How to divide fractions - SSAT Middle Level Quantitative

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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

$\small \frac{8}{9}\div2$

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Answer

$\small \frac{8}{9}\div2$

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

$\small \frac{8}{9}\times\frac{1}{2}=\frac{8}{18}$

$\small \frac{8}{18}$ can be reduced by dividing both sides by $\small 2.$

$\small \frac{8}{18}\div\frac{2}{2}=\frac{4}{9}$

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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:

$80.8 + 6.4 \div 0.16$

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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

$\small 4$ people are sharing a $\small 39$ pound bag of peanuts. How much will each person get? Select the answer with the pair of numbers that the answer will be between.

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Answer

We can think of this problem as an improper fraction and solve for the mixed number.

$\small \frac{39}{4}=9\frac{3}{4}$

$\small 4$ can go into $\small 39$ only $\small 9$ times with $\small \frac{3}{4}$ left over.

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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.

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

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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