Ratio and Proportion - SSAT Elementary Level Quantitative

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Question

$Which;number;is;bigger: \frac{3}{7};or;\frac{3}{8},?$

Answer

$For;example,;\frac{1}{2};is;bigger;than;\frac{1}{3}.$

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Question

What is 10% of 100?

Answer

10% of 100 is calculated by multiplying .10 by 100.

$.10\times100=10$

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Question

What is 13% of 100?

Answer

13% of 100 is calculated by multiplying .13 by 100.

$.13\times 100=13$

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Question

Solve for the variable:

$\frac{3}{4}=\frac{6}{x}$

Answer

There are two ways to solve. First, you may see that the top numbers are related by multiplying by 2.

This means that the bottom numbers must also be related by multiplying by 2.

The missing number is therefore 8.

The other way to solve is to cross multiply:

$\frac{3}{4}=\frac{6}{x}$

$3\times (x) = 4\times6$

Solve for by dividing 24 by 3:

$x = \frac{24}{3}=8$

$\frac{3}{4}=\frac{6}{8}$

The answer is again 8.

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Question

Solve for the variable:

$\frac{5}{9}=\frac{x}{27}$

Answer

Cross multiply:

$5\times27=9\times x$

Solve for by dividing 135 by 9:

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Question

Solve for the variable:

$\frac{x}{6}=\frac{10}{12}$

Answer

Cross multiply:

$(x) \times 12=6\times10$

Solve for x by dividing 60 by 12:

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Question

What is of ?

Answer

of is calculated by multiplying . by .

$.10\times 200=20$

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Question

What is of ?

Answer

of is calculated by multiplying by .

$.10 \times 25=2.5$

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Question

Sofia goes to the movies with . She spends on her ticket and on food and drink.

What fraction of Sofia's original was not spent?

Answer

Adding Sofia's expenses shows that she spent a total of dollars. Subtracting this from the original amount of money she had gives the unspent portion: .

The ratio of the unspent portion to the original amount gives the fraction of the money that was not spent: $\frac{8}{24} = \frac{1}{3}$ .

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Question

Brad is paid per hour at his current job. If a promotion would increase Brad's pay by , what would Brad make per hour after a promotion?

Answer

To find of Brad's pay, multiply it by (since is the original number and is twice that). $2 \times 10= 20$ , which is the amount of the increase to Brad's pay. Add this increase to the original pay to get the new pay: per hour.

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Question

Solve for x:

$\frac{x}{3} = \frac{7}{6}$

Answer

Multiply both sides by 3 to yield:

$\frac{x}{3} = \frac{7}{6} \equiv x =\frac{21}{6} \equiv x = 3.5$

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Question

Solve for y:

$\frac{y}{8} = \frac{5}{4}$

Answer

Multiply both sides by 8 to yield:

$8\times\frac{y}{8} = 8\times\frac{5}{4}$

Therefore:

$y = \frac{40}{4}$

Therefore:

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Question

A sweater is on sale for . What percentage of the original price has been discounted for the sale?

Answer

Set up a proportion of the new price to the old price to see how they relate.

$\frac{$45}{$75} = \frac{3}{5}$ of the original price

Subtract $\frac{3}{5}$ from to find the amount that was discounted.

$1 - \frac{3}{5} = \frac{2}{5}$

Convert $\frac{2}{5}$ to a decimal by multiplying both the top and bottom of the fraction by , then convert to a percentage.

$\frac{2}{5} \times\frac{2}{2}=\frac{4}{10}$ , which is equivalent to or

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Question

Mary wants to enlarge a picture that she has in her office. The original picture is cm (width) by cm (length). What would be the length of the enlarged picture if the width is cm?

Answer

To find the length of the enlarged picture, we must set up a proportion:

$\frac{5}{10}=\frac{8}{x}$

cross multiply:

Divide both sides by 5:

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Question

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

Answer

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:

$\frac{90}{100}$

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:

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

To solve this ratio, we need to cross multiply.

$90\times 50\ = 450$

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.

$450 \div 100 =: ?$

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

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Question

Find the unknown value: $\frac{2}{3}= \frac{8}{x}$

Answer

To solve the proportion, cross multiply and find the value of the missing variable.

$2x=8\times3$

Divide by on both sides.

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Question

Solve: $\frac{3}{7}= \frac{10}{x}$

Answer

Solve by cross multipling the two fractions.

$3x=10\times7$

Divide by on both sides.

$x=\frac{70}{3}$

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Question

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

Answer

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,

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

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Question

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

Answer

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,

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

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Question

Solve the following proportion:

Answer

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

can be re-written as

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

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.

$9 \cdot 24 = 4 \cdot x$

Now, we divide to solve for x.

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

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