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All courses Math Foundations · MF.PR.1 15 of 60
Write, interpret, and compare ratios using words, symbols, tables, and diagrams.

Write a ratio from words

Problem
A bag has \(5\) red marbles and \(8\) blue marbles. Write the ratio of red marbles to blue marbles in \(a:b\) form.
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Hint

Underline the words “red marbles to blue marbles.” That tells you which count goes first and which goes second.

A ratio compares two quantities in a specific order. Red to blue is not the same as blue to red.

Solution walkthrough

01

Identify the two counts

\[\text{red}~\text{marbles}~=~5;~\text{blue}~\text{marbles}~=~8\]

The bag contains 5 red marbles and 8 blue marbles.

02

Preserve the requested order

\[\text{red}~\text{to}~\text{blue}\]

The first ratio term must represent red because red is named first; the second must represent blue.

03

Substitute the counts

\[\text{red}~:~\text{blue}~=~5~:~8\]

Place 5 in the red position and 8 in the blue position.

04

Check the meaning

\[5~\text{red}~\text{for}~\text{every}~8~\text{blue}\]

Reading the ratio in words confirms that its terms have not been reversed.

05

Write in a:b form

\[5:8\]

The ratio of red marbles to blue marbles is 5:8.

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Another way

  1. Write the verbal skeleton red:blue first, then replace each word with its count.

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Common mistake

Do not write 8:5. That is the ratio of blue to red, the reverse of the requested order.

Solution walkthrough video