Pre-Algebra Examples

$\frac{4}{9} \div \frac{1}{3} + \frac{7}{10}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{9} \cdot 3 + \frac{7}{10}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{4}{3 (3)} \cdot 3 + \frac{7}{10}$

Step 1.2.2

Cancel the common factor.

$\frac{4}{3 \cdot 3} \cdot 3 + \frac{7}{10}$

Step 1.2.3

Rewrite the expression.

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

Step 2

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{4}{3} \cdot \frac{10}{10} + \frac{7}{10}$

Step 3

To write $\frac{7}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{3} \cdot \frac{10}{10} + \frac{7}{10} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{3}$ by $\frac{10}{10}$ .

$\frac{4 \cdot 10}{3 \cdot 10} + \frac{7}{10} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $10$ .

$\frac{4 \cdot 10}{30} + \frac{7}{10} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{7}{10}$ by $\frac{3}{3}$ .

$\frac{4 \cdot 10}{30} + \frac{7 \cdot 3}{10 \cdot 3}$

Step 4.4

Multiply $10$ by $3$ .

$\frac{4 \cdot 10}{30} + \frac{7 \cdot 3}{30}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 10 + 7 \cdot 3}{30}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $10$ .

$\frac{40 + 7 \cdot 3}{30}$

Step 6.2

Multiply $7$ by $3$ .

$\frac{40 + 21}{30}$

Step 6.3

Add $40$ and $21$ .

$\frac{61}{30}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{61}{30}$

Decimal Form:

$2.0\overline{3}$

Mixed Number Form:

$2 \frac{1}{30}$