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SSAT Middle Level Math : Fractions

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Example Questions

Example Question #1 : Fractions

$\displaystyle Z$ is larger than 0. Which of the following could be equal to $3 \times Z$ $\displaystyle 3 \times Z$ ?

I. $\displaystyle 6$

II. $2\frac{2}{7}$ $\displaystyle 2\frac{2}{7}$

III. $\displaystyle 8$

Possible Answers:

I, II and III

I and II

II only

III only

I only

Correct answer:

I, II and III

Explanation:

All of the answers can be divided by 3 to yield an answer larger than zero. In fact, any positive number would be a viable answer.

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Example Question #1142 : Ssat Middle Level Quantitative (Math)

Express the quotient as a fraction in lowest terms:

$5 \frac{3}{5} \div 4 \frac{1}{5}$ $\displaystyle 5 \frac{3}{5} \div 4 \frac{1}{5}$

Possible Answers:

$1 \frac{1}{4}$ $\displaystyle 1 \frac{1}{4}$

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$1 \frac{3}{4}$ $\displaystyle 1 \frac{3}{4}$

$1 \frac{1}{3}$ $\displaystyle 1 \frac{1}{3}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Correct answer:

$1 \frac{1}{3}$ $\displaystyle 1 \frac{1}{3}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$5 \frac{3}{5} \div 4 \frac{1}{5} = \frac{28}{5 } \div \frac{21}{5 } = \frac{28}{5 } \cdot \frac{5}{21 }= \frac{4}{1 } \cdot \frac{1}{3 }= \frac{4}{3 }$ $\displaystyle 5 \frac{3}{5} \div 4 \frac{1}{5} = \frac{28}{5 } \div \frac{21}{5 } = \frac{28}{5 } \cdot \frac{5}{21 }= \frac{4}{1 } \cdot \frac{1}{3 }= \frac{4}{3 }$

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Example Question #2 : Fractions

Express the quotient as a fraction in lowest terms:

$4 \frac{1}{5} \div 5 \frac{3}{5}$ $\displaystyle 4 \frac{1}{5} \div 5 \frac{3}{5}$

Possible Answers:

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

$1 \frac{1}{4}$ $\displaystyle 1 \frac{1}{4}$

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

$1 \frac{1}{3}$ $\displaystyle 1 \frac{1}{3}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Correct answer:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$4 \frac{1}{5} \div 5 \frac{3}{5} = \frac{21}{5} \div \frac{28}{5} = \frac{21}{5} \cdot \frac{5}{28} = \frac{3}{1} \cdot \frac{1}{4} = \frac{3}{4}$ $\displaystyle 4 \frac{1}{5} \div 5 \frac{3}{5} = \frac{21}{5} \div \frac{28}{5} = \frac{21}{5} \cdot \frac{5}{28} = \frac{3}{1} \cdot \frac{1}{4} = \frac{3}{4}$

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Example Question #2 : How To Divide Fractions

Evaluate:

$\frac{12}{5} \div \frac{4}{25}$ $\displaystyle \frac{12}{5} \div \frac{4}{25}$

Possible Answers:

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\displaystyle 15$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

$\frac{8}{25}$ $\displaystyle \frac{8}{25}$

Correct answer:

$\displaystyle 15$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{12}{5} \div \frac{4}{25} = \frac{12}{5} \times \frac{25}{4} = \frac{3}{1} \times \frac{5}{1} = \frac{15}{1} = 15$ $\displaystyle \frac{12}{5} \div \frac{4}{25} = \frac{12}{5} \times \frac{25}{4} = \frac{3}{1} \times \frac{5}{1} = \frac{15}{1} = 15$

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Example Question #64 : Fractions

Evaluate:

$\frac{4}{25} \div \frac{12}{5}$ $\displaystyle \frac{4}{25} \div \frac{12}{5}$

Possible Answers:

$\frac{5}{3}$ $\displaystyle \frac{5}{3}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

$\frac{8}{25}$ $\displaystyle \frac{8}{25}$

$\displaystyle 15$

Correct answer:

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{4}{25} \div \frac{12}{5} = \frac{4}{25} \times \frac{5}{12} = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$ $\displaystyle \frac{4}{25} \div \frac{12}{5} = \frac{4}{25} \times \frac{5}{12} = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$

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Example Question #3 : Fractions

Evaluate:

$\frac{5}{8} \div \frac{25}{16}$ $\displaystyle \frac{5}{8} \div \frac{25}{16}$

Possible Answers:

$\frac{4}{5}$ $\displaystyle \frac{4}{5}$

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

$\frac{5}{4}$ $\displaystyle \frac{5}{4}$

$\frac{5}{2}$ $\displaystyle \frac{5}{2}$

$\frac{1}{10}$ $\displaystyle \frac{1}{10}$

Correct answer:

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{5}{8} \div \frac{25}{16} = \frac{5}{8} \times \frac{16}{25} = \frac{1}{1} \times \frac{2}{5} = \frac{2}{5}$ $\displaystyle \frac{5}{8} \div \frac{25}{16} = \frac{5}{8} \times \frac{16}{25} = \frac{1}{1} \times \frac{2}{5} = \frac{2}{5}$

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Example Question #1 : How To Divide Fractions

Evaluate:

$\frac{8}{5} \div \frac{24}{35}$ $\displaystyle \frac{8}{5} \div \frac{24}{35}$

Possible Answers:

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

$\frac{1}{21}$ $\displaystyle \frac{1}{21}$

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

$\frac{8}{3}$ $\displaystyle \frac{8}{3}$

$\frac{7}{3}$ $\displaystyle \frac{7}{3}$

Correct answer:

$\frac{7}{3}$ $\displaystyle \frac{7}{3}$

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{8}{5} \div \frac{24}{35} = \frac{8}{5} \times \frac{35}{24} = \frac{1}{1} \times \frac{7}{3} =\frac{7}{3}$ $\displaystyle \frac{8}{5} \div \frac{24}{35} = \frac{8}{5} \times \frac{35}{24} = \frac{1}{1} \times \frac{7}{3} =\frac{7}{3}$

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Example Question #951 : Hspt Mathematics

Evaluate:

$3 \div \frac{1}{12}$ $\displaystyle 3 \div \frac{1}{12}$

Possible Answers:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\displaystyle 36$

$\displaystyle 48$

$\frac{1}{36}$ $\displaystyle \frac{1}{36}$

$\displaystyle 4$

Correct answer:

$\displaystyle 36$

Explanation:

$3 \div \frac{1}{12} = \frac{3}{1} \div \frac{1}{12} = \frac{3}{1}\times \frac{12}{1} = 3 \times 12 = 36$ $\displaystyle 3 \div \frac{1}{12} = \frac{3}{1} \div \frac{1}{12} = \frac{3}{1}\times \frac{12}{1} = 3 \times 12 = 36$

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Example Question #2 : Fractions

Evaluate:

$18 \div \frac{1}{6}$ $\displaystyle 18 \div \frac{1}{6}$

Possible Answers:

$\displaystyle 9$

108 $\displaystyle 108$

$\displaystyle 3$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{1}{108}$ $\displaystyle \frac{1}{108}$

Correct answer:

108 $\displaystyle 108$

Explanation:

$18 \div \frac{1}{6} = \frac{18}{1} \div \frac{1}{6} = \frac{18}{1} \times \frac{6}{1} = 18 \times 6 = 108$ $\displaystyle 18 \div \frac{1}{6} = \frac{18}{1} \div \frac{1}{6} = \frac{18}{1} \times \frac{6}{1} = 18 \times 6 = 108$

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Example Question #491 : Numbers And Operations

Evaluate:

$6.51 + 4.2 \div 14$ $\displaystyle 6.51 + 4.2 \div 14$

Possible Answers:

0.765 $\displaystyle 0.765$

6.54 $\displaystyle 6.54$

7.65 $\displaystyle 7.65$

6.81 $\displaystyle 6.81$

9.51 $\displaystyle 9.51$

Correct answer:

6.81 $\displaystyle 6.81$

Explanation:

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

$4.2 \div 14 = 0.3$ $\displaystyle 4.2 \div 14 = 0.3$

Add this quotient to 6.51.

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

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

6.51 $\displaystyle 6.51$

$\underline{0.30}$ $\displaystyle \underline{0.30}$

6.81 $\displaystyle 6.81$

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SSAT Middle Level Math : Fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Fractions

Example Question #1142 : Ssat Middle Level Quantitative (Math)

Example Question #2 : Fractions

Example Question #2 : How To Divide Fractions

Example Question #64 : Fractions

Example Question #3 : Fractions

Example Question #1 : How To Divide Fractions

Example Question #951 : Hspt Mathematics

Example Question #2 : Fractions

Example Question #491 : Numbers And Operations

All SSAT Middle Level Math Resources

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