Method 04 • fractions and ratios
Fractions that fit real life
A fraction tells you how much of a whole you have. A ratio compares quantities. Both become useful when the whole and the units are clearly named.
Scale a recipe
Start with what counts as one whole
One half of a small loaf is not the same quantity as one half of a large loaf. The fraction describes a relationship to the whole, not a fixed size by itself. In 3/4, the bottom number says the whole is divided into four equal parts; the top number says you are using three of those parts.
Equivalent fractions describe the same share. One half, two quarters and four eighths all represent half of the same whole. Multiplying the top and bottom by the same nonzero number preserves that share. Dividing both by a common factor simplifies the notation: 6/8 becomes 3/4 because both numbers divide by two.
Change a recipe with one scale factor
If a recipe serves four and you want three servings, the scale factor is 3 ÷ 4, or 3/4. Multiply every ingredient quantity by that factor. For a listed amount of 200 grams, calculate 200 ÷ 4 × 3 = 150 grams. Dividing first keeps the intermediate numbers friendly.
From four servings to three
Scale factor = wanted ÷ original = 3/4200 g × 3/4 = 150 g300 ml × 3/4 = 225 mlCheck: each new quantity is smaller than the original and larger than half of it.
To move from four servings to six, use 6/4 = 1.5. A listed 200 grams becomes 300 grams. Do not subtract a fixed quantity from every ingredient when reducing a recipe: removing 50 grams from both 200 grams and 60 grams changes their relationship dramatically.
Add fractions using equal-sized parts
To add 1/2 and 1/4, first rewrite the half as 2/4. Then 2/4 + 1/4 = 3/4. You are now counting three parts of the same size. Adding the bottom numbers would give 2/6, which describes a different quantity and is not a valid addition method.
For 1/3 + 1/4, use twelfths: 4/12 + 3/12 = 7/12. A quick size check helps: the result should be more than one half because one third plus one quarter exceeds one quarter plus one quarter. Seven twelfths is indeed more than six twelfths.
Read ratios as relationships between parts
A ratio of 2:3 describes two parts of one quantity for every three parts of another. There are five parts in total. For a hypothetical mixture totalling 500 millilitres with additive volumes, one part is 500 ÷ 5 = 100 millilitres. The two quantities are therefore 200 and 300 millilitres.
Check both the total and the ratio: 200 + 300 = 500, and 200:300 simplifies to 2:3. The first component is 2/5 of the total, not 2/3. The fraction 2/3 compares the first component with the second component. Naming the comparison prevents a common and understandable mistake.
These calculations describe a simple proportional model. Real chemical mixtures, medicines and cleaning products may have safety requirements or volumes that do not combine as simply as the model assumes. Follow product instructions; do not infer a safe mixture from a maths example.
Compare packs using a common unit
Two pack prices are hard to compare when their quantities differ. Divide the price by the amount, then express both results using the same unit. In an illustrative comparison, a 500-gram pack costing 3.00 costs 0.60 per 100 grams. A 750-gram pack costing 4.20 costs 0.56 per 100 grams.
| Pack | Example cost | Cost per 100 g |
|---|---|---|
| 500 g | 3.00 | 0.60 |
| 750 g | 4.20 | 0.56 |
The larger pack has the lower cost per equal quantity in this example, but it requires a larger total payment. It is not automatically the better choice if you will waste some of it, lack storage space or need a different product. A unit rate answers one useful question, not every question about value.
Keep measurement units consistent
Convert before comparing: 1 kilogram is 1,000 grams, and 1 litre is 1,000 millilitres. Do not directly compare a cost per kilogram with a cost per 100 grams. Also avoid treating grams and millilitres as interchangeable: one measures mass and the other volume. Converting between them requires information about the substance.
Measuring cups are not universally identical. US customary cups and metric cups can differ, so use the recipe’s stated convention or a specified mass where available. Keep units beside your numbers, and check that the final answer has the unit you actually need.
Measurement and practical references
The International Bureau of Weights and Measures explains SI units. BBC Good Food and King Arthur Baking provide recipe contexts where stated quantities and instructions matter. These references are not endorsements or affiliations.