Complex Fractions

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SAT Math › Complex Fractions

Questions 1 - 8

Add: $\frac{1}{\frac{3}{2}}+ \frac{\frac{4}{1}}{\frac{1}{5}}$

$20\frac{2}{3}$

$1\frac{11}{12}$

$\frac{43}{60}$

$\frac{31}{20}$

$2\frac{3}{10}$

Explanation

The terms shown are complex fractions. We first need to simplify each and find the least common denominator before solving.

Rewrite the complex fraction using a division sign.

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

Change the division sign to a multiplication sign, and take the reciprocal of the second term.

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

Repeat this step for the second term.

$\frac{\frac{4}{1}}{\frac{1}{5}} = \frac{4}{1} \div \frac{1}{5} = \frac{4}{1} \times \frac{5}{1}=20$

Add the two terms together.

The answer is: $20\frac{2}{3}$

Add: $\frac{1}{\frac{3}{2}}+ \frac{\frac{4}{1}}{\frac{1}{5}}$

$20\frac{2}{3}$

$1\frac{11}{12}$

$\frac{43}{60}$

$\frac{31}{20}$

$2\frac{3}{10}$

Explanation

The terms shown are complex fractions. We first need to simplify each and find the least common denominator before solving.

Rewrite the complex fraction using a division sign.

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

Change the division sign to a multiplication sign, and take the reciprocal of the second term.

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

Repeat this step for the second term.

$\frac{\frac{4}{1}}{\frac{1}{5}} = \frac{4}{1} \div \frac{1}{5} = \frac{4}{1} \times \frac{5}{1}=20$

Add the two terms together.

The answer is: $20\frac{2}{3}$

Simplify: $\frac{\frac{1}{2}}{\frac{3}{4}}$

$\frac{2}{3}$

$\frac{1}{5}$

$\frac{1}{24}$

$\frac{3}{2}$

Explanation

Rewrite this complex fraction using a division sign.

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

Take the reciprocal of the second term and change the division of the division sign. Simplify.

$\frac{1}{2}\times\frac{4}{3}=\frac{2}{3}$

Simplify: $\frac{\frac{1}{2}}{\frac{3}{4}}$

$\frac{2}{3}$

$\frac{1}{5}$

$\frac{1}{24}$

$\frac{3}{2}$

Explanation

Rewrite this complex fraction using a division sign.

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

Take the reciprocal of the second term and change the division of the division sign. Simplify.

$\frac{1}{2}\times\frac{4}{3}=\frac{2}{3}$

Solve:

$76-\frac{75}{6}=$

$\frac{1}{6}$

$\frac{7}{6}$

$\frac{127}{2}$

Explanation

First reduce the fraction. We can divide both the numerator and the denominator by 3.

$\frac{75\div 3}{6\div 3}=\frac{25}{2}$

Now our expression looks like this:

$76-\frac{25}{2}$

When you add or subtract fractions, you need to have the same denominator. The lowest common deonminator here is 2. So we need to multiply and solve:

$\left ( \frac{2}{2}\right)\cdot76-\frac{25}{2}=\frac{152}{2}-\frac{25}{2}=\frac{127}{2}$

Solve:

$76-\frac{75}{6}=$

$\frac{1}{6}$

$\frac{7}{6}$

$\frac{127}{2}$

Explanation

First reduce the fraction. We can divide both the numerator and the denominator by 3.

$\frac{75\div 3}{6\div 3}=\frac{25}{2}$

Now our expression looks like this:

$76-\frac{25}{2}$

When you add or subtract fractions, you need to have the same denominator. The lowest common deonminator here is 2. So we need to multiply and solve:

$\left ( \frac{2}{2}\right)\cdot76-\frac{25}{2}=\frac{152}{2}-\frac{25}{2}=\frac{127}{2}$

Add: $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$

$49\frac{9}{56}$

$\frac{71}{8}$

$\frac{79}{7}$

$56\frac{7}{8}$

$\frac{65}{56}$

Explanation

To add $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$ , first simply each term by rewriting the terms using a division sign.

$\frac{9}{8}\div7 + 7 \div \frac{1}{7}$

Take the reciprocal of the terms after the division sign, and change the division sign to a multiplication sign. Simplify.

$\frac{9}{8}\times \frac{1}{7}+ 7 \times 7 = \frac{9}{56} + 49= 49\frac{9}{56}$

Add: $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$

$49\frac{9}{56}$

$\frac{71}{8}$

$\frac{79}{7}$

$56\frac{7}{8}$

$\frac{65}{56}$

Explanation

To add $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$ , first simply each term by rewriting the terms using a division sign.

$\frac{9}{8}\div7 + 7 \div \frac{1}{7}$

Take the reciprocal of the terms after the division sign, and change the division sign to a multiplication sign. Simplify.

$\frac{9}{8}\times \frac{1}{7}+ 7 \times 7 = \frac{9}{56} + 49= 49\frac{9}{56}$

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