Algebra Examples

$4 (\frac{1}{2} + \frac{5}{4}) + - 5$

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 $1 \cdot - 1 = - 1$

$4 (\frac{1}{2} + \frac{5}{4}) - 5$

Step 2

Simplify each term.

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Step 2.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 (\frac{1}{2} \cdot \frac{2}{2} + \frac{5}{4}) - 5$

Step 2.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$4 (\frac{2}{2 \cdot 2} + \frac{5}{4}) - 5$

Step 2.2.2

Multiply $2$ by $2$ .

$4 (\frac{2}{4} + \frac{5}{4}) - 5$

Step 2.3

Combine the numerators over the common denominator.

$4 \frac{2 + 5}{4} - 5$

Step 2.4

Add $2$ and $5$ .

$4 (\frac{7}{4}) - 5$

Step 2.5

Cancel the common factor of $4$ .

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Step 2.5.1

Cancel the common factor.

$4 (\frac{7}{4}) - 5$

Step 2.5.2

Rewrite the expression.

$7 - 5$

Step 3

Subtract $5$ from $7$ .

$2$