SSAT Middle Level Math : Fractions

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

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Example Questions

Example Question #61 : Fractions

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

 

I.  \(\displaystyle 6\)

II. \(\displaystyle 2\frac{2}{7}\)

 

III. \(\displaystyle 8\)

Possible Answers:

I, II and III

III only

II only

I only

I and II

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.

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

Express the quotient as a fraction in lowest terms: 

\(\displaystyle 5 \frac{3}{5} \div 4 \frac{1}{5}\)

Possible Answers:

\(\displaystyle 1 \frac{1}{4}\)

\(\displaystyle \frac{4}{5}\)

\(\displaystyle 1 \frac{3}{4}\)

\(\displaystyle 1 \frac{1}{3}\)

\(\displaystyle \frac{3}{4}\)

Correct answer:

\(\displaystyle 1 \frac{1}{3}\)

Explanation:

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

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

Example Question #1 : How To Divide Fractions

Express the quotient as a fraction in lowest terms: 

\(\displaystyle 4 \frac{1}{5} \div 5 \frac{3}{5}\)

Possible Answers:

\(\displaystyle \frac{6}{7}\)

\(\displaystyle \frac{5}{7}\)

\(\displaystyle 1 \frac{1}{4}\)

\(\displaystyle 1 \frac{1}{3}\)

\(\displaystyle \frac{3}{4}\)

Correct answer:

\(\displaystyle \frac{3}{4}\)

Explanation:

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

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

Example Question #63 : Fractions

Evaluate:

\(\displaystyle \frac{12}{5} \div \frac{4}{25}\)

Possible Answers:

\(\displaystyle \frac{1}{15}\)

\(\displaystyle \frac{8}{25}\)

\(\displaystyle \frac{3}{5}\)

\(\displaystyle 15\)

\(\displaystyle \frac{5}{3}\)

Correct answer:

\(\displaystyle 15\)

Explanation:

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

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

Example Question #64 : Fractions

Evaluate:

\(\displaystyle \frac{4}{25} \div \frac{12}{5}\)

Possible Answers:

\(\displaystyle \frac{5}{3}\)

\(\displaystyle \frac{3}{5}\)

\(\displaystyle \frac{1}{15}\)

\(\displaystyle \frac{8}{25}\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle \frac{1}{15}\)

Explanation:

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

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

Example Question #951 : Hspt Mathematics

Evaluate:

\(\displaystyle \frac{5}{8} \div \frac{25}{16}\)

Possible Answers:

\(\displaystyle \frac{5}{2}\)

\(\displaystyle \frac{4}{5}\)

\(\displaystyle \frac{1}{10}\)

\(\displaystyle \frac{2}{5}\)

\(\displaystyle \frac{5}{4}\)

Correct answer:

\(\displaystyle \frac{2}{5}\)

Explanation:

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

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

Example Question #66 : Fractions

Evaluate:

\(\displaystyle \frac{8}{5} \div \frac{24}{35}\)

Possible Answers:

\(\displaystyle \frac{8}{3}\)

\(\displaystyle \frac{3}{7}\)

\(\displaystyle \frac{1}{21}\)

\(\displaystyle \frac{3}{8}\)

\(\displaystyle \frac{7}{3}\)

Correct answer:

\(\displaystyle \frac{7}{3}\)

Explanation:

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

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

Example Question #351 : Concepts

Evaluate:

\(\displaystyle 3 \div \frac{1}{12}\)

Possible Answers:

\(\displaystyle 36\)

\(\displaystyle \frac{1}{36}\)

\(\displaystyle 4\)

\(\displaystyle 48\)

\(\displaystyle \frac{1}{4}\)

Correct answer:

\(\displaystyle 36\)

Explanation:

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

Example Question #2 : Fractions

Evaluate:

\(\displaystyle 18 \div \frac{1}{6}\)

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 108\)

\(\displaystyle 3\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{1}{108}\)

Correct answer:

\(\displaystyle 108\)

Explanation:

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

Example Question #491 : Numbers And Operations

Evaluate: 

\(\displaystyle 6.51 + 4.2 \div 14\)

Possible Answers:

\(\displaystyle 0.765\)

\(\displaystyle 6.54\)

\(\displaystyle 7.65\)

\(\displaystyle 6.81\)

\(\displaystyle 9.51\)

Correct answer:

\(\displaystyle 6.81\)

Explanation:

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

\(\displaystyle 4.2 \div 14 = 0.3\)

Add this quotient to 6.51.

\(\displaystyle 6.51 + 4.2 \div 14 = 6.51 + 0.3\)

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

\(\displaystyle 6.51\)

\(\displaystyle \underline{0.30}\)

\(\displaystyle 6.81\)

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