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SSAT Middle Level Math : How to find a proportion

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

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Example Questions

Example Question #1 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{70}{30}$

Possible Answers:

$N = 23 \frac{1}{3}$

N = 21

$N = 42 \frac{6}{7}$

$N = 233 \frac{1}{3}$

$N = 33 \frac{1}{3}$

Correct answer:

$N = 42 \frac{6}{7}$

Explanation:

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{70}{30}$

$70 N = 100 \cdot 30$

70 N = 3,000

$70 N \div 70= 3,000\div 70$

$N = 42 \frac{6}{7}$

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Example Question #2 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{40}{30}$

Possible Answers:

$N = 66 \frac{2}{3}$

$N = 133 \frac{1}{3}$

N = 75

N = 12

$N = 83 \frac{1}{3}$

Correct answer:

N = 75

Explanation:

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{40}{30}$

$40 N = 100 \cdot 30$

40 N = 3,000

$40 N \div 40= 3,000\div 40$

N = 75

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Example Question #3 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{N}{80} = \frac{40}{30}$

Possible Answers:

N = 60

N = 150

$N = 106 \frac{2}{3}$

N = 120

$N = 133 \frac{1}{3}$

Correct answer:

$N = 106 \frac{2}{3}$

Explanation:

Multiply both sides by 80 and solve for :

$\frac{N}{80} = \frac{40}{30}$

$\frac{N}{80} \cdot80 = \frac{40}{30} \cdot80$

$N = \frac{40 \cdot 80}{30} = 106 \frac{2}{3}$

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Example Question #4 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{N}{75} = \frac{40}{30}$

Possible Answers:

N = 100

$N = 83 \frac{1}{3}$

N = 80

N = 120

$N = 56 \frac{1}{4}$

Correct answer:

N = 100

Explanation:

Multiply both sides by 75 and solve for :

$\frac{N}{75} = \frac{40}{30}$

$\frac{N}{75} \cdot 75 = \frac{40}{30} \cdot 75$

$N = \frac{40 \cdot 75}{30} = 100$

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Example Question #5 : How To Find A Proportion

Read this problem, but do not solve it.

4 out of every 5 dentists surveyed recommend Triton sugarless gum to patients who chew gum. If 2,100 dentists were surveyed, how many dentists recommended Triton?

If we let be the number of dentists who recommended Triton, what proportion statement could be used to solve this problem?

Possible Answers:

$\frac{N}{2,100} = \frac{5}{4}$

$\frac{N}{2,100} = \frac{1}{5}$

$\frac{N}{4} = \frac{5}{2,100}$

$\frac{2,100}{N} = \frac{4}{5}$

$\frac{N}{2,100} = \frac{4}{5}$

Correct answer:

$\frac{N}{2,100} = \frac{4}{5}$

Explanation:

The ratios that are set equal to each other in a proportion statement must compare the same quantities in the same order.

In each ratio, we can put number of dentists who recommended Triton in the numerator, and number of dentists who were surveyed in the denominator.

One ratio is 4 dentists recommending Triton to 5 dentists surveyed (the general ratio): this is $\frac{4}{5}$ .

The other ratio is dentists recommending Triton to 2,100 dentists surveyed (the actual number); this is $\frac{N}{2,100}$ .

The proportion statement sets these equal:

$\frac{N}{2,100} = \frac{4}{5}$

which is the correct choice.

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Example Question #5 : How To Find A Proportion

If Jason eats one-third of half a dozen donuts, how many donuts has he eaten?

Possible Answers:

donuts

Correct answer:

donuts

Explanation:

Half a dozen donuts is equal to 6 donuts, given that there are 12 items per dozen.

One-third of 6 is 2. Therefore, 2 donuts is the correct answer.

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Example Question #6 : How To Find A Proportion

Kenny is having a party, and he is experimenting with different mixtures of soda to come up with something original. He particularly likes a mixture of four ounces of lemon lime soda and three ounces of cream soda. He has two and a half liters of lemon lime soda and wants to use it all; how much cream soda does he need?

Possible Answers:

$2 \frac{3}{8} \textrm{ L}$

None of the other responses gives the correct answer.

$4 \frac{4}{5} \textrm{ L}$

$1 \frac{7}{8} \textrm{ L}$

$3 \frac{1}{3} \textrm{ L}$

Correct answer:

$1 \frac{7}{8} \textrm{ L}$

Explanation:

The ratio of ounces of lemon lime soda to ounces of cream soda in the initial mixture can be expressed as $\frac{4}{3}$ . This ratio must remain the same for the mixture Ken will make for the party. Let be the number of liters of cream soda. Then the ratio is $\frac{2\frac{1}{2}}{N}$ . Set the two ratios equal to each other and solve for :

$\frac{2\frac{1}{2}}{N} = \frac{4}{3}$

Set the cross-products equal to each other:

$4 N = 2\frac{1}{2} \cdot 3$

$4 N = 7\frac{1}{2}$

$4 N \div 4= 7\frac{1}{2} \div 4$

$N= 7\frac{1}{2} \div 4 = \frac{15}{2} \times \frac{1}{4} = \frac{15}{8} = 1 \frac{7}{8}$

Ken will use $1 \frac{7}{8}$ liters of cream soda in the final mixture.

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Example Question #1 : How To Find A Proportion

What is the value of in the proportion?

$\frac{24}{64} = \frac{x}{8}$

Possible Answers:

Correct answer:

Explanation:

Simplify $\frac{24}{64}$ by dividing both the numerator and denominator by 8 so that it simplifies to $\frac{3}{8}$ . Now it should be obvious that x=3 in order for both sides of the equation to be equal.

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Example Question #1 : How To Find A Proportion

For every $3 I earn at work, I donate $1 to charity. How much money will I donate if I make $27.00/week.

Possible Answers:

Correct answer:

Explanation:

To find the amount of the donation, divide 27 by 3.

$27\div 3=9$

The answer is 9.

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Example Question #2 : How To Find A Proportion

A Spanish class has $\small 14$ seniors and $\small 13$ juniors. What proportion of the class is juniors?

Possible Answers:

$\frac{13}{27}$

$\frac{13}{14}$

$\frac{14}{13}$

$\frac{14}{27}$

Correct answer:

$\frac{13}{27}$

Explanation:

A proportion is an amount that is part of a whole. There are $\small 27$ students in the class in total. This question asks for the proportion that are juniors. There are $\small 13$ juniors out of $\small 27$ students, therefore the proportion is:

$\frac{13}{27}$

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SSAT Middle Level Math : How to find a proportion

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : How To Find A Proportion

Example Question #2 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

Example Question #4 : How To Find A Proportion

Example Question #5 : How To Find A Proportion

Example Question #5 : How To Find A Proportion

Example Question #6 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #2 : How To Find A Proportion

All SSAT Middle Level Math Resources

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