Algebra Examples

$\frac{5}{8} y^{2} - 1 \frac{1}{2} y^{2} + 3$

Step 1

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$\frac{5}{8} y^{2} - (1 + \frac{1}{2}) y^{2} + 3$

Step 1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.2.1

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

$\frac{5}{8} y^{2} - (\frac{2}{2} + \frac{1}{2}) y^{2} + 3$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{5}{8} y^{2} - \frac{2 + 1}{2} y^{2} + 3$

Step 1.2.3

Add $2$ and $1$ .

$\frac{5}{8} y^{2} - \frac{3}{2} y^{2} + 3$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{5}{8}$ and $y^{2}$ .

$\frac{5 y^{2}}{8} - \frac{3}{2} y^{2} + 3$

Step 2.2

Combine $y^{2}$ and $\frac{3}{2}$ .

$\frac{5 y^{2}}{8} - \frac{y^{2} \cdot 3}{2} + 3$

Step 2.3

Move $3$ to the left of $y^{2}$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2}}{2} + 3$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{3 y^{2}}{2}$ by $\frac{4}{4}$ .

$\frac{5 y^{2}}{8} - (\frac{3 y^{2}}{2} \cdot \frac{4}{4}) + 3$

Step 3.2

Multiply $\frac{3 y^{2}}{2}$ by $\frac{4}{4}$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2} \cdot 4}{2 \cdot 4} + 3$

Step 3.3

Write $3$ as a fraction with denominator $1$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2} \cdot 4}{2 \cdot 4} + \frac{3}{1}$

Step 3.4

Multiply $\frac{3}{1}$ by $\frac{8}{8}$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2} \cdot 4}{2 \cdot 4} + \frac{3}{1} \cdot \frac{8}{8}$

Step 3.5

Multiply $\frac{3}{1}$ by $\frac{8}{8}$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2} \cdot 4}{2 \cdot 4} + \frac{3 \cdot 8}{8}$

Step 3.6

Multiply $2$ by $4$ .

$\frac{5 y^{2}}{8} - \frac{3 y^{2} \cdot 4}{8} + \frac{3 \cdot 8}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 y^{2} - 3 y^{2} \cdot 4 + 3 \cdot 8}{8}$

Step 5

Simplify each term.

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Step 5.1

Multiply $4$ by $- 3$ .

$\frac{5 y^{2} - 12 y^{2} + 3 \cdot 8}{8}$

Step 5.2

Multiply $3$ by $8$ .

$\frac{5 y^{2} - 12 y^{2} + 24}{8}$

Step 6

Simplify terms.

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Step 6.1

Subtract $12 y^{2}$ from $5 y^{2}$ .

$\frac{- 7 y^{2} + 24}{8}$

Step 6.2

Factor $- 1$ out of $- 7 y^{2}$ .

$\frac{- (7 y^{2}) + 24}{8}$

Step 6.3

Rewrite $24$ as $- 1 (- 24)$ .

$\frac{- (7 y^{2}) - 1 (- 24)}{8}$

Step 6.4

Factor $- 1$ out of $- (7 y^{2}) - 1 (- 24)$ .

$\frac{- (7 y^{2} - 24)}{8}$

Step 6.5

Simplify the expression.

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Step 6.5.1

Rewrite $- (7 y^{2} - 24)$ as $- 1 (7 y^{2} - 24)$ .

$\frac{- 1 (7 y^{2} - 24)}{8}$

Step 6.5.2

Move the negative in front of the fraction.

$- \frac{7 y^{2} - 24}{8}$