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SSAT Elementary Level Math : Ratio and Proportion

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

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All SSAT Elementary Level Math Resources

12 Diagnostic Tests 526 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Ratio And Proportion

What is $10\%$ $\displaystyle 10\%$ of $\displaystyle 25$ ?

Possible Answers:

$\displaystyle 2$

$\displaystyle 5$

$\displaystyle 10$

2.5 $\displaystyle 2.5$

1.5 $\displaystyle 1.5$

Correct answer:

2.5 $\displaystyle 2.5$

Explanation:

$10\%$ $\displaystyle 10\%$ of $\displaystyle 25$ is calculated by multiplying $\displaystyle .10$ by $\displaystyle 25$ .

$.10 \times 25=2.5$ $\displaystyle .10 \times 25=2.5$

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Example Question #32 : Ratio And Proportion

Megan's teacher says that if Megan wants to join the girl's basketball team, she has to have at least $90\%$ $\displaystyle 90\%$ of this quarter's homework turned in. If there have been $\displaystyle 50$ assignments so far this quarter, how many of these does Megan have to have turned in so that she can join the team?

Possible Answers:

$30\ \text{assignments}$ $\displaystyle 30\ \text{assignments}$

$47\ \text{assignments}$ $\displaystyle 47\ \text{assignments}$

$35\ \text{assignments}$ $\displaystyle 35\ \text{assignments}$

$45\ \text{assignments}$ $\displaystyle 45\ \text{assignments}$

$27\ \text{assignments}$ $\displaystyle 27\ \text{assignments}$

Correct answer:

$45\ \text{assignments}$ $\displaystyle 45\ \text{assignments}$

Explanation:

In order to solve this problem, we need to make a ratio. Megan's teacher says she needs to have turned in 90% of her homework. First we need to change 90% into a fraction:

$\frac{90}{100}$ $\displaystyle \frac{90}{100}$

Using this information, we need to fill in the following ratio to find out how many assignments Megan needs to have turned in to be at 90% completion:

$\frac{90}{100} =$ $\displaystyle \frac{90}{100} =$ $\frac{?}{50}$ $\displaystyle \frac{?}{50}$

To solve this ratio, we need to cross multiply.

$90\times 50\ = 450$ $\displaystyle 90\times 50\ = 450$

Now we have an equation to solve.

$450 = 100\times \textup{?}$

If we divide both sides by 100, we are left with our final answer.

$450 \div 100 =\: ?$ $\displaystyle 450 \div 100 =\: ?$

Megan must have at least 45 assignments turned in if she wants to join the basketball team.

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Example Question #33 : Ratio And Proportion

If I have 6 red marbles and 5 blue marbles, what proportion of the marbles are red.

Possible Answers:

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

$\frac{5}{11}$ $\displaystyle \frac{5}{11}$

$\frac{6}{11}$ $\displaystyle \frac{6}{11}$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

Correct answer:

$\frac{6}{11}$ $\displaystyle \frac{6}{11}$

Explanation:

To find a proportion, simply divide what you desire by the total.

In this problem the desired is the number of red marbles and the total is all of the marbels.

Thus,

$proportion=\frac{\#\ of\ reds}{\#\ of\ total}=\frac{6}{5+6}=\frac{6}{11}$ $\displaystyle proportion=\frac{\#\ of\ reds}{\#\ of\ total}=\frac{6}{5+6}=\frac{6}{11}$

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Example Question #34 : Ratio And Proportion

I have 7 green marbles and 4 blue marbles. Find the proportion of green marbles.

Possible Answers:

4:7 $\displaystyle 4:7$

7:4 $\displaystyle 7:4$

$\frac{7}{11}$ $\displaystyle \frac{7}{11}$

$\frac{4}{11}$ $\displaystyle \frac{4}{11}$

Correct answer:

$\frac{7}{11}$ $\displaystyle \frac{7}{11}$

Explanation:

To find a proportion, simply divide the desired amount by the total amount. We know our total by simply adding the marble amounts that compose it. Thus,

$Proportion=\frac{\#blue}{\#total}=\frac{7}{11}$ $\displaystyle Proportion=\frac{\#blue}{\#total}=\frac{7}{11}$

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Example Question #35 : Ssat Elementary Level Quantitative (Math)

Solve the following proportion:

$\displaystyle 9:4 = x:24$

Possible Answers:

x=13 $\displaystyle x=13$

x=54 $\displaystyle x=54$

x=63 $\displaystyle x=63$

x=29 $\displaystyle x=29$

x=36 $\displaystyle x=36$

Correct answer:

x=54 $\displaystyle x=54$

Explanation:

When solving a proportion, it is easiest to re-write it using fraction. So,

$\displaystyle 9:4 = x:24$

can be re-written as

$\frac{9}{4} = \frac{x}{24}$ $\displaystyle \frac{9}{4} = \frac{x}{24}$

Now, to solve this, we will cross multiply and divide.

To cross multiply, we will take the numerator of the first fraction and multiply it by the denominator of the second fraction. Then, we multiply the denominator of the first fraction by the numerator in the second, and set them equal to each other.

It might be easier to see an example.

$9 \cdot 24 = 4 \cdot x$ $\displaystyle 9 \cdot 24 = 4 \cdot x$

$\displaystyle 216 = 4x$

Now, we divide to solve for x.

$\frac{216}{4} = \frac{4x}{4}$ $\displaystyle \frac{216}{4} = \frac{4x}{4}$

54 = x $\displaystyle 54 = x$

x = 54 $\displaystyle x = 54$

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All SSAT Elementary Level Math Resources

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SSAT Elementary Level Math : Ratio and Proportion

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

All SSAT Elementary Level Math Resources

Example Questions

Example Question #31 : Ratio And Proportion

Example Question #32 : Ratio And Proportion

Example Question #33 : Ratio And Proportion

Example Question #34 : Ratio And Proportion

Example Question #35 : Ssat Elementary Level Quantitative (Math)

All SSAT Elementary Level Math Resources

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