Pre-Algebra Examples

$2 \frac{1}{4} \cdot m + 3 = 4 \frac{1}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{1}{4} \cdot m + 3$ .

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Step 1.1.1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1.1

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

$(2 + \frac{1}{4}) \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(2 \cdot \frac{4}{4} + \frac{1}{4}) \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$(\frac{2 \cdot 4}{4} + \frac{1}{4}) \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} \cdot m + 3 = 4 \frac{1}{8}$

Step 1.1.2

Combine $\frac{9}{4}$ and $m$ .

$\frac{9 m}{4} + 3 = 4 \frac{1}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $4 \frac{1}{8}$ to an improper fraction.

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Step 2.1.1

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

$\frac{9 m}{4} + 3 = 4 + \frac{1}{8}$

Step 2.1.2

Add $4$ and $\frac{1}{8}$ .

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Step 2.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{9 m}{4} + 3 = 4 \cdot \frac{8}{8} + \frac{1}{8}$

Step 2.1.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{9 m}{4} + 3 = \frac{4 \cdot 8}{8} + \frac{1}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{9 m}{4} + 3 = \frac{4 \cdot 8 + 1}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $4$ by $8$ .

$\frac{9 m}{4} + 3 = \frac{32 + 1}{8}$

Step 2.1.2.4.2

Add $32$ and $1$ .

$\frac{9 m}{4} + 3 = \frac{33}{8}$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$\frac{9 m}{4} = \frac{33}{8} - 3$

Step 3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{9 m}{4} = \frac{33}{8} - 3 \cdot \frac{8}{8}$

Step 3.3

Combine $- 3$ and $\frac{8}{8}$ .

$\frac{9 m}{4} = \frac{33}{8} + \frac{- 3 \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{9 m}{4} = \frac{33 - 3 \cdot 8}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 3$ by $8$ .

$\frac{9 m}{4} = \frac{33 - 24}{8}$

Step 3.5.2

Subtract $24$ from $33$ .

$\frac{9 m}{4} = \frac{9}{8}$

Step 4

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 m}{4} = \frac{4}{9} \cdot \frac{9}{8}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{4}{9} \cdot \frac{9 m}{4}$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 m}{4} = \frac{4}{9} \cdot \frac{9}{8}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 m) = \frac{4}{9} \cdot \frac{9}{8}$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 m$ .

$\frac{1}{9} (9 (m)) = \frac{4}{9} \cdot \frac{9}{8}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 m) = \frac{4}{9} \cdot \frac{9}{8}$

Step 5.1.1.2.3

Rewrite the expression.

$m = \frac{4}{9} \cdot \frac{9}{8}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{4}{9} \cdot \frac{9}{8}$ .

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Step 5.2.1.1

Cancel the common factor of $4$ .

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Step 5.2.1.1.1

Factor $4$ out of $8$ .

$m = \frac{4}{9} \cdot \frac{9}{4 (2)}$

Step 5.2.1.1.2

Cancel the common factor.

$m = \frac{4}{9} \cdot \frac{9}{4 \cdot 2}$

Step 5.2.1.1.3

Rewrite the expression.

$m = \frac{1}{9} \cdot \frac{9}{2}$

Step 5.2.1.2

Cancel the common factor of $9$ .

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Step 5.2.1.2.1

Cancel the common factor.

$m = \frac{1}{9} \cdot \frac{9}{2}$

Step 5.2.1.2.2

Rewrite the expression.

$m = \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{1}{2}$

Decimal Form:

$m = 0.5$