SSAT Upper Level Math : Proportion / Ratio / Rate

Study concepts, example questions & explanations for SSAT Upper Level Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #4 : How To Express A Fraction As A Ratio

In a garden with \(\displaystyle 120\) plants, \(\displaystyle 40\) are tulips, \(\displaystyle 15\) are daisies, \(\displaystyle 25\) are roses, and the rest are bluebonnets. What is the ratio of bluebonnets to tulips in this garden?

Possible Answers:

\(\displaystyle 8:3\)

\(\displaystyle 1:1\)

\(\displaystyle 8:5\)

\(\displaystyle 1:3\)

Correct answer:

\(\displaystyle 1:1\)

Explanation:

First, find the number of bluebonnets in the garden.

\(\displaystyle \text{Number of bluebonnets}=120-40-15-25=40\)

The ratio of bluebonnets to tulips can be expressed as a fraction:

\(\displaystyle \frac{40}{40}=\frac{1}{1}\)

The fraction can also be expressed as the ratio \(\displaystyle 1:1\).

Example Question #101 : Number Concepts And Operations

Express \(\displaystyle \frac{1}{10}\) as a ratio.

Possible Answers:

\(\displaystyle 0.1\)

\(\displaystyle 1:1\)

\(\displaystyle 1:10\)

\(\displaystyle 10:1\)

Correct answer:

\(\displaystyle 1:10\)

Explanation:

In the colon form of a ratio, the fraction becomes numerator:denominator.

\(\displaystyle \frac{1}{10}=1:10\)

Example Question #6 : How To Express A Fraction As A Ratio

A smoothie is made with \(\displaystyle 2\) cups of apple juice, \(\displaystyle 1\) cup of mango juice, \(\displaystyle 4\) cups of orange juice, and \(\displaystyle 2\) cups of blueberry juice. What is the ratio of the amount of orange juice to the amount of blueberry juice?

Possible Answers:

\(\displaystyle 1:2\)

\(\displaystyle 1:1\)

\(\displaystyle 2:1\)

\(\displaystyle 1:4\)

Correct answer:

\(\displaystyle 2:1\)

Explanation:

The ratio of orange juice to blueberry juice can be expressed as a fraction:

\(\displaystyle \frac{4}{2}=\frac{2}{1}\)

That fraction can also be expressed as \(\displaystyle 2:1\).

Example Question #102 : Number Concepts And Operations

Express \(\displaystyle \frac{10}{12}\) as a ratio in simplest terms.

Possible Answers:

\(\displaystyle 2:3\)

\(\displaystyle 10:12\)

\(\displaystyle 5:6\)

\(\displaystyle 6:5\)

Correct answer:

\(\displaystyle 5:6\)

Explanation:

First, reduce the fraction.

\(\displaystyle \frac{10}{12}=\frac{5}{6}\)

Now, the simplified fraction can also be expressed as \(\displaystyle 5:6\).

Example Question #1171 : Ssat Upper Level Quantitative (Math)

A pan of cupcakes had \(\displaystyle 48\) cupcakes on Monday. After one day, \(\displaystyle 8\) cupcakes were eaten. What is the ratio of cupcakes eaten to cupcakes remaining?

Possible Answers:

\(\displaystyle 1:5\)

\(\displaystyle 1:6\)

\(\displaystyle 6:1\)

\(\displaystyle 5:1\)

Correct answer:

\(\displaystyle 1:5\)

Explanation:

First, find the number of cupcakes that remain.

\(\displaystyle \text{Remaining cupcakes}=48-8=40\)

Now, set up the ratio of cupcakes eaten to cupcakes remaining as a fraction:

\(\displaystyle \frac{8}{40}=\frac{1}{5}\)

That fraction is equivalent to \(\displaystyle 1:5\).

 

Example Question #103 : Number Concepts And Operations

In a group of dolphins, there are \(\displaystyle 5\) male dolphins for every \(\displaystyle 30\) female dolphins. What is the ratio of female dolphins to male dolphins in this group?

Possible Answers:

\(\displaystyle 6:1\)

\(\displaystyle 5:6\)

\(\displaystyle 6:5\)

\(\displaystyle 1:6\)

Correct answer:

\(\displaystyle 6:1\)

Explanation:

The ratio of female to male dolphins can be expressed as the following fraction:

\(\displaystyle \frac{30}{5}=\frac{6}{1}\)

That fraction can be expressed using the colon form of a ratio as \(\displaystyle 6:1\).

 

Example Question #1172 : Ssat Upper Level Quantitative (Math)

In an animal shelter, there are \(\displaystyle 12\) cats, \(\displaystyle 14\) birds, and \(\displaystyle 20\) dogs. What is the ratio of dogs to the total number of animals at the shelter?

Possible Answers:

\(\displaystyle 5:3\)

\(\displaystyle 3:5\)

\(\displaystyle 1:5\)

\(\displaystyle 10:23\)

Correct answer:

\(\displaystyle 10:23\)

Explanation:

First, find the total number of animals at the shelter.

\(\displaystyle \text{Total Number of Animals}=12+14+20=46\)

The ratio of dogs to the total number of animals can be expressed as the following fraction:

\(\displaystyle \frac{20}{46}=\frac{10}{23}\)

That fraction can also be expressed as \(\displaystyle 10:23\).

Example Question #45 : Fractions

There are \(\displaystyle 30\) marbles in a bag. In the bag, there are \(\displaystyle 6\) red marbles, \(\displaystyle 12\) blue marbles, and the rest of the marbles are yellow. What is the ratio of yellow marbles to red marbles?

Possible Answers:

\(\displaystyle 4:5\)

\(\displaystyle 1:2\)

\(\displaystyle 1:1\)

\(\displaystyle 2:1\)

Correct answer:

\(\displaystyle 2:1\)

Explanation:

First, find the number of yellow marbles in the bag.

\(\displaystyle \text{Number of yellow marbles}=30-12-6=12\)

The ratio of yellow marbles to red marbles can be expressed as a fraction:

\(\displaystyle \frac{12}{6}=\frac{2}{1}\)

That fraction can then be expressed as \(\displaystyle 2:1\).

Example Question #46 : Fractions

A video store lent out \(\displaystyle 80\) videos during the fall semester. \(\displaystyle 18\) of the videos were lost, and the rest were returned. What is the ratio of lost videos to returned videos?

Possible Answers:

\(\displaystyle 9:31\)

\(\displaystyle 31:9\)

\(\displaystyle 9:50\)

\(\displaystyle 5:12\)

Correct answer:

\(\displaystyle 9:31\)

Explanation:

First, find the number of videos that were returned.

\(\displaystyle \text{Number of videos returned}=80-18=62\)

Now, the ratio of videos lost to videos returned can be expressed as the following fraction:

\(\displaystyle \frac{18}{62}=\frac{9}{31}\)

This fraction can then be expressed as \(\displaystyle 9:31\).

Learning Tools by Varsity Tutors