Simplify 5 4/7-4 5/8

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

Step 1

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

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

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

Add $5$ and $\frac{4}{7}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Combine $5$ and $\frac{7}{7}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $7$ .

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

Add $35$ and $4$ .

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

Step 2

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

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

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

Add $4$ and $\frac{5}{8}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Combine $4$ and $\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $8$ .

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

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 $1$ .

Multiply $\frac{39}{7}$ by $\frac{8}{8}$ .

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

Multiply $7$ by $8$ .

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

Multiply $\frac{37}{8}$ by $\frac{7}{7}$ .

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

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.

Multiply $39$ by $8$ .

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

Multiply $- 37$ by $7$ .

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

Subtract $259$ from $312$ .

$\frac{53}{56}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{53}{56}$

Decimal Form:

$0.94642857 \dots$

Simplify 5 4/7-4 5/8

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