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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
There are 5 red marbles and 8 blue marbles in a bag. Write the ratio of red marbles to blue marbles as a:b.
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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 marble counts

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

The problem compares red marbles and blue marbles, so those are the two quantities we need to use.

02

Match the order named in the question

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

A ratio must follow the order in the words. Since the question says red marbles to blue marbles, 5 goes first and 8 goes second.

03

Write the ratio as a:b

\[5:8\]

The question asks for ratio notation in the form a:b, so write the comparison 5 to 8 with a colon.

04

State the ratio in context

\[\text{The}~\text{ratio}~\text{of}~\text{red}~\text{marbles}~\text{to}~\text{blue}~\text{marbles}~\text{is}~5:8.\]

This answer uses the correct numbers and keeps the comparison in the exact order the question asked for.

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Another way

  1. Check by reading 5:8 out loud as '5 red marbles to 8 blue marbles.' If the words match the question, the ratio is written correctly.

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Common mistake

Writing 8:5 instead of 5:8. That reverses the order and gives the ratio of blue marbles to red marbles, which is not what the question asks.