How to divide fractions - ISEE Middle Level Math

Card 0 of 20

Question

$\dpi{100} 9\div \frac{1}{7}=$

Answer

We never actually divide fractions. When given a division problem, you multiply by the reciprocal of the 2nd fraction.

So, $\dpi{100} 9\div \frac{1}{7}$ becomes $\dpi{100} 9\times \frac{7}{1}$ .

This is the same as $\dpi{100} 9\times7=63$

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Question

$\frac{4^{^{2}}+\left ( 12-4 \right )}{2}$

Answer

In order to solve:

First, solve the exponent equation within the numerator portion of the fraction:

$\small \small \frac{4^{2} + \left ( 12-4 \right )}{2}=$

Then, solve the equation within the parentheses:

$\small \small \frac{16+8}{2}=$

Then, solve the entire equation in the numerator portion and divide the numerator by the denominator.

$\small \small \frac{24}{2}=12$

Answer: 12

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Question

$\small 2 \frac{1}{5} \div 1 \frac{2}{4}=$

Answer

To solve:

First, turn the mixed fractions into improper fractions.

$\small \small \small \frac{11}{5}\div \frac{6}{4}=$

Then, change the operation to multiplication and flip the second fraction. Solve accordingly and simplify the answer if possible.

$\small \small \frac{11}{5}\cdot \frac{4}{6}=$

The answer is $\small 1\frac{7}{15}$ .

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Question

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

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

What is $\frac{3}{5}$ divided by $\frac{3}{25}$ ?

Answer

$\frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$

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Question

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

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

$\frac{2}{5}\div 2\frac{3}{5}=$

Answer

First, convert each fraction into an improper fraction

$\frac{2}{5}\div 2\frac{3}{5}=\frac{2}{5}\div \frac{13}{5}=$

Then, change the operation to mulitplication and flip the second fraction:

$\frac{2}{5}*\frac{5}{13}=$

Reduce and solve accordingly:

Answer: $\frac{2}{13}$

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Question

Evaluate:

$\frac{\frac{2}{7}}{\frac{9}{14}}$

Answer

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

$\frac{\frac{2}{7}}{\frac{9}{14}}$ $= \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \cdot \frac{14}{9} = \frac{2}{1} \cdot \frac{2}{9} = \frac{2\cdot 2}{1\cdot 9} =\frac{4}{9}$

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Question

Divide: $0.17 \div 32$

Answer

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

$0.17 \div 32 = 0.0053125$

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Question

Solve:

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

Answer

$\frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\times\frac{3}{1}=\frac{9}{4}$

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Question

Simplify: $\frac{\frac{2}{7}}{\frac{9}{14}}$

Answer

Rewrite this as a division, dividing the numerator by the denominator:

$\frac{\frac{2}{7}}{\frac{9}{14}} = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \times \frac{14}{9}= \frac{2}{1} \times \frac{2}{9}=\frac{2 \times 2}{1 \times 9}= \frac{4}{9}$

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Question

Simplify:

$\frac{\frac{2}{5}}{\frac{7}{10}}$

Answer

Rewrite as a division, then solve:

$\frac{\frac{2}{5}}{\frac{7}{10}} = \frac{2}{5} \div \frac{7}{10} = \frac{2}{5} \times \frac{10}{7} = \frac{2}{1} \times \frac{2}{7} = \frac{4}{7}$

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Question

Simplify:

$\frac{ 2 \frac{1}{5}}{7 \frac{1}{3}}$

Answer

Rewrite as a division, then solve:

$\frac{ 2 \frac{1}{5}}{7 \frac{1}{3}}$

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

$= \frac{1+ 2 \times 5}{5} \div \frac{1+ 7 \times 3}{3}$

$= \frac{11}{5} \div \frac{22}{3}$

$= \frac{11}{5} \times \frac{3}{22}$

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

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Question

Simplify:

$\frac{\frac{4}{x}}{(\frac{1}{x}-4x)}$

Answer

We can first find a common denominator for the expression in the numerator, which is . This gives us:

$\frac{\frac{4}{x}}{\left(\frac{1}{x}-\frac{4x^2}{x}\right)}=\frac{\frac{4}{x}}{\left(\frac{1-4x^2}{x}\right)}$

$=\frac{4}{x}\times \left(\frac{x}{1-4x^2}\right)$

$=\frac{4}{(1-4x^2)}$

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Question

Evaluate:

$\sqrt{3}\div \frac{3}{4}$

Answer

To divide any number by a fraction, we can multiply that number by the reciprocal of the fraction. That means:

$\frac{a}{b}\div \frac{c}{d} = \frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$

So we have:

$\sqrt{3}\div \frac{3}{4}= \frac{\sqrt{3}}{1}\times \frac{4}{3}$

$=\frac{4\sqrt{3}}{3}$

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Question

Simplify:

$\frac{2+\frac{5}{6}}{2-\frac{5}{6}}$

Answer

Multiply each term by 6:

$\frac{2+\frac{5}{6}}{2-\frac{5}{6}} = \frac{12+5}{12-5}$

$=\frac{17}{7}$

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Question

Evaluate:

$8\frac{1}{3}\div \frac{1}{6}$

Answer

A mixed number represents the sum of an integer and a fraction. In order to evaluate this problem first we need to change the mixed number ( $8\frac{1}{3}$ ) to an improper fraction. Improper fractions are fractions whose numerator is greater than the denominator. So we can write:

$8\frac{1}{3}=\frac{8\times 3+1}{3}=\frac{25}{3}$

Now we should evaluate $\frac{25}{3}\div \frac{1}{6}$ and we have:

$\frac{25}{3}\div \frac{1}{6}=\frac{25}{3}\times \frac{6}{1}=50$

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Question

Which of the following is the reciprocal of 2.8?

Answer

First, rewrite this as an improper fraction:

$2.8 = \frac{28}{10} = \frac{28\div 2}{10\div 2} = \frac{14}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, so the reciprocal is $\frac{5}{14}$ .

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Question

Which of the following is the reciprocal of $-1 \frac {4}{5}$ ?

Answer

First, rewrite this as an improper fraction:

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

The reciprocal of an improper fraction can be found by switching its numerator and denominator, retaining the negative sign, so the reciprocal is $-\frac {5}{9}$ .

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Question

Solve:

$\frac{3}{7}\div \frac{1}{5}$

Answer

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

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