Pre-Algebra Examples

$\frac{11}{21} a - \frac{3}{35} a$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{11}{21}$ and $a$ .

$\frac{11 a}{21} - \frac{3}{35} a$

Step 1.2

Combine $a$ and $\frac{3}{35}$ .

$\frac{11 a}{21} - \frac{a \cdot 3}{35}$

Step 1.3

Move $3$ to the left of $a$ .

$\frac{11 a}{21} - \frac{3 a}{35}$

Step 2

To write $\frac{11 a}{21}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11 a}{21} \cdot \frac{5}{5} - \frac{3 a}{35}$

Step 3

To write $- \frac{3 a}{35}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11 a}{21} \cdot \frac{5}{5} - \frac{3 a}{35} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $105$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{11 a}{21}$ by $\frac{5}{5}$ .

$\frac{11 a \cdot 5}{21 \cdot 5} - \frac{3 a}{35} \cdot \frac{3}{3}$

Step 4.2

Multiply $21$ by $5$ .

$\frac{11 a \cdot 5}{105} - \frac{3 a}{35} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{3 a}{35}$ by $\frac{3}{3}$ .

$\frac{11 a \cdot 5}{105} - \frac{3 a \cdot 3}{35 \cdot 3}$

Step 4.4

Multiply $35$ by $3$ .

$\frac{11 a \cdot 5}{105} - \frac{3 a \cdot 3}{105}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 a \cdot 5 - 3 a \cdot 3}{105}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $a$ out of $11 a \cdot 5 - 3 a \cdot 3$ .

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Step 6.1.1

Factor $a$ out of $11 a \cdot 5$ .

$\frac{a (11 \cdot 5) - 3 a \cdot 3}{105}$

Step 6.1.2

Factor $a$ out of $- 3 a \cdot 3$ .

$\frac{a (11 \cdot 5) + a (- 3 \cdot 3)}{105}$

Step 6.1.3

Factor $a$ out of $a (11 \cdot 5) + a (- 3 \cdot 3)$ .

$\frac{a (11 \cdot 5 - 3 \cdot 3)}{105}$

Step 6.2

Multiply $11$ by $5$ .

$\frac{a (55 - 3 \cdot 3)}{105}$

Step 6.3

Multiply $- 3$ by $3$ .

$\frac{a (55 - 9)}{105}$

Step 6.4

Subtract $9$ from $55$ .

$\frac{a \cdot 46}{105}$

Step 7

Move $46$ to the left of $a$ .

$\frac{46 a}{105}$