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All courses Math Foundations · MF.PR.3 17 of 60
Generate and justify equivalent ratios using scaling, tables, and diagrams.

Scale a ratio up

Problem
A paint mix uses a ratio of 3:5 red to blue. Multiply both parts of the ratio by 4. What is the new equivalent ratio?
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Hint

Keep the ratio in red-to-blue order. Start by multiplying the first number, 3, by 4, and then plan to do the same to 5.

Equivalent ratios are made by multiplying both parts by the same scale factor. Here, both numbers must be scaled by 4.

Solution walkthrough

01

Identify the starting ratio

\[3:5~\text{ red to blue}\]

The ratio starts with red and then blue, so we must keep that same order in the new ratio.

02

Apply the scale factor to red

\[3~\times~4~=~12\]

Scaling up by 4 means multiplying the red part, 3, by 4.

03

Apply the same scale factor to blue

\[5~\times~4~=~20\]

Equivalent ratios come from multiplying both parts by the same number. Since the factor is 4, blue becomes 20.

04

Write the new equivalent ratio

\[12:20\]

The new paint-mix ratio is 12:20, still in the order red to blue.

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Another way

  1. Use a quick ratio table: red 3 -> 12 and blue 5 -> 20 by multiplying each entry by 4.

  2. Check by dividing back by 4: 12 ÷ 4 = 3 and 20 ÷ 4 = 5, so 12:20 matches 3:5.

!

Common mistake

Changing only one part, such as writing 12:5. That is not equivalent to 3:5 because both red and blue must be multiplied by 4.