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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 #242 : Rational Numbers

Define an operation $\blacklozenge$ as follows:

For all real numbers a,b :

$a\blacklozenge b = \frac{ab}{a+b}$

Which of the following is equal to $\frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Possible Answers:

0.25

The correct answer is not among the other choices.

$0.1\overline{6}$

0.2

$0.\overline{2}$

Correct answer:

0.2

Explanation:

$a\blacklozenge b = \frac{ab}{a+b}$

$\frac{1}{2} \blacklozenge \frac{1}{3}=\frac{\frac{1}{2} \times \frac{1}{3}}{\frac{1}{2} +\frac{1}{3}}=\frac{\frac{1}{6} }{\frac{5}{6} } = \frac{1}{6} \div \frac{5}{6} = \frac{1}{6} \times \frac{6} {5} = \frac{1}{1} \times \frac{1} {5} = \frac{1}{5}$

$\frac{1}{5} = 1 \div 5 = 0.2$ ,

is the correct response.

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Example Question #11 : Decimals With Fractions

Which of the following is a true statement?

Possible Answers:

$0.56 < \frac{7}{13} < 0.57$

$0.54 < \frac{7}{13} < 0.55$

$0.55 < \frac{7}{13} < 0.56$

$0.53 < \frac{7}{13} < 0.54$

$0.52 < \frac{7}{13} < 0.53$

Correct answer:

$0.53 < \frac{7}{13} < 0.54$

Explanation:

Divide 7 by 13. The result is as follows:

Division

The correct choice is that $0.53 < \frac{7}{13} < 0.54$ .

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Example Question #243 : Fractions

Which of the following is closest to the sum of two thirds and four fifths?

Possible Answers:

1.5

1.55

1.6

1.45

1.4

Correct answer:

1.45

Explanation:

$\frac{2}{3} + \frac{4}{5} = \frac{2 \cdot 5}{3\cdot 5} + \frac{3\cdot 4}{3\cdot 5} = \frac{10}{15} + \frac{12}{15} =\frac{22}{15}$

Divide 22 by 15:

Division

Of the five choices, the closest is 1.45.

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Example Question #14 : How To Find The Decimal Equivalent Of A Fraction

Which of the following is a true statement?

Possible Answers:

$-0.73< -\frac{19}{27}< -0.72$

$-0.72< -\frac{19}{27}< -0.71$

$-0.75< -\frac{19}{27}< -0.74$

$-0.74< -\frac{19}{27}< -0.73$

$-0.71< -\frac{19}{27}< -0.70$

Correct answer:

$-0.71< -\frac{19}{27}< -0.70$

Explanation:

Divide 19 by 27:

Division

$0.70 < \frac{19}{27}< 0.71$ ,

$-0.71< -\frac{19}{27}< -0.70$ .

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Example Question #13 : Decimals With Fractions

Which of the following falls between 0.32 and 0.33?

Possible Answers:

$\frac{25}{77}$

$\frac{23}{77}$

$\frac{26}{77}$

$\frac{27}{77}$

$\frac{24}{77}$

Correct answer:

$\frac{25}{77}$

Explanation:

Since all of the fractions have 77 as a denominator, one way to solve this problem is to let be the numerator of the correct fraction. Therefore, the equivalent problem is to find integer such that

$0.32 < \frac{N}{77} < 0.33$

Multiply each expression by :

$0.32 \cdot 77 < \frac{N}{77} \cdot 77 < 0.33 \cdot 77$

24.64 < N < 25.41

Therefore, N = 25 , making $\frac{25}{77}$ the correct choice.

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Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Which of the following fractions is closest to 0.6?

Possible Answers:

$\frac{9}{16}$

$\frac{13}{20}$

$\frac{5}{8}$

$\frac{2}{3}$

$\frac{4}{7}$

Correct answer:

$\frac{5}{8}$

Explanation:

For each fraction, divide each numerator by its denominator to get its decimal representation, then subtract to find its difference from 0.6.

$\frac{4}{7} \approx 0.5714 ; 0.6 - 0.5714 =0.0286$

$\frac{5}{8}=0.625; 0.625-0.6 = 0.025$

$\frac{9}{16} = 0.5625; 0.6-0.5625=0.0375$

$\frac{2}{3}\approx 0.6667; 0.6667-0.6=0.0667$

$\frac{13}{20} = 0.65; 0.65-0.6=0.05$

$\frac{5}{8}$ is the closest to 0.6 of the five.

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Example Question #11 : Decimals With Fractions

Give the decimal equivalent of $\frac{1}{6}$ .

Possible Answers:

$0.1\overline{6}$

0.16

0.166

$0.\overline{16}$

0.167

Correct answer:

$0.1\overline{6}$

Explanation:

Divide 1 by 6; the result is

$\frac{1}{6}= 1 \div 6 = 0.166666...$ .

That is, the 6 is repeated infinitely. This is equal to $0.1\overline{6}$ .

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Example Question #16 : Decimals With Fractions

Convert 0.38 into a fraction in simplest form.

Possible Answers:

$\frac{19}{25}$

$\frac{38}{50}$

$\frac{19}{50}$

$\frac{5}{19}$

Correct answer:

$\frac{19}{50}$

Explanation:

Think of the decimal as the fraction $\frac{0.38}{1}$ .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by 100 .

$\frac{0.38}{1}\times 100=\frac{38}{100}$

Now, simplify this fraction.

$\frac{38}{100}=\frac{19}{50}$

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Example Question #252 : Rational Numbers

What is the fractional equivalent of

0.25

Possible Answers:

$\frac{25}{101}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{5}$

Correct answer:

$\frac{1}{4}$

Explanation:

To find the fractional equivalent, we convert the number given into a whole number and divide by the corresponding tenth power needed to move the decimal into a whole number.

So for

0.25

we need to multiply by 100 to turn the decimal into the whole number

We divide by 100 to get our fraction

$\frac{25}{100}$

this can be reduced to

$\frac{1}{4}$

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of

0.125

Possible Answers:

$\frac{1}{9}$

$\frac{1}{8}$

$\frac{1}{7}$

$\frac{1}{6}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{8}$

Explanation:

To find the fractional equivalent, we first convert the decimal into a whole number.

So to convert 0.125 into a fraction we need to multiply by 1000 to change the decimal into the whole number 125 .

We can now put 125 over the number we used to convert the decimal into a whole number.

$\frac{125}{1000}$

This can be reduced to

$\frac{1}{8}$

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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 #242 : Rational Numbers

Example Question #11 : Decimals With Fractions

Example Question #243 : Fractions

Example Question #14 : How To Find The Decimal Equivalent Of A Fraction

Example Question #13 : Decimals With Fractions

Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Example Question #11 : Decimals With Fractions

Example Question #16 : Decimals With Fractions

Example Question #252 : Rational Numbers

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

All SSAT Upper Level Math Resources

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