Equivalent Ratio Tables and Word Problems: Recipes and Stock

Keep one scale factor across each row

Both component columns scale together, and the total scales by the same factor. The total is seven parts, so flour is 5/7 of the mixture and water is 2/7. The ratio 5:2 does not mean flour is 5/2 of the total. This is a mathematical mass example, not a tested cooking or food-safety recipe.

See the parts before changing the quantity

For 350 g total at 5:2, one part is 350 / 7 = 50 g. Flour is 5 × 50 = 250 g; water is 2 × 50 = 100 g. Check 250 + 100 = 350 and 250 / 100 = 5/2. If instead you are given 350 g flour, the required water is 350 × 2/5 = 140 g; the question’s starting quantity changes the calculation.

A 2:1 stock allocation is a separate family

Allocate 36 units in a 2:1 ratio. There are three total parts, so each part is 12 units. Allocate 24 blue and 12 red. For 37 indivisible units, an exact 2:1 allocation of all stock is impossible: 37/3 is not an integer. You could allocate 36 and leave one unassigned, if the task permits; do not round the components independently and still claim an exact ratio.

Why 5:2 and 2:1 are not equivalent

Cross products give 5 × 1 = 5 and 2 × 2 = 4. Because those differ, no common nonzero scaling factor changes 5:2 into 2:1. The first mix has 5/7 ≈ 71.43% of its first component; the second has 2/3 ≈ 66.67%. Compare component order and units before concluding two mixes are the same.

Use the equivalent ratio calculator to check both families or generate scaled rows. For a missing entry, use the stepwise missing-value method. A table is useful for repeated scaling; cross multiplication checks an isolated unknown.

Convert units before comparing columns

A fictional mix contains 0.5 kg dry material and 200 g liquid, measured by mass. Convert 0.5 kg to 500 g first: 500:200 simplifies to 5:2. Calling the raw numbers 0.5:200 would compare different units and misstate the relationship. Do not convert mass to volume without an appropriate density; a gram is not automatically a milliliter.

Translate a word problem into a table

Name both quantities and choose their order. Identify whether the supplied number is one component or the whole. Divide by its corresponding base component to find the scale factor, multiply all other components, then verify the total and original relationship. If a result must be a whole stock unit, test divisibility before rounding.

For example, if the 5:2 row has 60 g water, the factor is 60/2 = 30. Flour is 5 × 30 = 150 g and total mass is 210 g. If the task gives a 210 g total, divide by seven first and reach the same row. These are equivalent descriptions of that one case, not interchangeable instructions for every starting number.

Common mistakes

Adding the same amount to both components, mixing a component-to-component ratio with a component-to-total fraction, reversing the order, ignoring units and rounding indivisible stock can all invalidate a table. Recipe proportions alone do not price ingredients or establish nutrition, shelf life or business profitability.

Reference and example scope

OpenStax’s proportion applications supplies the equality-of-ratios method and consistent quantity-order principle. All table rows, the 350 g illustration and the indivisible-stock problem above are original. They teach proportional reasoning rather than financial leverage or accounting ratios.