Basic Math Examples

\frac{2}{3} + \frac{5}{7}

$\frac{2}{3} + \frac{5}{7}$

Step 1

To write

\frac{2}{3}

$\frac{2}{3}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{2}{3} \cdot \frac{7}{7} + \frac{5}{7}

$\frac{2}{3} \cdot \frac{7}{7} + \frac{5}{7}$

Step 2

To write

\frac{5}{7}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2}{3} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{3}{3}

$\frac{2}{3} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of

21

$21$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{2 \cdot 7}{3 \cdot 7} + \frac{5}{7} \cdot \frac{3}{3}

$\frac{2 \cdot 7}{3 \cdot 7} + \frac{5}{7} \cdot \frac{3}{3}$

Step 3.2

Multiply

3

$3$ by

7

$7$ .

\frac{2 \cdot 7}{21} + \frac{5}{7} \cdot \frac{3}{3}

$\frac{2 \cdot 7}{21} + \frac{5}{7} \cdot \frac{3}{3}$

Step 3.3

Multiply

\frac{5}{7}

$\frac{5}{7}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{7 \cdot 3}

$\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{7 \cdot 3}$

Step 3.4

Multiply

7

$7$ by

3

$3$ .

\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{21}

$\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{21}$

\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{21}

$\frac{2 \cdot 7}{21} + \frac{5 \cdot 3}{21}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 7 + 5 \cdot 3}{21}

$\frac{2 \cdot 7 + 5 \cdot 3}{21}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

7

$7$ .

\frac{14 + 5 \cdot 3}{21}

$\frac{14 + 5 \cdot 3}{21}$

Step 5.2

Multiply

5

$5$ by

3

$3$ .

\frac{14 + 15}{21}

$\frac{14 + 15}{21}$

Step 5.3

Add

14

$14$ and

15

$15$ .

\frac{29}{21}

$\frac{29}{21}$

\frac{29}{21}

$\frac{29}{21}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{29}{21}

$\frac{29}{21}$

Decimal Form:

1.\overline{380952}

$1.\overline{380952}$

Mixed Number Form:

1 \frac{8}{21}

$1 \frac{8}{21}$