Basic Math Examples

$\frac{1}{8} + \frac{3}{7} + \frac{3}{8} + \frac{1}{10}$

Step 1

Combine the numerators over the common denominator.

$\frac{1 + 3}{8} + \frac{3}{7} + \frac{1}{10}$

Step 2

Add $1$ and $3$ .

$\frac{4}{8} + \frac{3}{7} + \frac{1}{10}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{4}{8}$ by $\frac{35}{35}$ .

$\frac{4}{8} \cdot \frac{35}{35} + \frac{3}{7} + \frac{1}{10}$

Step 3.2

Multiply $\frac{4}{8}$ by $\frac{35}{35}$ .

$\frac{4 \cdot 35}{8 \cdot 35} + \frac{3}{7} + \frac{1}{10}$

Step 3.3

Multiply $\frac{3}{7}$ by $\frac{40}{40}$ .

$\frac{4 \cdot 35}{8 \cdot 35} + \frac{3}{7} \cdot \frac{40}{40} + \frac{1}{10}$

Step 3.4

Multiply $\frac{3}{7}$ by $\frac{40}{40}$ .

$\frac{4 \cdot 35}{8 \cdot 35} + \frac{3 \cdot 40}{7 \cdot 40} + \frac{1}{10}$

Step 3.5

Multiply $\frac{1}{10}$ by $\frac{28}{28}$ .

$\frac{4 \cdot 35}{8 \cdot 35} + \frac{3 \cdot 40}{7 \cdot 40} + \frac{1}{10} \cdot \frac{28}{28}$

Step 3.6

Multiply $\frac{1}{10}$ by $\frac{28}{28}$ .

$\frac{4 \cdot 35}{8 \cdot 35} + \frac{3 \cdot 40}{7 \cdot 40} + \frac{28}{10 \cdot 28}$

Step 3.7

Multiply $8$ by $35$ .

$\frac{4 \cdot 35}{280} + \frac{3 \cdot 40}{7 \cdot 40} + \frac{28}{10 \cdot 28}$

Step 3.8

Multiply $7$ by $40$ .

$\frac{4 \cdot 35}{280} + \frac{3 \cdot 40}{280} + \frac{28}{10 \cdot 28}$

Step 3.9

Multiply $10$ by $28$ .

$\frac{4 \cdot 35}{280} + \frac{3 \cdot 40}{280} + \frac{28}{280}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 35 + 3 \cdot 40 + 28}{280}$

Step 5

Simplify each term.

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Step 5.1

Multiply $4$ by $35$ .

$\frac{140 + 3 \cdot 40 + 28}{280}$

Step 5.2

Multiply $3$ by $40$ .

$\frac{140 + 120 + 28}{280}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Add $140$ and $120$ .

$\frac{260 + 28}{280}$

Step 6.2

Add $260$ and $28$ .

$\frac{288}{280}$

Step 6.3

Cancel the common factor of $288$ and $280$ .

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Step 6.3.1

Factor $8$ out of $288$ .

$\frac{8 (36)}{280}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $8$ out of $280$ .

$\frac{8 \cdot 36}{8 \cdot 35}$

Step 6.3.2.2

Cancel the common factor.

$\frac{8 \cdot 36}{8 \cdot 35}$

Step 6.3.2.3

Rewrite the expression.

$\frac{36}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{36}{35}$

Decimal Form:

$1.02857142 \dots$

Mixed Number Form:

$1 \frac{1}{35}$