How to divide fractions - SSAT Middle Level Quantitative

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Question

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

I.

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

III.

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Answer

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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Question

$$\frac{7}{49}$\div $\frac{2}{14}$=$

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Answer

Change division to multiplication by flipping the second fraction. Then, simplify and perform the multiplication.

$$\frac{7}{49}$\div $\frac{2}{14}$=$

$$\frac{7}{49}$\times $\frac{14}{2}$= $\frac{1}{7}$\times $\frac{7}{1}$=\frac{7}{7}$=1$

The answer is 1.

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Question

Express the quotient as a fraction in lowest terms:

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

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Answer

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 }$$

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Question

Express the quotient as a fraction in lowest terms:

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

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Answer

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}$$

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Question

$12 $\frac{4}{6}$ \div 4$\frac{2}{4}$=$

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Answer

First convert each fraction into an improper fraction.

$$\frac{76}{6}$\div $\frac{18}{4}$=$

Then flip the second fraction, reduce and multiply:

$$\frac{76}{6}$\ast $\frac{4}{18}$=$

The answer is $2$\frac{22}{27}$$ .

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Question

Evaluate:

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

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Answer

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}$

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Question

Evaluate:

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

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Answer

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$

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Question

Evaluate:

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

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Answer

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 $\frac{1}{3}$ = $\frac{1}{15}$

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Question

Evaluate:

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

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Answer

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 $\frac{2}{5}$ = $\frac{2}{5}$

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Question

Evaluate:

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

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Answer

$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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Question

Evaluate:

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

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Answer

$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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Question

Evaluate:

$80.8 + 6.4 \div 0.16$

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Answer

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:

$\underline{40.0}$

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Question

Evaluate:

$6.51 + 4.2 \div 14$

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Answer

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):

$\underline{0.30}$

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Question

Which of the following yields the largest number?

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Answer

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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Question

Evaluate:

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

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Answer

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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Question

Evaluate:

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

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Answer

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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Question

Evaluate:

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

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Answer

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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Question

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

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Answer

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\t$\frac{2}{6}$

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.

$1\t$\frac{2}{6}\rightarrow1\t$\frac{1}{3}$$

Your final answer is $1\t$\frac{1}{3}$$

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Question

Divide: $1.2 \div 64$

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Answer

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

$12 \div 64 = 0.01875$

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Question

Simplify:

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

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Answer

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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