Basic Math Examples

$\frac{3}{2} h - \frac{1}{3} h + 11 = a$

Step 1

Simplify $\frac{3}{2} h - \frac{1}{3} h + 11$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{2}$ and $h$ .

$\frac{3 h}{2} - \frac{1}{3} h + 11 = a$

Step 1.1.2

Combine $h$ and $\frac{1}{3}$ .

$\frac{3 h}{2} - \frac{h}{3} + 11 = a$

Step 1.2

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

$\frac{3 h}{2} \cdot \frac{3}{3} - \frac{h}{3} + 11 = a$

Step 1.3

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

$\frac{3 h}{2} \cdot \frac{3}{3} - \frac{h}{3} \cdot \frac{2}{2} + 11 = a$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$\frac{3 h \cdot 3}{2 \cdot 3} - \frac{h}{3} \cdot \frac{2}{2} + 11 = a$

Step 1.4.2

Multiply $2$ by $3$ .

$\frac{3 h \cdot 3}{6} - \frac{h}{3} \cdot \frac{2}{2} + 11 = a$

Step 1.4.3

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

$\frac{3 h \cdot 3}{6} - \frac{h \cdot 2}{3 \cdot 2} + 11 = a$

Step 1.4.4

Multiply $3$ by $2$ .

$\frac{3 h \cdot 3}{6} - \frac{h \cdot 2}{6} + 11 = a$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 h \cdot 3 - h \cdot 2}{6} + 11 = a$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $h$ out of $3 h \cdot 3 - h \cdot 2$ .

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Step 1.6.1.1.1

Factor $h$ out of $3 h \cdot 3$ .

$\frac{h (3 \cdot 3) - h \cdot 2}{6} + 11 = a$

Step 1.6.1.1.2

Factor $h$ out of $- h \cdot 2$ .

$\frac{h (3 \cdot 3) + h (- 1 \cdot 2)}{6} + 11 = a$

Step 1.6.1.1.3

Factor $h$ out of $h (3 \cdot 3) + h (- 1 \cdot 2)$ .

$\frac{h (3 \cdot 3 - 1 \cdot 2)}{6} + 11 = a$

Step 1.6.1.2

Multiply $3$ by $3$ .

$\frac{h (9 - 1 \cdot 2)}{6} + 11 = a$

Step 1.6.1.3

Multiply $- 1$ by $2$ .

$\frac{h (9 - 2)}{6} + 11 = a$

Step 1.6.1.4

Subtract $2$ from $9$ .

$\frac{h \cdot 7}{6} + 11 = a$

Step 1.6.2

Move $7$ to the left of $h$ .

$\frac{7 h}{6} + 11 = a$

Step 2

Subtract $11$ from both sides of the equation.

$\frac{7 h}{6} = a - 11$

Step 3

Multiply both sides of the equation by $\frac{6}{7}$ .

$\frac{6}{7} \cdot \frac{7 h}{6} = \frac{6}{7} (a - 11)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{6}{7} \cdot \frac{7 h}{6}$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{6}{7} \cdot \frac{7 h}{6} = \frac{6}{7} (a - 11)$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 h) = \frac{6}{7} (a - 11)$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 h$ .

$\frac{1}{7} (7 (h)) = \frac{6}{7} (a - 11)$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 h) = \frac{6}{7} (a - 11)$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{6}{7} (a - 11)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6}{7} (a - 11)$ .

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Step 4.2.1.1

Apply the distributive property.

$h = \frac{6}{7} a + \frac{6}{7} \cdot - 11$

Step 4.2.1.2

Combine $\frac{6}{7}$ and $a$ .

$h = \frac{6 a}{7} + \frac{6}{7} \cdot - 11$

Step 4.2.1.3

Multiply $\frac{6}{7} \cdot - 11$ .

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Step 4.2.1.3.1

Combine $\frac{6}{7}$ and $- 11$ .

$h = \frac{6 a}{7} + \frac{6 \cdot - 11}{7}$

Step 4.2.1.3.2

Multiply $6$ by $- 11$ .

$h = \frac{6 a}{7} + \frac{- 66}{7}$

Step 4.2.1.4

Move the negative in front of the fraction.

$h = \frac{6 a}{7} - \frac{66}{7}$