Basic Math Examples

6 \frac{21}{24} - 7 \frac{8}{24}

$6 \frac{21}{24} - 7 \frac{8}{24}$

Step 1

Convert

6 \frac{21}{24}

$6 \frac{21}{24}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

6 + \frac{21}{24} - 7 \frac{8}{24}

$6 + \frac{21}{24} - 7 \frac{8}{24}$

Step 1.2

Add

6

$6$ and

\frac{21}{24}

$\frac{21}{24}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{24}{24}

$\frac{24}{24}$ .

6 \cdot \frac{24}{24} + \frac{21}{24} - 7 \frac{8}{24}

$6 \cdot \frac{24}{24} + \frac{21}{24} - 7 \frac{8}{24}$

Step 1.2.2

Combine

6

$6$ and

\frac{24}{24}

$\frac{24}{24}$ .

\frac{6 \cdot 24}{24} + \frac{21}{24} - 7 \frac{8}{24}

$\frac{6 \cdot 24}{24} + \frac{21}{24} - 7 \frac{8}{24}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 24 + 21}{24} - 7 \frac{8}{24}

$\frac{6 \cdot 24 + 21}{24} - 7 \frac{8}{24}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

24

$24$ .

\frac{144 + 21}{24} - 7 \frac{8}{24}

$\frac{144 + 21}{24} - 7 \frac{8}{24}$

Step 1.2.4.2

Add

144

$144$ and

21

$21$ .

\frac{165}{24} - 7 \frac{8}{24}

$\frac{165}{24} - 7 \frac{8}{24}$

\frac{165}{24} - 7 \frac{8}{24}

$\frac{165}{24} - 7 \frac{8}{24}$

\frac{165}{24} - 7 \frac{8}{24}

$\frac{165}{24} - 7 \frac{8}{24}$

\frac{165}{24} - 7 \frac{8}{24}

$\frac{165}{24} - 7 \frac{8}{24}$

Step 2

Convert

7 \frac{8}{24}

$7 \frac{8}{24}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

\frac{165}{24} - (7 + \frac{8}{24})

$\frac{165}{24} - (7 + \frac{8}{24})$

Step 2.2

Add

7

$7$ and

\frac{8}{24}

$\frac{8}{24}$ .

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Step 2.2.1

To write

7

$7$ as a fraction with a common denominator, multiply by

\frac{24}{24}

$\frac{24}{24}$ .

\frac{165}{24} - (7 \cdot \frac{24}{24} + \frac{8}{24})

$\frac{165}{24} - (7 \cdot \frac{24}{24} + \frac{8}{24})$

Step 2.2.2

Combine

7

$7$ and

\frac{24}{24}

$\frac{24}{24}$ .

\frac{165}{24} - (\frac{7 \cdot 24}{24} + \frac{8}{24})

$\frac{165}{24} - (\frac{7 \cdot 24}{24} + \frac{8}{24})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{165}{24} - \frac{7 \cdot 24 + 8}{24}

$\frac{165}{24} - \frac{7 \cdot 24 + 8}{24}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

7

$7$ by

24

$24$ .

\frac{165}{24} - \frac{168 + 8}{24}

$\frac{165}{24} - \frac{168 + 8}{24}$

Step 2.2.4.2

Add

168

$168$ and

8

$8$ .

\frac{165}{24} - \frac{176}{24}

$\frac{165}{24} - \frac{176}{24}$

\frac{165}{24} - \frac{176}{24}

$\frac{165}{24} - \frac{176}{24}$

\frac{165}{24} - \frac{176}{24}

$\frac{165}{24} - \frac{176}{24}$

\frac{165}{24} - \frac{176}{24}

$\frac{165}{24} - \frac{176}{24}$

Step 3

Combine the numerators over the common denominator.

\frac{165 - 176}{24}

$\frac{165 - 176}{24}$

Step 4

Simplify the expression.

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Step 4.1

Subtract

176

$176$ from

165

$165$ .

\frac{- 11}{24}

$\frac{- 11}{24}$

Step 4.2

Move the negative in front of the fraction.

- \frac{11}{24}

$- \frac{11}{24}$

- \frac{11}{24}

$- \frac{11}{24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

- \frac{11}{24}

$- \frac{11}{24}$

Decimal Form:

- 0.458 ¯ 3

$- 0.458\overline{3}$