Basic Math Examples

5 \frac{4}{7} - 4 \frac{5}{8}

$5 \frac{4}{7} - 4 \frac{5}{8}$

Step 1

Convert

5 \frac{4}{7}

$5 \frac{4}{7}$ to an improper fraction.

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Step 1.1

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

5 + \frac{4}{7} - 4 \frac{5}{8}

$5 + \frac{4}{7} - 4 \frac{5}{8}$

Step 1.2

Add

5

$5$ and

\frac{4}{7}

$\frac{4}{7}$ .

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Step 1.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

5 \cdot \frac{7}{7} + \frac{4}{7} - 4 \frac{5}{8}

$5 \cdot \frac{7}{7} + \frac{4}{7} - 4 \frac{5}{8}$

Step 1.2.2

Combine

5

$5$ and

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5 \cdot 7}{7} + \frac{4}{7} - 4 \frac{5}{8}

$\frac{5 \cdot 7}{7} + \frac{4}{7} - 4 \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{5 \cdot 7 + 4}{7} - 4 \frac{5}{8}

$\frac{5 \cdot 7 + 4}{7} - 4 \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

5

$5$ by

7

$7$ .

\frac{35 + 4}{7} - 4 \frac{5}{8}

$\frac{35 + 4}{7} - 4 \frac{5}{8}$

Step 1.2.4.2

Add

35

$35$ and

4

$4$ .

\frac{39}{7} - 4 \frac{5}{8}

$\frac{39}{7} - 4 \frac{5}{8}$

\frac{39}{7} - 4 \frac{5}{8}

$\frac{39}{7} - 4 \frac{5}{8}$

\frac{39}{7} - 4 \frac{5}{8}

$\frac{39}{7} - 4 \frac{5}{8}$

\frac{39}{7} - 4 \frac{5}{8}

$\frac{39}{7} - 4 \frac{5}{8}$

Step 2

Convert

4 \frac{5}{8}

$4 \frac{5}{8}$ to an improper fraction.

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Step 2.1

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

\frac{39}{7} - (4 + \frac{5}{8})

$\frac{39}{7} - (4 + \frac{5}{8})$

Step 2.2

Add

4

$4$ and

\frac{5}{8}

$\frac{5}{8}$ .

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Step 2.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{39}{7} - (4 \cdot \frac{8}{8} + \frac{5}{8})$

Step 2.2.2

Combine

$4$ and

$\frac{8}{8}$ .

$\frac{39}{7} - (\frac{4 \cdot 8}{8} + \frac{5}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{39}{7} - \frac{4 \cdot 8 + 5}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$4$ by

$8$ .

$\frac{39}{7} - \frac{32 + 5}{8}$

Step 2.2.4.2

Add

$32$ and

$5$ .

$\frac{39}{7} - \frac{37}{8}$

Step 3

To write

$\frac{39}{7}$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{39}{7} \cdot \frac{8}{8} - \frac{37}{8}$

Step 4

To write

$- \frac{37}{8}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{39}{7} \cdot \frac{8}{8} - \frac{37}{8} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of

$56$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{39}{7}$ by

$\frac{8}{8}$ .

$\frac{39 \cdot 8}{7 \cdot 8} - \frac{37}{8} \cdot \frac{7}{7}$

Step 5.2

Multiply

$7$ by

$8$ .

$\frac{39 \cdot 8}{56} - \frac{37}{8} \cdot \frac{7}{7}$

Step 5.3

Multiply

$\frac{37}{8}$ by

$\frac{7}{7}$ .

$\frac{39 \cdot 8}{56} - \frac{37 \cdot 7}{8 \cdot 7}$

Step 5.4

Multiply

$8$ by

$7$ .

$\frac{39 \cdot 8}{56} - \frac{37 \cdot 7}{56}$

Step 6

Combine the numerators over the common denominator.

$\frac{39 \cdot 8 - 37 \cdot 7}{56}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$39$ by

$8$ .

$\frac{312 - 37 \cdot 7}{56}$

Step 7.2

Multiply

$- 37$ by

$7$ .

$\frac{312 - 259}{56}$

Step 7.3

Subtract

$259$ from

$312$ .

$\frac{53}{56}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{53}{56}$

Decimal Form:

$0.94642857 \dots$