Pre-Algebra Examples

$\frac{5}{6} h - \frac{7}{12} = - \frac{3}{4} h - \frac{13}{6}$

Step 1

Combine $\frac{5}{6}$ and $h$ .

$\frac{5 h}{6} - \frac{7}{12} = - \frac{3}{4} h - \frac{13}{6}$

Step 2

Simplify each term.

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Step 2.1

Combine $h$ and $\frac{3}{4}$ .

$\frac{5 h}{6} - \frac{7}{12} = - \frac{h \cdot 3}{4} - \frac{13}{6}$

Step 2.2

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

$\frac{5 h}{6} - \frac{7}{12} = - \frac{3 h}{4} - \frac{13}{6}$

Step 3

Move all terms containing $h$ to the left side of the equation.

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Step 3.1

Add $\frac{3 h}{4}$ to both sides of the equation.

$\frac{5 h}{6} - \frac{7}{12} + \frac{3 h}{4} = - \frac{13}{6}$

Step 3.2

To write $\frac{5 h}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 h}{6} \cdot \frac{2}{2} + \frac{3 h}{4} - \frac{7}{12} = - \frac{13}{6}$

Step 3.3

To write $\frac{3 h}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 h}{6} \cdot \frac{2}{2} + \frac{3 h}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{5 h}{6}$ by $\frac{2}{2}$ .

$\frac{5 h \cdot 2}{6 \cdot 2} + \frac{3 h}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.2

Multiply $6$ by $2$ .

$\frac{5 h \cdot 2}{12} + \frac{3 h}{4} \cdot \frac{3}{3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.3

Multiply $\frac{3 h}{4}$ by $\frac{3}{3}$ .

$\frac{5 h \cdot 2}{12} + \frac{3 h \cdot 3}{4 \cdot 3} - \frac{7}{12} = - \frac{13}{6}$

Step 3.4.4

Multiply $4$ by $3$ .

$\frac{5 h \cdot 2}{12} + \frac{3 h \cdot 3}{12} - \frac{7}{12} = - \frac{13}{6}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{5 h \cdot 2 + 3 h \cdot 3}{12} - \frac{7}{12} = - \frac{13}{6}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{5 h \cdot 2 + 3 h \cdot 3 - 7}{12} = - \frac{13}{6}$

Step 3.7

Simplify each term.

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Step 3.7.1

Multiply $2$ by $5$ .

$\frac{10 h + 3 h \cdot 3 - 7}{12} = - \frac{13}{6}$

Step 3.7.2

Multiply $3$ by $3$ .

$\frac{10 h + 9 h - 7}{12} = - \frac{13}{6}$

Step 3.8

Add $10 h$ and $9 h$ .

$\frac{19 h - 7}{12} = - \frac{13}{6}$

Step 4

Multiply both sides by $12$ .

$\frac{19 h - 7}{12} \cdot 12 = - \frac{13}{6} \cdot 12$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $12$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{19 h - 7}{12} \cdot 12 = - \frac{13}{6} \cdot 12$

Step 5.1.1.2

Rewrite the expression.

$19 h - 7 = - \frac{13}{6} \cdot 12$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{13}{6} \cdot 12$ .

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Step 5.2.1.1

Cancel the common factor of $6$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{13}{6}$ into the numerator.

$19 h - 7 = \frac{- 13}{6} \cdot 12$

Step 5.2.1.1.2

Factor $6$ out of $12$ .

$19 h - 7 = \frac{- 13}{6} \cdot (6 (2))$

Step 5.2.1.1.3

Cancel the common factor.

$19 h - 7 = \frac{- 13}{6} \cdot (6 \cdot 2)$

Step 5.2.1.1.4

Rewrite the expression.

$19 h - 7 = - 13 \cdot 2$

Step 5.2.1.2

Multiply $- 13$ by $2$ .

$19 h - 7 = - 26$

Step 6

Solve for $h$ .

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Step 6.1

Move all terms not containing $h$ to the right side of the equation.

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Step 6.1.1

Add $7$ to both sides of the equation.

$19 h = - 26 + 7$

Step 6.1.2

Add $- 26$ and $7$ .

$19 h = - 19$

Step 6.2

Divide each term in $19 h = - 19$ by $19$ and simplify.

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Step 6.2.1

Divide each term in $19 h = - 19$ by $19$ .

$\frac{19 h}{19} = \frac{- 19}{19}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $19$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{19 h}{19} = \frac{- 19}{19}$

Step 6.2.2.1.2

Divide $h$ by $1$ .

$h = \frac{- 19}{19}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $- 19$ by $19$ .

$h = - 1$