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SSAT Upper Level Math : Decimals with Fractions

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : How To Find The Fractional Equivalent Of A Decimal

What is 0.125 as a fraction?

Possible Answers:

$\frac{3}{8}$

$\frac{1}{8}$

$\frac{2}{5}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{8}$

Explanation:

Write the decimal divided by .

$0.125=\frac{0.125}{1}$

Multiply the numerator and denominator by 1000 to get rid of the decimal, then simplify.

$\frac{0.125\times1000}{1\times1000}=\frac{125}{1000}=\frac{1}{8}$

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Example Question #266 : Rational Numbers

Convert 0.652 into a fraction.

Possible Answers:

$\frac{81}{125}$

$\frac{163}{250}$

$\frac{7}{25}$

$\frac{13}{100}$

Correct answer:

$\frac{163}{250}$

Explanation:

Write the decimal divided by .

$0.652=\frac{0.652}{1}$

Multiply the numerator and denominator by 1000 to get rid of the decimal, then simplify.

$\frac{0.652\times1000}{1\times1000}=\frac{652}{1000}=\frac{163}{250}$

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Example Question #1 : How To Find Decimal Fractions

Rewrite as a fraction with whole numerator and denominator in lowest terms:

$\frac{3.5}{2.1}$

Possible Answers:

$\frac{10}{7}$

$\frac{5}{3}$

$\frac{9}{5}$

$\frac{11}{6}$

None of the other responses is correct.

Correct answer:

$\frac{5}{3}$

Explanation:

$\frac{3.5}{2.1} = \frac{3.5 \times 10}{2.1 \times 10} = \frac{35}{21} = \frac{35 \div 7}{21\div 7} = \frac{5}{3}$

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Example Question #2 : How To Find Decimal Fractions

Rewrite as a fraction with whole numerator and denominator in lowest terms:

$\frac{1.28}{0.4}$

Possible Answers:

None of the other responses is correct.

$\frac{15}{4}$

$\frac{14}{3}$

$\frac{16}{5}$

$\frac{18}{7}$

Correct answer:

$\frac{16}{5}$

Explanation:

Simplify as follows:

$\frac{1.28}{0.4} = \frac{1.28 \times 100}{0.4 \times 100} = \frac{128}{40} = \frac{128 \div 8}{40 \div 8} = \frac{16}{5}$

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Example Question #261 : Fractions

Simplify:

$0.35+\frac{0.75}{0.2}-0.4*\frac{0.5}{0.1}$

Possible Answers:

$\frac{21}{10}$

$\frac{25}{4}$

$\frac{213}{10}$

$\frac{30}{7}$

Correct answer:

$\frac{21}{10}$

Explanation:

Begin by multiplying all of your decimal fractions by $\frac{100}{100}$ :

$0.35+\frac{0.75}{0.2}*\frac{100}{100}-0.4*\frac{0.5}{0.1}*\frac{100}{100}$

Simplify:

$0.35+\frac{75}{20}-0.4*\frac{50}{10}=0.35+\frac{15}{4}-0.4*5$

Now perform the multiplication:

$0.35+\frac{15}{4}-2$

The easiest thing to do next is to subtract from 0.35 :

$0.35+\frac{15}{4}-2=\frac{15}{4}-1.65$

Next, convert 1.65 into the fraction $\frac{165}{100}$ :

$\frac{15}{4}-\frac{165}{100}$

Now, the common denominator can be 100 :

$\frac{15}{4}*\frac{25}{25}-\frac{165}{100}=\frac{375}{100}-\frac{165}{100}$

Simplify:

$\frac{375}{100}-\frac{165}{100}=\frac{210}{100}=\frac{21}{10}$

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Example Question #1 : How To Find Decimal Fractions

Rewrite the following fraction in simplest form: $\frac{0.42}{0.84}$

Possible Answers:

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to rewrite $\frac{0.42}{0.84}$ in simplest form, multiply by a form of that makes the fraction easier to reduce - in this case , $\frac{100}{100}$ :

$\frac{0.42\times 100}{0.84\times 100}=\frac{42}{84}=\frac{1}{2}$

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Example Question #3 : How To Find Decimal Fractions

What is the decimal fraction of

$\frac{1}{8}$

Possible Answers:

0.333

0.12

0.13

0.125

0.25

Correct answer:

0.125

Explanation:

To find the decimal equivalent of a fraction, we just apply long division. We divide the numerator by the denominator.

1.000

divided by

This results in

0.125

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Example Question #3 : How To Find Decimal Fractions

Convert $\frac{1}{7}$ to a decimal to three decimal places.

Possible Answers:

0.128

14.3

0.123

0.143

0.170

Correct answer:

0.143

Explanation:

To convert any fraction to a decimal, the numerator is in the dividend and the denominator is the divisor. Then divide as you would normally. Just remember that since can't divide into , add a decimal point after the and however many s needed.

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Example Question #6 : How To Find Decimal Fractions

Convert $\frac{35}{40}$ to a decimal. Answer to 3 decimal places.

Possible Answers:

0.875

0.500

0.850

0.900

0.975

Correct answer:

0.875

Explanation:

See if you can reduce the fraction before converting to a decimal. They both are divisible by , so the new fraction becomes $\frac{7}{8}$ . To convert any fraction to a decimal, the numerator is in the dividend and the denominator is the divisor. Then divide as you would normally. Just remember that since can't divide into , add a decimal point after the and however many s needed.

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Example Question #271 : Fractions

Which of the following is the smallest?

I. $\frac{99}{198}$

II. $\frac{101}{201}$

III. $\frac{97}{195}$

IV. 0.49

V. $\frac{100}{190}$

Possible Answers:

IV.

III

Correct answer:

IV.

Explanation:

There is no other way but to analyze each answer choice. We do have a decimal choice so lets compare the decimal to all of the fractions. Choice I. is 0.5 . Even if you don't see that, first divide the numerator and denominator by , then , and you will see that it's 0.5. Choice I is wrong. Choice II is definitely bigger than 0.49 . Reason is because if you look at the numerator, if I double it, that number is 202 . Because this value is bigger than the denominator, this means the overall fraction is bigger than 0.5 Remember, the bigger the denominator, the smaller the fraction. ( $\frac{1}{2}$ is greater than $\frac{1}{3}$ even though is bigger than ) The converse is the same. If apply this reasoning to both Choice III and V, only choice V can be eliminated. Choice III is hard to figure out the exact decimal value but if we didn't have a calculator, we can surely compare their values. Let's force choice IV into a fraction. The only way to compare these fractions easily is by having the same denominator. So, lets multiply 0.49 with 195 which gives us 95.55 . So we are comparing 95.55 with . Since is greater than 95.55 this makes choice III bigger than 0.49 and therefore makes choice IV the smallest value.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Decimals with Fractions

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #12 : How To Find The Fractional Equivalent Of A Decimal

Example Question #266 : Rational Numbers

Example Question #1 : How To Find Decimal Fractions

Example Question #2 : How To Find Decimal Fractions

Example Question #261 : Fractions

Example Question #1 : How To Find Decimal Fractions

Example Question #3 : How To Find Decimal Fractions

Example Question #3 : How To Find Decimal Fractions

Example Question #6 : How To Find Decimal Fractions

Example Question #271 : Fractions

All SSAT Upper Level Math Resources

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