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SSAT Upper Level Math : Number Concepts and Operations

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 #3 : Decimals With Fractions

Let $a = \frac{3}{5}$ , $b= \frac{2}{3}$ , $c = \frac{4}{7}$

Which of the following is closest to a + b + c ?

Possible Answers:

1.6

1.9

1.7

1.5

1.8

Correct answer:

1.8

Explanation:

a + b + c

$= \frac{3}{5}+ \frac{2}{3}+ \frac{4}{7}$

$= \frac{3 \times 21}{5 \times 21}+ \frac{2\times 35}{3 \times 35}+ \frac{4\times 15}{7 \times 15}$

$= \frac{63}{105}+ \frac{70}{105}+ \frac{60}{105} = \frac{193}{105}$

$= 193 \div 105 \approx 1.84$

The correct choice is 1.8.

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Example Question #7 : Decimals With Fractions

Let $a =3 \frac{3}{5}$ and $b=1 \frac{5}{6}$

Which of the following is closest to a - b ?

Possible Answers:

1.6

1.4

1.5

1.7

1.8

Correct answer:

1.8

Explanation:

$a - b = 3\frac{3}{5} - 1\frac{5}{6}$

$= \frac{18}{5} - \frac{11}{6}$

$= \frac{18\times 6 }{5 \times 6} - \frac{11\times 5}{6\times 5}$

$= \frac{108}{30} - \frac{55}{30}$

$= \frac{53}{30}$

$= 53 \div 30 \approx 1.77$

The correct choice is 1.8.

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Example Question #241 : Rational Numbers

Define an operation $\blacklozenge$ as follows:

For all real numbers a,b :

$a\blacklozenge b = a^{2} - b^{2}$

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

Possible Answers:

0.3

0.2

0.1

0.15

0.25

Correct answer:

0.15

Explanation:

$a\blacklozenge b = a^{2} - b^{2}$

$\frac{1}{2} \blacklozenge \frac{1}{3} =\left ( \frac{1}{2} \right ) ^{2} - \left ( \frac{1}{3} \right )^{2}= \frac{1}{4} - \frac{1}{9}= \frac{9}{36} - \frac{4}{36}= \frac{5}{36}$

$= 5 \div 36 = 0.13888...$

The correct choice is 0.15.

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Example Question #1371 : Ssat Upper Level Quantitative (Math)

Let $a =1 \frac{4}{9}$ , $b = 1\frac{3}{8}$ , and $c= \frac{1}{2}$ .

Which of the following is closest to a bc ?

Possible Answers:

1.3

1.4

1.2

1.1

Correct answer:

Explanation:

$a bc=1 \frac{4}{9} \times 1\frac{3}{8} \times \frac{1}{2}= \frac{13}{9} \times \frac{11}{8} \times \frac{1}{2}= \frac{143}{144}= 143 \div 144 \approx 0.99$

The correct response is 1.

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Example Question #4 : Decimals With Fractions

Simplify and express as a decimal:

$\frac{4\frac{2}{3}}{5\frac{3}{5}}$

Possible Answers:

0.875

0.9

$0.\overline{8}$

0.8

$0.8\overline{3}$

Correct answer:

$0.8\overline{3}$

Explanation:

$\frac{4\frac{2}{3}}{5\frac{3}{5}} = 4\frac{2}{3} \div 5\frac{3}{5} = \frac{14}{3} \div \frac{28}{5} = \frac{14}{3} \times \frac{5} {28} = \frac{1}{3} \times \frac{5} {2} = \frac{5}{6}$

$\frac{5}{6}= 5 \div 6 = 0.8333...$ ,

so the correct response is $0.8\overline{3}$ .

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Example Question #11 : Decimals With Fractions

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.

$0.\overline{2}$

0.2

$0.1\overline{6}$

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:

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

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

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

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

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

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 #12 : Decimals With Fractions

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

Possible Answers:

1.6

1.45

1.55

1.4

1.5

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

Which of the following is a true statement?

Possible Answers:

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

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

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

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

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

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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : Decimals With Fractions

Example Question #7 : Decimals With Fractions

Example Question #241 : Rational Numbers

Example Question #1371 : Ssat Upper Level Quantitative (Math)

Example Question #4 : Decimals With Fractions

Example Question #11 : Decimals With Fractions

Example Question #11 : Decimals With Fractions

Example Question #12 : Decimals With Fractions

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

Example Question #13 : Decimals With Fractions

All SSAT Upper Level Math Resources

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