GOZUNTA
Try it now
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 \(\text{both}~\text{parts}\) of the ratio by \(4\). What is the new equivalent ratio?
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Practice the problem type you meant to practice.

Navigate by objective and problem type instead of taking whichever free problem happens to come next.

Create a free account
With paid access

Keep going when the starter set ends.

A subscription removes the locked gaps from your selected course so practice can continue through the full sequence.

Compare plans

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

Keep the ratio order and scale factor

\[\text{red}~:~\text{blue}~=~3~:~5;~\text{scale}~\text{factor}~=~4\]

The first term represents red and the second blue; both must be multiplied by 4.

02

Scale both terms

\[3~\times~4~=~12;~5~\times~4~=~20\]

Applying the same factor to both terms preserves the ratio relationship.

03

Check equivalence

\[12/20~=~3/5\]

Dividing both new terms by 4 recovers the original ratio.

04

State the equivalent ratio

\[12:20\]

The new red-to-blue ratio is 12:20.

+

Another way

  1. Write 3:5 = (3 × 4):(5 × 4) before calculating.

!

Common mistake

Do not multiply only one term. Equivalent ratios require the same nonzero scale factor on both terms.

Solution walkthrough video