Why do I need to convert units like grams to kilograms first?

You can only compare cost per unit if both options use the same unit. Convert one to match the other before dividing. There are 1000 grams in 1 kilogram and 1000 millilitres in 1 litre.

Why do I need to convert units like grams to kilograms first?

You can only compare cost per unit if both options use the same unit. Convert one to match the other before dividing. There are 1000 grams in 1 kilogram and 1000 millilitres in 1 litre.

Year 11 General Consumer Arithmetic: Personal Finance

Comparing using the unit cost method

Q: What is the unit cost method?

The unit cost method finds the cost of one common unit (such as 1 kg, 1 L, or 1 item) for each option so you can compare prices fairly. Divide the total price by the quantity to get the unit cost. The option with the lower unit cost is the better buy.

Q: How do you find the best buy when packets are different sizes?

Convert both prices to the same unit (for example, dollars per kilogram). Divide the price by the quantity in that unit, then compare. The lower number is the better buy.

Q: Is the cheaper packet always the better buy?

No. A small packet usually has a lower total price but a higher cost per unit. Always compare unit cost, not the total price on the shelf tag.

Q: How do you compare a percent off discount with a dollar off discount?

Work out the sale price for each. For a percent off, multiply the original price by 1 minus the percent as a decimal. For a dollar off, subtract the discount. Then compare the two sale prices.

Q: How do you find the unit cost of a buy 3 get 1 free offer?

You pay for 3 but receive 4 items. Divide the price of 3 by 4 to get the effective cost per item, then compare to the regular unit cost.

12 practice questions 2 video lessons Theory + worked examples

Theory

The unit cost method compares prices fairly by reducing each option to the cost of one common unit — per kilogram, per litre, per item, or per wash. The option with the lower unit cost is the better buy, no matter the packet size or special offer.

The unit cost of a product is the price of one common unit — $1$ kg, $1$ L, $1$ mL, or $1$ item. Dividing the total price by the quantity gives this figure, which lets you compare options of different sizes on equal terms.

The better buy is the option with the lower unit cost. A bigger packet usually has a lower unit cost, but not always — large sizes can be more expensive per kg if the brand uses size as a premium signal. Always do the calculation.

The same idea covers cost per wash for detergent, cost per litre for petrol, and cost per item for multi-packs. Pick whichever unit makes the comparison simplest.

Special offers like "25% off" or "buy 3 get 1 free" change the effective price. Convert the offer to a sale price first, then compare unit costs.

Cheaper per kg wins, not cheaper total

Divide price by quantity for each option

The core formula for any unit-cost comparison:

unit cost = \frac{total price}{quantity}

unit cost = \frac{total price}{quantity}

Sale price after a percentage discount:

sale price = original \times (1 - \frac{r}{100})

sale = original \times (1 - \frac{r}{100})

Effective unit cost for a buy $n$ get $1$ free deal:

effective unit cost = \frac{price of n}{n + 1}

effective unit cost = \frac{price of n}{n + 1}

Useful conversions: 1 kg =1000 g, 1 L =1000 mL. Always put both options into the same unit before dividing.

Common units for different products:

Product type	Unit to use
Food in packets	per kg or per g
Drinks	per L or per mL
Multi-packs	per item
Detergent	per wash
Petrol	per L

How to compare two or more prices

Choose a common unit (per kg, per L, per item, per wash). If sizes are mixed, convert one to match the other.
Divide price by quantity for each option to get the unit cost.
Compare unit costs. The option with the lowest unit cost is the better buy.

For special offers, calculate the effective sale price (or effective unit cost) first, then compare as usual.

Example 1 — Best buy per kg

Brand X cheese:

750

g for

$ 6.30

. Brand Y cheese:

2

kg for

$ 15.60

. Which is the better buy?

Solution

Convert each to dollars per kg ( $750$ g $= 0.750$ kg).

$X$	$=$	$\frac{6.30}{0.750}$
$X$	$=$	$$ 8.40 / kg$
$Y$	$=$	$\frac{15.60}{2}$
$Y$	$=$	$$ 7.80 / kg$

X = 8.40 /kg, Y = 7.80 /kg

Brand Y is cheaper per kg — the better buy.

Example 2 — Three sizes

Rice is sold in three sizes:

1

kg for

$ 3.40

2.5

kg for

$ 8

5

kg for

$ 17

. Which is the best value?

Solution

Cost per kg for each.

$1 kg$	$:$	$3.40 \div 1 = $ 3.40$
$2.5 kg$	$:$	$8 \div 2.5 = $ 3.20$
$5 kg$	$:$	$17 \div 5 = $ 3.40$

3.40, 3.20, 3.40

The $2.5$ kg bag has the lowest cost per kg — the best value.

Example 3 — Two discount types

A pair of jeans is

$ 90

at two stores. Store A has "

20 %

off". Store B has "

$ 20

off". Which is cheaper?

Solution

Calculate each sale price.

$A$	$=$	$90 \times 0.80$
$A$	$=$	$$ 72$
$B$	$=$	$90 - 20$
$B$	$=$	$$ 70$

A = 72, B = 70

Store B is cheaper, by $$ 2$ .

Example 4 — Cost per use

Detergent A:

2

L for

$ 22

, good for

40

washes. Detergent B:

3

L for

$ 36

, good for

60

washes. Which has the lower cost per wash?

Solution

Divide price by number of washes.

$A$	$=$	$\frac{22}{40}$
$A$	$=$	$$ 0.55 / wash$
$B$	$=$	$\frac{36}{60}$
$B$	$=$	$$ 0.60 / wash$

A = 0.55, B = 0.60

Detergent A is cheaper per wash.

Common pitfalls

Cheaper packet is not always the better buy. A small packet often has a lower total price but a higher unit cost. Always compare unit cost, not the shelf price.

Mismatched units. "

500

g for

$ 4

" and "

1.2

kg for

$ 9

" cannot be compared until both are in the same unit. Convert one before you divide.

Forgetting to apply the discount first. If a question mixes a sale offer with a unit-cost comparison, apply the discount to get the sale price, then work out cost per unit.

"Buy $3$ get $1$ free" arithmetic. You pay for

3

and receive

4

. Divide the price of

3

4

, not by

3

, to get the effective unit cost.

Frequently asked questions

What is the unit cost method?

It is a way of comparing prices by reducing each option to the cost of one common unit (per kg, per L, per item). Divide the total price by the quantity. The option with the lower unit cost is the better buy.

How do you find the best buy when packets are different sizes?

Convert both prices to the same unit, divide price by quantity, and pick the option with the lower result.

Is the cheaper packet always the better buy?

No. Smaller packets often have a higher unit cost even though the total price looks lower. Always compare per-unit prices.

How do you compare a percent off discount with a dollar off discount?

Work out each sale price separately. For percent off, multiply the original by $1 - r / 100$ . For dollar off, subtract the discount. Compare the two sale prices.

How do you find the unit cost of a "buy 3 get 1 free" offer?

Divide the price of $3$ items by $4$ , because you receive $4$ items in total. The result is the effective cost per item.

Why do I have to convert grams to kilograms first?

You can only compare options if both use the same unit. Use $1$ kg $= 1000$ g (or $1$ L $= 1000$ mL) to convert one option to match the other before dividing.