Pre-Algebra Examples

$\frac{7}{40} \cdot \frac{5}{63} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $7$ .

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Step 1.1.1

Factor $7$ out of $63$ .

$\frac{7}{40} \cdot \frac{5}{7 (9)} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.1.2

Cancel the common factor.

$\frac{7}{40} \cdot \frac{5}{7 \cdot 9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.1.3

Rewrite the expression.

$\frac{1}{40} \cdot \frac{5}{9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Factor $5$ out of $40$ .

$\frac{1}{5 (8)} \cdot \frac{5}{9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{5 \cdot 8} \cdot \frac{5}{9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{8} \cdot \frac{1}{9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.3

Multiply $\frac{1}{8}$ by $\frac{1}{9}$ .

$\frac{1}{8 \cdot 9} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.4

Multiply $8$ by $9$ .

$\frac{1}{72} + \frac{3}{15} \cdot \frac{5}{9}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $9$ .

$\frac{1}{72} + \frac{3}{15} \cdot \frac{5}{3 (3)}$

Step 1.5.2

Cancel the common factor.

$\frac{1}{72} + \frac{3}{15} \cdot \frac{5}{3 \cdot 3}$

Step 1.5.3

Rewrite the expression.

$\frac{1}{72} + \frac{1}{15} \cdot \frac{5}{3}$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Factor $5$ out of $15$ .

$\frac{1}{72} + \frac{1}{5 (3)} \cdot \frac{5}{3}$

Step 1.6.2

Cancel the common factor.

$\frac{1}{72} + \frac{1}{5 \cdot 3} \cdot \frac{5}{3}$

Step 1.6.3

Rewrite the expression.

$\frac{1}{72} + \frac{1}{3} \cdot \frac{1}{3}$

Step 1.7

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$\frac{1}{72} + \frac{1}{3 \cdot 3}$

Step 1.8

Multiply $3$ by $3$ .

$\frac{1}{72} + \frac{1}{9}$

Step 2

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{72} + \frac{1}{9} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{9}$ by $\frac{8}{8}$ .

$\frac{1}{72} + \frac{8}{9 \cdot 8}$

Step 3.2

Multiply $9$ by $8$ .

$\frac{1}{72} + \frac{8}{72}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{1 + 8}{72}$

Step 4.2

Add $1$ and $8$ .

$\frac{9}{72}$

Step 5

Cancel the common factor of $9$ and $72$ .

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Step 5.1

Factor $9$ out of $9$ .

$\frac{9 (1)}{72}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $9$ out of $72$ .

$\frac{9 \cdot 1}{9 \cdot 8}$

Step 5.2.2

Cancel the common factor.

$\frac{9 \cdot 1}{9 \cdot 8}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$