Match each quantity relationship to its equivalent simplified ratio.

$10$ instructors for every $50$ recruits (ratio of instructors to recruits) $1:5$
$12$ utility trucks for every $8$ transport vans (ratio of trucks to vans) $3:2$
$15$ gallons of fuel for every $5$ quarts of oil (ratio of fuel to oil) $3:1$
$20$ standard rifles for every $15$ sidearms (ratio of rifles to sidearms) $4:3$

Answer

The unsimplified ratios match to their reduced forms as follows: instructors to recruits (

10:50

) is

1:5

, trucks to vans (

12:8

) is

3:2

, fuel to oil (

15:5

) is

3:1

, and rifles to sidearms (

20:15

) is

4:3

Each relationship is found by writing down the initial numerical counts in the order specified and reducing them to their lowest integer terms using their greatest common factors.

Step-by-Step Solution

Set up the initial part-to-part ratio for each scenario in the exact order requested by the text.

The raw ratios are

10:50

12:8

15:5

, and

20:15

Ratio order matters. Ensuring the first mentioned item is the first number in the ratio prevents inverted answers.

Simplify each ratio by finding the greatest common factor (GCF) for each pair and dividing both numbers by it.

10:50

reduces to

1:5

12:8

reduces to

3:2

15:5

reduces to

3:1

20:15

reduces to

4:3

A ratio is properly expressed when the two numbers have no common factors other than

1

Key Concept

Basic Ratios

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Common Mistakes

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