Pre-Algebra Examples

$1 \frac{3}{4} \cdot (\frac{2}{7} - \frac{2}{3})$

Step 1

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(1 + \frac{3}{4}) \cdot (\frac{2}{7} - \frac{2}{3})$

Step 1.2

Add $1$ and $\frac{3}{4}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{4}{4} + \frac{3}{4}) \cdot (\frac{2}{7} - \frac{2}{3})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} \cdot (\frac{2}{7} - \frac{2}{3})$

Step 1.2.3

Add $4$ and $3$ .

$\frac{7}{4} \cdot (\frac{2}{7} - \frac{2}{3})$

Step 2

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{4} \cdot (\frac{2}{7} \cdot \frac{3}{3} - \frac{2}{3})$

Step 3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{7}{4} \cdot (\frac{2}{7} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{7}{7})$

Step 4

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{7}$ by $\frac{3}{3}$ .

$\frac{7}{4} \cdot (\frac{2 \cdot 3}{7 \cdot 3} - \frac{2}{3} \cdot \frac{7}{7})$

Step 4.2

Multiply $7$ by $3$ .

$\frac{7}{4} \cdot (\frac{2 \cdot 3}{21} - \frac{2}{3} \cdot \frac{7}{7})$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{7}{7}$ .

$\frac{7}{4} \cdot (\frac{2 \cdot 3}{21} - \frac{2 \cdot 7}{3 \cdot 7})$

Step 4.4

Multiply $3$ by $7$ .

$\frac{7}{4} \cdot (\frac{2 \cdot 3}{21} - \frac{2 \cdot 7}{21})$

Step 5

Combine the numerators over the common denominator.

$\frac{7}{4} \cdot \frac{2 \cdot 3 - 2 \cdot 7}{21}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $3$ .

$\frac{7}{4} \cdot \frac{6 - 2 \cdot 7}{21}$

Step 6.2

Multiply $- 2$ by $7$ .

$\frac{7}{4} \cdot \frac{6 - 14}{21}$

Step 6.3

Subtract $14$ from $6$ .

$\frac{7}{4} \cdot \frac{- 8}{21}$

Step 7

Cancel the common factor of $7$ .

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Step 7.1

Factor $7$ out of $21$ .

$\frac{7}{4} \cdot \frac{- 8}{7 (3)}$

Step 7.2

Cancel the common factor.

$\frac{7}{4} \cdot \frac{- 8}{7 \cdot 3}$

Step 7.3

Rewrite the expression.

$\frac{1}{4} \cdot \frac{- 8}{3}$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $- 8$ .

$\frac{1}{4} \cdot \frac{4 (- 2)}{3}$

Step 8.2

Cancel the common factor.

$\frac{1}{4} \cdot \frac{4 \cdot - 2}{3}$

Step 8.3

Rewrite the expression.

$\frac{- 2}{3}$

Step 9

Move the negative in front of the fraction.

$- \frac{2}{3}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{3}$

Decimal Form:

$- 0.\overline{6}$