945 ≈ ₦228.39 Total: ₦3,197.52 + ₦228.39 = ₦3,425.91 Direct calculation: ₦45,678.90 × 0.075 = ₦3,425.9175 ≈ ₦3,425.92 (Rounding difference: 0.0075 naira or 0.75 kobo) Multiplication Problems If one shirt costs ₦2,345.50, what is the cost of 15 shirts? Calculate: ₦12,456.78 × 8.5% A car rental costs ₦7,890 per day. What is the cost for 28 days? What is 12.5% of ₦36,789.00? If ₦456.75 is multiplied by 24.5, what is the product rounded to nearest naira? Division with Money Dividing money can mean either splitting an amount into equal parts or finding how many items can be purchased with a given amount. When dividing money by money, we get a unitless ratio. Example 1: Dividing Money Equally ₦15,678.90 is to be divided equally among 7 people. How much does each person get? Solution: ₦15,678.90 ÷ 7 7 into 15 = 2 remainder 1 → 2,000 naira each Bring down 6: 16 ÷ 7 = 2 remainder 2 → 200 naira each Bring down 7: 27 ÷ 7 = 3 remainder 6 → 30 naira each Bring down 8: 68 ÷ 7 = 9 remainder 5 → 8 naira each Bring down 9: 59 ÷ 7 = 8 remainder 3 → 0.80 naira each Bring down 0: 30 ÷ 7 = 4 remainder 2 → 0.04 naira each Remainder 2 kobo divided by 7 = 0.2857... kobo ≈ 0.29 kobo Total: ₦2,000 + ₦200 + ₦30 + ₦8 + ₦0.80 + ₦0.04 + ₦0.0029 ≈ ₦2,238.8429 Rounded to nearest kobo: ₦2,238.84 per person Check: 7 × ₦2,238.84 = ₦15,671.88 (slight rounding difference) Example 2: How Many Items Can Be Purchased With ₦5,000, how many items costing ₦345.75 each can be purchased, and how much money remains? Solution: ₦5,000 ÷ ₦345.75 First, estimate: ₦345.75 ≈ ₦350 ₦5,000 ÷ ₦350 ≈ 14.28, so about 14 items Exact calculation: 345.75 × 14 = ₦4,840.50 Remaining: ₦5,000 - ₦4,840.50 = ₦159.50 Can we buy another? ₦159.50 < ₦345.75, so no Answer: 14 items can be purchased with ₦159.50 remaining Division Problems Divide ₦12,345.67 equally among 9 people (round to nearest kobo) How many books costing ₦1,245.75 each can be bought with ₦15,000? If ₦45,678 is divided in the ratio 2:3:4, how much does each part get? A budget of ₦25,000 must cover 18 items. What is the average price per item? ₦8,456.78 shared among 5.5 people. How much per person? Percentages with Money Percentages are frequently used with money for calculating discounts, taxes, tips, interest, and profit margins. Understanding how to calculate and apply percentages is crucial for financial literacy. Example 1: Complex Percentage Calculation What is 18.5% of ₦45,678.90? If this amount represents a discount, what is the final price? Solution: 18.5% = 0.185 Discount amount = ₦45,678.90 × 0.185 = ₦45,678.90 × 0.18 + ₦45,678.90 × 0.005 = ₦8,222.202 + ₦228.3945 = ₦8,450.5965 ≈ ₦8,450.60 Final price = ₦45,678.90 - ₦8,450.60 = ₦37,228.30 Alternative: 100% - 18.5% = 81.5% Final price = ₦45,678.90 × 0.815 = ₦37,228.3035 ≈ ₦37,228.30 Example 2: Finding Percentage If an item originally priced at ₦12,500 is sold for ₦10,000, what percentage discount was given? Solution: Discount amount = ₦12,500 - ₦10,000 = ₦2,500 Percentage discount = $frac{2,500}{12,500} × 100%$ = $frac{1}{5} × 100% = 20%$ Alternative calculation: Sale price/Original price = $frac{10,000}{12,500} = 0.8 = 80%$ of original So discount = 100% - 80% = 20% Percentage Problems What is 15.5% of ₦28,456.75? If a ₦8,456 item is discounted by 25%, what is the sale price? An investment grows from ₦15,000 to ₦18,750. What is the percentage increase? What percentage of ₦45,678 is ₦12,345? A salary of ₦75,000 increases by 12.5%. What is the new salary? Discounts and Sales Tax Discounts reduce the price of an item, while sales tax increases it. When both apply, the order matters: typically discount is applied first, then tax on the discounted price. Example 1: Multiple Discounts and Tax An item priced at ₦8,456 has a 15% discount, then an additional 10% off the discounted price. If sales tax is 7.5%, what is the final price? Solution: First discount: 15% of ₦8,456 = ₦1,268.40 First discounted price: ₦8,456 - ₦1,268.40 = ₦7,187.60 Second discount: 10% of ₦7,187.60 = ₦718.76 Second discounted price: ₦7,187.60 - ₦718.76 = ₦6,468.84 Sales tax: 7.5% of ₦6,468.84 = ₦485.163 ≈ ₦485.16 Final price: ₦6,468.84 + ₦485.16 = ₦6,954.00 Check with combined multipliers: Discount multiplier: 0.85 × 0.90 = 0.765 Tax multiplier: 1.075 Combined: 0.765 × 1.075 = 0.822375 ₦8,456 × 0.822375 = ₦6,954.00 ✓ Example 2: Finding Original Price After Discount After a 20% discount, an item costs ₦3,200. What was the original price? Solution: Discounted price = 80% of original Let original price = x 0.8x = ₦3,200 x = ₦3,200 ÷ 0.8 = ₦4,000 Check: 20% of ₦4,000 = ₦800, ₦4,000 - ₦800 = ₦3,200 ✓ Discount and Tax Problems An item costs ₦12,500 with 15% discount and 7.5% tax. What is the final price? After a 25% discount, a phone costs ₦18,750. What was the original price? A store offers "30% off, then an additional 20% off." What is the equivalent single discount? An item priced at ₦8,456 has tax of ₦634.20. What is the tax rate? Which is better: 25% off or 20% off then 5% off? Profit and Loss Calculations Profit occurs when selling price exceeds cost price; loss occurs when cost price exceeds selling price. Profit/loss percentage is always calculated relative to the cost price. Example 1: Complex Profit Calculation A merchant buys goods for ₦45,678 and sells them for ₦56,789. What is the profit percentage? If he then reduces the selling price by 10%, what is the new profit percentage? Solution: Profit = ₦56,789 - ₦45,678 = ₦11,111 Profit percentage = $frac{11,111}{45,678} × 100% ≈ 24.32%$ Reduced selling price = ₦56,789 × 0.90 = ₦51,110.10 New profit = ₦51,110.10 - ₦45,678 = ₦5,432.10 New profit percentage = $frac{5,432.10}{45,678} × 100% ≈ 11.89%$ Example 2: Finding Cost Price from Selling Price An item is sold for ₦12,345 at a profit of 23%. What was the cost price? Solution: Selling price = 123% of cost price Let cost price = x 1.23x = ₦12,345 x = ₦12,345 ÷ 1.23 = ₦10,036.585 ≈ ₦10,036.59 Check: 23% of ₦10,036.59 = ₦2,308.42 (approximately) ₦10,036.59 + ₦2,308.42 = ₦12,345.01 (rounding difference) Profit and Loss Problems Cost price = ₦8,456, selling price = ₦10,567. Find profit percentage. An item sold for ₦15,000 at 20% profit. Find cost price. If cost is ₦12,345 and loss is 15%, find selling price. A trader gains 25% by selling for ₦25,000. Find cost price. Which gives higher profit: 30% on ₦10,000 or 25% on ₦12,000? Simple Interest Calculations Simple interest is calculated only on the principal amount. The formula is: I = P × r × t, where I = interest, P = principal, r = annual interest rate (as decimal), t = time in years. Example 1: Complex Interest Calculation ₦45,678 is invested at 7.5% simple interest for 2 years 6 months. What is the total amount? Solution: Principal P = ₦45,678 Rate r = 7.5% = 0.075 Time t = 2.5 years (2 years 6 months = 2.5 years) Interest I = P × r × t = ₦45,678 × 0.075 × 2.5 = ₦45,678 × 0.1875 = ₦8,564.625 ≈ ₦8,564.63 Total amount = Principal + Interest = ₦45,678 + ₦8,564.63 = ₦54,242.63 Example 2: Finding Time from Interest ₦25,000 earns ₦3,750 in simple interest at 6% per annum. How long was it invested? Solution: I = P × r × t ₦3,750 = ₦25,000 × 0.06 × t ₦3,750 = ₦1,500 × t t = ₦3,750 ÷ ₦1,500 = 2.5 years = 2 years 6 months Interest Problems ₦15,000 at 8% simple interest for 3 years. Find total amount. What principal earns ₦2,400 in 2 years at 6% simple interest? ₦30,000 becomes ₦36,000 in simple interest. If rate was 8%, find time. Which earns more: ₦20,000 at 7.5% for 2 years or ₦25,000 at 6% for 3 years? At what rate will ₦12,345 double in 8 years with simple interest? Budgeting and Financial Planning Budgeting involves allocating money to different categories and tracking income and expenses. Financial planning requires understanding percentages, proportions, and making calculations to achieve financial goals. Example 1: Complex Budget Allocation A monthly income of ₦75,000 is allocated as follows: 30% for housing, 25% for food, 15% for transportation, 10% for savings, and the rest for miscellaneous. How much is allocated to each category? If miscellaneous is split equally among entertainment, clothing, and healthcare, how much for each? Solution: Housing: 30% of ₦75,000 = ₦22,500 Food: 25% of ₦75,000 = ₦18,750 Transportation: 15% of ₦75,000 = ₦11,250 Savings: 10% of ₦75,000 = ₦7,500 Total so far: ₦22,500 + ₦18,750 + ₦11,250 + ₦7,500 = ₦60,000 Miscellaneous: ₦75,000 - ₦60,000 = ₦15,000 Miscellaneous split 3 ways: ₦15,000 ÷ 3 = ₦5,000 each Entertainment: ₦5,000, Clothing: ₦5,000, Healthcare: ₦5,000 Example 2: Financial Goal Planning You want to save ₦100,000 in 2 years. If you save the same amount each month, how much must you save monthly? If you can earn 5% simple interest on your savings, how does this affect your monthly saving requirement? Solution: Without interest: ₦100,000 ÷ 24 months = ₦4,166.67 per month With 5% simple interest over 2 years: Let monthly deposit = x Total deposits = 24x Interest earned = Average balance × rate × time Average balance ≈ (First deposit + Last deposit) ÷ 2 = (x + 24x) ÷ 2 = 12.5x Interest = 12.5x × 0.05 × 2 = 1.25x Total = Deposits + Interest = 24x + 1.25x = 25.25x = ₦100,000 x = ₦100,000 ÷ 25.25 ≈ ₦3,960.40 per month Interest reduces required monthly savings by about ₦206.27 Budgeting Problems A budget allocates ₦50,000 as: 40% housing, 30% food, 20% other, 10% savings. Find each amount. To save ₦60,000 in 18 months, how much monthly saving is needed? Income ₦90,000, expenses ₦75,000. What percentage is saved? If expenses increase by 15% but income stays at ₦80,000, what new savings percentage? A vacation costs ₦150,000. If saved over 10 months with 4% interest, find monthly deposit. Cumulative Exercises Calculate: ₦12,345.67 + ₦8,456.78 - ₦5,678.90 If 15 shirts cost ₦35,678, what is the cost per shirt? What is 18.5% of ₦45,678.90? An item costs ₦12,500 after 20% discount. Find original price. Cost = ₦8,456, sold for ₦10,567. Find profit percentage. ₦25,000 at 7.5% simple interest for 3 years. Find total amount. Budget: ₦75,000, with 30% housing, 25% food, 20% other, rest savings. Find savings amount. ₦15,000 becomes ₦18,750. Find percentage increase. With ₦10,000, how many items at ₦456.75 each can be bought? Which is better: 25% off or 20% off then 10% off? Show/Hide Answers Problem: Calculate: ₦12,345.67 + ₦8,456.78 - ₦5,678.90 Answer: ₦12,345.67 + ₦8,456.78 = ₦20,802.45 ₦20,802.45 - ₦5,678.90 = ₦15,123.55 Problem: If 15 shirts cost ₦35,678, what is the cost per shirt? Answer: ₦35,678 ÷ 15 = ₦2,378.533... ≈ ₦2,378.53 per shirt Problem: What is 18.5% of ₦45,678.90? Answer: 18.5% = 0.185 ₦45,678.90 × 0.185 = ₦8,450.5965 ≈ ₦8,450.60 Problem: An item costs ₦12,500 after 20% discount. Find original price. Answer: Sale price = 80% of original Original = ₦12,500 ÷ 0.8 = ₦15,625 Problem: Cost = ₦8,456, sold for ₦10,567. Find profit percentage. Answer: Profit = ₦10,567 - ₦8,456 = ₦2,111 Profit % = $frac{2,111}{8,456} × 100% ≈ 24.96%$ Problem: ₦25,000 at 7.5% simple interest for 3 years. Find total amount. Answer: Interest = ₦25,000 × 0.075 × 3 = ₦5,625 Total = ₦25,000 + ₦5,625 = ₦30,625 Problem: Budget: ₦75,000, with 30% housing, 25% food, 20% other, rest savings. Find savings amount. Answer: Housing: 30% of ₦75,000 = ₦22,500 Food: 25% = ₦18,750 Other: 20% = ₦15,000 Total allocated: ₦22,500 + ₦18,750 + ₦15,000 = ₦56,250 Savings: ₦75,000 - ₦56,250 = ₦18,750 Problem: ₦15,000 becomes ₦18,750. Find percentage increase. Answer: Increase = ₦18,750 - ₦15,000 = ₦3,750 Percentage increase = $frac{3,750}{15,000} × 100% = 25%$ Problem: With ₦10,000, how many items at ₦456.75 each can be bought? Answer: ₦10,000 ÷ ₦456.75 ≈ 21.89 Can buy 21 items (since we can't buy part of an item) Cost for 21 items = 21 × ₦456.75 = ₦9,591.75 Remaining = ₦10,000 - ₦9,591.75 = ₦408.25 Problem: Which is better: 25% off or 20% off then 10% off? Answer: Single 25% off: Pay 75% of original Double discount: 0.80 × 0.90 = 0.72 = Pay 72% of original 20% off then 10% off is better (28% total discount vs 25%) Conclusion/Recap Money operations form the foundation of financial literacy and practical mathematics. Mastery of addition, subtraction, multiplication, and division with monetary values, along with understanding percentages, discounts, profit/loss, interest, and budgeting, enables informed financial decision-making. These skills are essential for personal finance management, business calculations, and understanding economic concepts in everyday life. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c
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