Basic Math Examples

\frac{5}{6} + \frac{3}{7}

$\frac{5}{6} + \frac{3}{7}$

Step 1

To write

\frac{5}{6}

$\frac{5}{6}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5}{6} \cdot \frac{7}{7} + \frac{3}{7}

$\frac{5}{6} \cdot \frac{7}{7} + \frac{3}{7}$

Step 2

To write

\frac{3}{7}

$\frac{3}{7}$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5}{6} \cdot \frac{7}{7} + \frac{3}{7} \cdot \frac{6}{6}

$\frac{5}{6} \cdot \frac{7}{7} + \frac{3}{7} \cdot \frac{6}{6}$

Step 3

Write each expression with a common denominator of

42

$42$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{6}

$\frac{5}{6}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{5 \cdot 7}{6 \cdot 7} + \frac{3}{7} \cdot \frac{6}{6}

$\frac{5 \cdot 7}{6 \cdot 7} + \frac{3}{7} \cdot \frac{6}{6}$

Step 3.2

Multiply

6

$6$ by

7

$7$ .

\frac{5 \cdot 7}{42} + \frac{3}{7} \cdot \frac{6}{6}

$\frac{5 \cdot 7}{42} + \frac{3}{7} \cdot \frac{6}{6}$

Step 3.3

Multiply

\frac{3}{7}

$\frac{3}{7}$ by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{7 \cdot 6}

$\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{7 \cdot 6}$

Step 3.4

Multiply

7

$7$ by

6

$6$ .

\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{42}

$\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{42}$

\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{42}

$\frac{5 \cdot 7}{42} + \frac{3 \cdot 6}{42}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 7 + 3 \cdot 6}{42}

$\frac{5 \cdot 7 + 3 \cdot 6}{42}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

7

$7$ .

\frac{35 + 3 \cdot 6}{42}

$\frac{35 + 3 \cdot 6}{42}$

Step 5.2

Multiply

3

$3$ by

6

$6$ .

\frac{35 + 18}{42}

$\frac{35 + 18}{42}$

Step 5.3

Add

35

$35$ and

18

$18$ .

\frac{53}{42}

$\frac{53}{42}$

\frac{53}{42}

$\frac{53}{42}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{53}{42}

$\frac{53}{42}$

Decimal Form:

1.26190476 \dots

$1.26190476 \dots$

Mixed Number Form:

1 \frac{11}{42}

$1 \frac{11}{42}$