Grade 10 essential mathematics Measurements and Geometry – Commercial Arithmetic I Notes
Essential Mathematics — Strand 2.0 Measurements & Geometry
Sub-topic 2.8: Commercial Arithmetic I (age ~15, Kenyan context)
- identify and outline the sub-sub-strands: Budget, Discounts and Commission, Profit and Loss, Conversion of different currencies,
- prepare budget for use in clubs or societies,
- calculate discount and percentage discounts in different situations,
- determine commission and percentage commissions in different situations,
- determine percentage profit and loss made in the sale of goods,
- convert currencies using exchange rate tables,
- recognise the role of commercial arithmetic in day-to-day life.
- Budget = plan of expected income and planned expenditure. Balance = Income − Total expenditure.
- Discount amount = Original price × (discount% / 100). Sale price = Original price − Discount amount.
- Commission = Total sales × (commission% / 100). (Often paid to agents or salespeople.)
- Profit / Loss:
- Profit = Selling price − Cost price (if positive).
- Loss = Cost price − Selling price (if positive).
- Profit% = (Profit ÷ Cost price) × 100. Loss% = (Loss ÷ Cost price) × 100.
- Currency conversion:
- To convert Foreign → KES: Amount × Exchange rate (KES per 1 unit of foreign currency).
- To convert KES → Foreign: Amount ÷ Exchange rate.
Example 1 — Preparing a simple club budget
The Drama Club has KSh 5,000 for a performance. Planned items:
Balance = Income − Expenditure = 5,000 − 4,700 = KSh 300 (leftover). If expenditure > income, plan fundraising or reduce items.
The Drama Club has KSh 5,000 for a performance. Planned items:
- Refreshments: KSh 2,000
- Costumes: KSh 1,500
- Props: KSh 800
- Posters/printing: KSh 400
Balance = Income − Expenditure = 5,000 − 4,700 = KSh 300 (leftover). If expenditure > income, plan fundraising or reduce items.
Example 2 — Discount
A pair of earphones costs KSh 2,400 with a 15% discount.
Discount amount = 2,400 × 15/100 = 2,400 × 0.15 = KSh 360.
Sale price = 2,400 − 360 = KSh 2,040.
A pair of earphones costs KSh 2,400 with a 15% discount.
Discount amount = 2,400 × 15/100 = 2,400 × 0.15 = KSh 360.
Sale price = 2,400 − 360 = KSh 2,040.
Example 3 — Commission
A sales agent sells solar lamps worth KSh 45,000 in a month; commission = 6%.
Commission = 45,000 × 6/100 = 45,000 × 0.06 = KSh 2,700.
A sales agent sells solar lamps worth KSh 45,000 in a month; commission = 6%.
Commission = 45,000 × 6/100 = 45,000 × 0.06 = KSh 2,700.
Example 4 — Profit & Loss
A retailer buys a bag of maize flour at KSh 350 and sells at KSh 420.
Profit = 420 − 350 = KSh 70.
Profit% = (70 ÷ 350) × 100 = 0.2 × 100 = 20%.
If sold at KSh 320 → Loss = 350 − 320 = KSh 30; Loss% = (30 ÷ 350) × 100 ≈ 8.57%.
A retailer buys a bag of maize flour at KSh 350 and sells at KSh 420.
Profit = 420 − 350 = KSh 70.
Profit% = (70 ÷ 350) × 100 = 0.2 × 100 = 20%.
If sold at KSh 320 → Loss = 350 − 320 = KSh 30; Loss% = (30 ÷ 350) × 100 ≈ 8.57%.
Example 5 — Currency conversion
Exchange table (example rates): 1 USD = KSh 150; 1 GBP = KSh 190; 1 EUR = KSh 165.
Convert US$25 to KSh: 25 × 150 = KSh 3,750.
Convert KSh 5,000 to USD: 5,000 ÷ 150 ≈ US$33.33.
Exchange table (example rates): 1 USD = KSh 150; 1 GBP = KSh 190; 1 EUR = KSh 165.
Convert US$25 to KSh: 25 × 150 = KSh 3,750.
Convert KSh 5,000 to USD: 5,000 ÷ 150 ≈ US$33.33.
- The Chess Club has KSh 6,200. Prepare a budget if they plan: prizes KSh 2,200; snacks KSh 1,900; printing KSh 600; transport KSh 800. How much will remain or is there a deficit?
- A shop marks a radio at KSh 8,500 and offers 12% discount. Find the discount amount and sale price.
- An agent sells mattresses totaling KSh 120,000 in a quarter. If commission rate is 5%, what is the agent’s commission?
- A phone is bought for KSh 9,000 and sold for KSh 10,350. Find profit and profit%.
- Using the example rate 1 USD = KSh 150, convert KSh 12,000 to USD. Then convert US$40 to KSh.
- Optional challenge: A shop buys 20 boxes of soap at KSh 280 each. If they want a 25% profit on cost, what selling price per box should they set?
- Total planned = 2,200 + 1,900 + 600 + 800 = KSh 5,500. Balance = 6,200 − 5,500 = KSh 700 (leftover).
- Discount = 8,500 × 12/100 = 1,020. Sale price = 8,500 − 1,020 = KSh 7,480.
- Commission = 120,000 × 5/100 = KSh 6,000.
- Profit = 10,350 − 9,000 = KSh 1,350. Profit% = (1,350 ÷ 9,000) × 100 = 15%.
- KSh → USD: 12,000 ÷ 150 = US$80. USD → KSh: 40 × 150 = KSh 6,000.
- Cost per box = KSh 280. Required selling price = cost × (1 + profit%) = 280 × 1.25 = KSh 350 per box.
- School-club budgeting: learners prepare a full budget for a class party, sports day or club activity. Include incomes (subscriptions, small fundraisers) and detailed expenditures. Discuss cuts if income is insufficient.
- Market visit activity: visit a local market (or simulate) to record prices, calculate discounts during sales, compare marked price vs sale price. Use local items (soap, ugali flour, airtime bundles).
- Role-play sales & commission: set up stalls; some learners act as sales agents earning commission based on sales value. Calculate commissions weekly.
- Profit & loss shop project: run a small class kiosk for a week (candies, stationery). Record cost price and selling price for items and compute profit or loss and profit%. Reflect on pricing strategy.
- Currency table exercise: using real exchange rates (check bank/post office rates), convert pocket money from KSh to USD/EUR/GBP and back. Discuss fees and why rates vary.
- Use spreadsheets or a simple calculator: show how Excel / Google Sheets can help prepare budgets, apply % formulas, and create automatic conversion tables.
- Project: prepare a one-page simple business plan for a small enterprise (e.g., selling roasted groundnuts). Include budget, expected sales, estimated profit and break-even point.
- Encourage using Kenyan currency (KSh) and local examples to make learning relevant.
- Assess learners with real-life tasks: prepare budgets, calculate discounts on receipts, compute commission from sales logs.
- Allow calculators but check understanding by asking for formula explanation and written steps.
- For stronger learners, add compound problems (e.g., sequential discounts, commission on profit instead of sales, currency conversion with commission/fees).