Basic Math Examples

\frac{3}{5} + \frac{5}{7}

$\frac{3}{5} + \frac{5}{7}$

Step 1

To write

\frac{3}{5}

$\frac{3}{5}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{3}{5} \cdot \frac{7}{7} + \frac{5}{7}

$\frac{3}{5} \cdot \frac{7}{7} + \frac{5}{7}$

Step 2

To write

\frac{5}{7}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3}{5} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{5}{5}

$\frac{3}{5} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

35

$35$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{3 \cdot 7}{5 \cdot 7} + \frac{5}{7} \cdot \frac{5}{5}

$\frac{3 \cdot 7}{5 \cdot 7} + \frac{5}{7} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

7

$7$ .

\frac{3 \cdot 7}{35} + \frac{5}{7} \cdot \frac{5}{5}

$\frac{3 \cdot 7}{35} + \frac{5}{7} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{5}{7}

$\frac{5}{7}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{7 \cdot 5}

$\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{7 \cdot 5}$

Step 3.4

Multiply

7

$7$ by

5

$5$ .

\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{35}

$\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{35}$

\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{35}

$\frac{3 \cdot 7}{35} + \frac{5 \cdot 5}{35}$

Step 4

Combine the numerators over the common denominator.

\frac{3 \cdot 7 + 5 \cdot 5}{35}

$\frac{3 \cdot 7 + 5 \cdot 5}{35}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

7

$7$ .

\frac{21 + 5 \cdot 5}{35}

$\frac{21 + 5 \cdot 5}{35}$

Step 5.2

Multiply

5

$5$ by

5

$5$ .

\frac{21 + 25}{35}

$\frac{21 + 25}{35}$

Step 5.3

Add

21

$21$ and

25

$25$ .

\frac{46}{35}

$\frac{46}{35}$

\frac{46}{35}

$\frac{46}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{46}{35}

$\frac{46}{35}$

Decimal Form:

1.31428571 \dots

$1.31428571 \dots$

Mixed Number Form:

1 \frac{11}{35}

$1 \frac{11}{35}$