Scale quantities up using a ratio

Scaling a ratio means multiplying each related quantity by the same positive factor, preserving the multiplicative relationship: a ratio $a:b$ becomes $ka:kb$ . Learners interpret this relationship in contexts such as equivalent recipes, quantities, and measurements, using ratio tables or double number lines, and distinguish multiplicative scaling from adding the same amount to each quantity; the focus is on concrete whole-number scaling rather than formal similarity or more advanced proportional functions.

Detailed Explanation: Scale quantities up using a ratio

To scale a ratio, multiply both quantities by the same positive number. This keeps the relationship between them equivalent.

Example

A recipe uses flour and sugar in a ratio of $(2:3)$ . You want to make 4 times the recipe.

Identify the original quantities:
- Flour: $2$ cups
- Sugar: $3$ cups
Multiply each quantity by the scale factor, $4$ :

2 \times 4 = 8

3 \times 4 = 12

Write the new ratio:

8:12

So, you need 8 cups of flour and 12 cups of sugar.

A ratio table shows the scaling:

Flour	Sugar
$2$	$3$
$(2 \times 4=8)$	$(3 \times 4=12)$

The ratio is scaled correctly because both quantities were multiplied by $4$ . You should not add $4$ to each quantity, because $(2+4:3+4)$ would be $(6:7)$ , which does not keep the same multiplicative relationship.

Learn by doing: Scale quantities up using a ratio

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Ratios - Equivalent, Expanding Recipes with Integer Multiples - Whole Numbers

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