The four operations and what they do
We use four operations to solve work problems.
- Add (+): put amounts together. Two bills of 120 and 80 make 200.
- Subtract (−): find what is left or the difference. 200 − 150 = 50.
- Multiply (×): repeat the same amount many times. 7 pens at 5 each is 7 × 5.
- Divide (÷): share equally or find the amount for one. 20 shared by 4 is 5.
Read the problem slowly. Ask: am I putting together, taking away, repeating, or sharing?
Unit price: the price of one
The unit price is the price of ONE thing: one pen, one kilogram, one litre, one metre. It lets you compare things that come in different sizes.
Unit price = total price ÷ number of units
Example: 4 pens cost 20. Unit price = 20 ÷ 4 = 5 per pen. For loose goods, the unit may be a kilogram: 3 kg of rice for 150 is 150 ÷ 3 = 50 per kg.
Total cost and change
When you know the price of one, you can find the cost of any amount.
Total cost = unit price × quantity
Then find the money you get back.
Change = money paid − total cost
If the answer is negative, you did not pay enough. The negative number tells you how much more you need.
Check your answer by going backwards: if 50 − 35 = 15, then 35 + 15 should be 50.
Best buy: compare unit prices
A big pack looks cheaper, but you must check. Find the unit price of each pack. The smaller unit price is the better buy.
Pack A: 6 pens for 33 gives 33 ÷ 6 = 5.5. Pack B: 10 pens for 50 gives 50 ÷ 10 = 5. Pack B is the better buy.
Be careful: use the same unit for both (both in grams, or both in kilograms). Also, a cheaper pack is only a good deal if you will really use all of it.
Try it
In the 3D: before you move a slider, predict the cost and the change on paper. Then move the slider and check.
At home: look at two sizes of the same biscuit, soap or rice pack. Write each price and weight. Divide to find the price per 100 g. Which is the best buy? Is it the one you expected?
Key formulas and definitions
- Unit price = total price ÷ number of units
- Total cost = unit price × quantity
- Change = money paid − total cost
- Best buy = the smaller unit price (same unit for both)
- Check: cost + change = money paid
Worked examples
1. A pack of 5 notebooks costs 150. Find the price of one notebook.
Unit price = 150 ÷ 5 = 30. One notebook costs 30.
2. Tomatoes cost 40 per kg. Find the cost of 3 kg.
Total = 40 × 3 = 120.
3. Asha buys 3 kg of tomatoes (40 per kg) and pays with 200. How much change does she get?
Cost = 40 × 3 = 120. Change = 200 − 120 = 80.
4. A 12-pack of juice costs 180. How much do 7 bottles cost at the same unit price?
Unit price = 180 ÷ 12 = 15. Cost of 7 = 7 × 15 = 105.
5. Shop A sells 6 eggs for 42. Shop B sells 10 eggs for 65. Which is the better buy?
A: 42 ÷ 6 = 7 per egg. B: 65 ÷ 10 = 6.5 per egg. B is cheaper per egg, so B is the better buy.
6. A worker buys 8 metres of cable at 12.50 per metre and 5 plugs at 18 each. She pays with 200. Find the change.
Cable = 8 × 12.50 = 100. Plugs = 5 × 18 = 90. Total = 100 + 90 = 190. Change = 200 − 190 = 10.
7. Rice costs 90 for 2 kg (brand X) and 140 for 3 kg (brand Y). Which is cheaper per kg, and how much do you save buying 6 kg of the cheaper one instead of the dearer one?
X: 90 ÷ 2 = 45 per kg. Y: 140 ÷ 3 = 46.67 per kg (about). X is cheaper. For 6 kg: X = 6 × 45 = 270, Y = 6 × 46.67 = 280. You save about 10.
Common mistakes
- Dividing the wrong way round. Unit price is total price ÷ number of items, not items ÷ price.
- Choosing the bigger pack without checking the unit price. Always divide first.
- Comparing different units, such as 500 g and 2 kg. Change both to the same unit first.
- Forgetting to subtract at the end. The change is money paid minus cost, not the cost.