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SSAT Middle Level Math : Numbers and Operations

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

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All SSAT Middle Level Math Resources

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Example Questions

Example Question #491 : Numbers And Operations

Evaluate:

$6.51 + 4.2 \div 14$

Possible Answers:

0.765

6.54

9.51

7.65

6.81

Correct answer:

6.81

Explanation:

By order of operations, divide first. Since the divisor is a whole number, divide as is:

$4.2 \div 14 = 0.3$

Add this quotient to 6.51.

$6.51 + 4.2 \div 14 = 6.51 + 0.3$

Add vertically, aligning the decimal points (appending a zero to 0.3):

6.51

$\underline{0.30}$

6.81

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Example Question #492 : Numbers And Operations

Evaluate:

$80.8 + 6.4 \div 0.16$

Possible Answers:

545

480.8

84.8

54.5

120.8

Correct answer:

120.8

Explanation:

By order of operations, divide first. Move the decimal point right two places in both dividend and divisor to make the divisor a whole number, and divide the resulting whole numbers:

$6.4 \div 0.16 = 640 \div 16 = 40$

Add this quotient to 80.8:

$80.8 + 6.4 \div 0.16 = 80.8 + 40$

Append a decimal point and a zero to 40, align the decimal points, and add:

80. 8

$\underline{40.0}$

120.8

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Example Question #493 : Numbers And Operations

Evaluate:

$\dpi{150} \frac{\frac{3}{5}}{\frac{9}{20}}$

Possible Answers:

$\frac{100}{27}$

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{21}{20}$

$\frac{27}{100}$

Correct answer:

$\frac{4}{3}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\dpi{150} \frac{\frac{3}{5}}{\frac{9}{20}}$ $= \frac{3}{5} \div \frac{9}{20} = \frac{3}{5} \cdot \frac{20}{9} = \frac{1}{1} \cdot \frac{4}{3} = \frac{4}{3}$

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Example Question #494 : Numbers And Operations

Evaluate:

$\frac{7\frac{1}{2}}{5 }$

Possible Answers:

$\frac{2}{3}$

$1 \frac{2}{3}$

$1 \frac{1}{2}$

$1 \frac{1}{3}$

$\frac{3}{4}$

Correct answer:

$1 \frac{1}{2}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\frac{7\frac{1}{2}}{5 } = 7\frac{1}{2} \div 5 = \frac{15} {2} \div \frac{5}{1} = \frac{15} {2} \cdot \frac{1} {5}=\frac{3} {2} \cdot \frac{1} {1} =\frac{3} {2}$

Since $3 \div 2 = 1 \textrm{ R }1$ ,

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

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Example Question #495 : Numbers And Operations

Evaluate:

$\frac{6}{4 \frac{1}{2}}$

Possible Answers:

$1 \frac{2}{3}$

$1 \frac{1}{3}$

$\frac{3}{4}$

$1 \frac{1}{2}$

$\frac{2}{3}$

Correct answer:

$1 \frac{1}{3}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and finally multiply across:

$\frac{6}{4 \frac{1}{2}} = 6 \div 4 \frac{1}{2} = \frac{6}{1}\div \frac{9}{2}= \frac{6}{1}\cdot \frac{2}{9} = \frac{2}{1}\cdot \frac{2}{3} = \frac{2\cdot 2}{1\cdot 3} = \frac{4}{3}$

Since $4 \div 3 = 1 \textrm{ R }3$ ,

$\frac{4}{3} = 1 \frac{1}{3}$ ,

which is the correct answer.

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Example Question #496 : Numbers And Operations

Which of the following yields the largest number?

Possible Answers:

$\frac{1}{3}+\frac{1}{6}$

$\frac{1}{3}\times\frac{1}{6}$

$\frac{1}{3}\div\frac{1}{6}$

$\frac{1}{3}-\frac{1}{6}$

Correct answer:

$\frac{1}{3}\div\frac{1}{6}$

Explanation:

When dividing by a fraction between 0 and 1, the answer will always get larger. In this case it is larger than simply adding the two fractions together.

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Example Question #497 : Numbers And Operations

Divide: $1.2 \div 64$

Possible Answers:

0.00768

0.01875

0.0768

0.1875

0.001875

Correct answer:

0.01875

Explanation:

Simply use the long division process. The quotient will be:

$12 \div 64 = 0.01875$

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Example Question #11 : Fractions

Simplify:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

Possible Answers:

$1 \frac {4}{5}$

$\frac {5}{9}$

$\frac {1}{15}$

Correct answer:

Explanation:

Rewrite as a division and evaluate:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

$= 4\frac{1 }{2} \div \frac{3}{10}$

$= \frac{1 + 4 \times 2}{2} \div \frac{3}{10}$

$= \frac{9}{2} \div \frac{3}{10}= \frac{9}{2} \times \frac{10}{3}= \frac{3}{1} \times \frac{5}{1}= \frac{15}{1} = 15$

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Example Question #17 : Fractions

Simplify:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

Possible Answers:

$\frac{6}{49}$

$3 \frac{3}{8}$

$\frac{8}{27}$

$8 \frac{1}{6}$

$5 \frac{9}{20}$

Correct answer:

$3 \frac{3}{8}$

Explanation:

Rewrite as a division, then solve:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

$= 5 \frac{1}{4} \div 1 \frac{5}{9}$

$= \frac{1 + 5 \times 4}{4} \div \frac{5 + 1 \times 9}{9}$

$= \frac{21}{4} \div \frac{14}{9}$

$= \frac{21}{4} \times \frac{9}{14}$

$= \frac{3}{4} \times \frac{9}{2}$

$= \frac{3 \times 9}{4 \times 2} = \frac{27}{8} = 3 \frac{3}{8}$

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Example Question #371 : Arithmetic

$\frac{1}{2}\div\frac{3}{8}=$

Possible Answers:

$\frac{3}{4}$

$\frac{3}{16}$

$5\tfrac{1}{3}$

$\frac{1}{2}$

$1\tfrac{1}{3}$

Correct answer:

$1\tfrac{1}{3}$

Explanation:

When dividing fractions, first find the reciprocal of the second fraction and change the problem to multiplication:

$\frac{1}{2}\div\frac{3}{8}\rightarrow\frac{1}{2}\times\frac{8}{3}$

You then treat the problem like any other multiplication problem and multiply straight across.

$\frac{1}{2}\times\frac{8}{3}=\frac{8}{6}$

Since the numerator is larger than the denominator, we know our answer will be greater than 1.

$\frac{8}{6} \rightarrow 1\tfrac{2}{6}$

6 divides into 8 one time, with 2 remaining. The 2 remains on top of the 6 as the numerator. This answer can still be reduced; however, as 2 and 6 are both evenly divisible by 2.

$1\tfrac{2}{6}\rightarrow1\tfrac{1}{3}$

Your final answer is $1\tfrac{1}{3}$

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #491 : Numbers And Operations

Example Question #492 : Numbers And Operations

Example Question #493 : Numbers And Operations

Example Question #494 : Numbers And Operations

Example Question #495 : Numbers And Operations

Example Question #496 : Numbers And Operations

Example Question #497 : Numbers And Operations

Example Question #11 : Fractions

Example Question #17 : Fractions

Example Question #371 : Arithmetic

All SSAT Middle Level Math Resources

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