Pre-Algebra Examples

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

Step 1

Replace all occurrences of

$+$

$-$ with a single

$-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because

$1 \cdot - 1 = - 1$

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

Step 2

To write

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

$\frac{7}{7}$ .

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

Step 3

To write

$- \frac{4}{7}$ as a fraction with a common denominator, multiply by

$\frac{10}{10}$ .

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

Step 4

Write each expression with a common denominator of

$70$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{3}{10}$ by

$\frac{7}{7}$ .

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

Step 4.2

Multiply

$10$ by

$7$ .

$\frac{3 \cdot 7}{70} - \frac{4}{7} \cdot \frac{10}{10}$

Step 4.3

Multiply

$\frac{4}{7}$ by

$\frac{10}{10}$ .

$\frac{3 \cdot 7}{70} - \frac{4 \cdot 10}{7 \cdot 10}$

Step 4.4

Multiply

$7$ by

$10$ .

$\frac{3 \cdot 7}{70} - \frac{4 \cdot 10}{70}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 - 4 \cdot 10}{70}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$3$ by

$7$ .

$\frac{21 - 4 \cdot 10}{70}$

Step 6.2

Multiply

$- 4$ by

$10$ .

$\frac{21 - 40}{70}$

Step 6.3

Subtract

$40$ from

$21$ .

$\frac{- 19}{70}$

Step 7

Move the negative in front of the fraction.

$- \frac{19}{70}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{19}{70}$

Decimal Form:

$- 0.2\overline{714285}$