Basic Math Examples

$\frac{15}{8} + \frac{2}{5} + \frac{- 7}{8}$

Step 1

To write $\frac{15}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{15}{8} \cdot \frac{5}{5} + \frac{2}{5} + \frac{- 7}{8}$

Step 2

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{15}{8} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{8}{8} + \frac{- 7}{8}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{15}{8}$ by $\frac{5}{5}$ .

$\frac{15 \cdot 5}{8 \cdot 5} + \frac{2}{5} \cdot \frac{8}{8} + \frac{- 7}{8}$

Step 3.2

Multiply $8$ by $5$ .

$\frac{15 \cdot 5}{40} + \frac{2}{5} \cdot \frac{8}{8} + \frac{- 7}{8}$

Step 3.3

Multiply $\frac{2}{5}$ by $\frac{8}{8}$ .

$\frac{15 \cdot 5}{40} + \frac{2 \cdot 8}{5 \cdot 8} + \frac{- 7}{8}$

Step 3.4

Multiply $5$ by $8$ .

$\frac{15 \cdot 5}{40} + \frac{2 \cdot 8}{40} + \frac{- 7}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{15 \cdot 5 + 2 \cdot 8}{40} + \frac{- 7}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $15$ by $5$ .

$\frac{75 + 2 \cdot 8}{40} + \frac{- 7}{8}$

Step 5.2

Multiply $2$ by $8$ .

$\frac{75 + 16}{40} + \frac{- 7}{8}$

Step 5.3

Add $75$ and $16$ .

$\frac{91}{40} + \frac{- 7}{8}$

Step 6

To write $\frac{- 7}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{91}{40} + \frac{- 7}{8} \cdot \frac{5}{5}$

Step 7

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{- 7}{8}$ by $\frac{5}{5}$ .

$\frac{91}{40} + \frac{- 7 \cdot 5}{8 \cdot 5}$

Step 7.2

Multiply $8$ by $5$ .

$\frac{91}{40} + \frac{- 7 \cdot 5}{40}$

Step 8

Combine the numerators over the common denominator.

$\frac{91 - 7 \cdot 5}{40}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 7$ by $5$ .

$\frac{91 - 35}{40}$

Step 9.2

Subtract $35$ from $91$ .

$\frac{56}{40}$

Step 10

Cancel the common factor of $56$ and $40$ .

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Step 10.1

Factor $8$ out of $56$ .

$\frac{8 (7)}{40}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $8$ out of $40$ .

$\frac{8 \cdot 7}{8 \cdot 5}$

Step 10.2.2

Cancel the common factor.

$\frac{8 \cdot 7}{8 \cdot 5}$

Step 10.2.3

Rewrite the expression.

$\frac{7}{5}$