Pre-Algebra Examples

$1 \frac{7}{8} \cdot 1 \frac{1}{4} = 1 \frac{1}{3} \cdot x$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{7}{8} \cdot 1 \frac{1}{4}$ .

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Step 1.1.1

Convert $1 \frac{7}{8}$ 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.

$(1 + \frac{7}{8}) \cdot 1 \frac{1}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.1.2

Add $1$ and $\frac{7}{8}$ .

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Step 1.1.1.2.1

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

$(\frac{8}{8} + \frac{7}{8}) \cdot 1 \frac{1}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{8 + 7}{8} \cdot 1 \frac{1}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.1.2.3

Add $8$ and $7$ .

$\frac{15}{8} \cdot 1 \frac{1}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.2

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

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Step 1.1.2.1

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

$\frac{15}{8} \cdot (1 + \frac{1}{4}) = 1 \frac{1}{3} \cdot x$

Step 1.1.2.2

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

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Step 1.1.2.2.1

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

$\frac{15}{8} \cdot (\frac{4}{4} + \frac{1}{4}) = 1 \frac{1}{3} \cdot x$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{15}{8} \cdot \frac{4 + 1}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.2.2.3

Add $4$ and $1$ .

$\frac{15}{8} \cdot \frac{5}{4} = 1 \frac{1}{3} \cdot x$

Step 1.1.3

Multiply $\frac{15}{8} \cdot \frac{5}{4}$ .

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Step 1.1.3.1

Multiply $\frac{15}{8}$ by $\frac{5}{4}$ .

$\frac{15 \cdot 5}{8 \cdot 4} = 1 \frac{1}{3} \cdot x$

Step 1.1.3.2

Multiply $15$ by $5$ .

$\frac{75}{8 \cdot 4} = 1 \frac{1}{3} \cdot x$

Step 1.1.3.3

Multiply $8$ by $4$ .

$\frac{75}{32} = 1 \frac{1}{3} \cdot x$

Step 2

Simplify the right side.

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Step 2.1

Simplify $1 \frac{1}{3} \cdot x$ .

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Step 2.1.1

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1.1

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

$\frac{75}{32} = (1 + \frac{1}{3}) \cdot x$

Step 2.1.1.2

Add $1$ and $\frac{1}{3}$ .

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Step 2.1.1.2.1

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

$\frac{75}{32} = (\frac{3}{3} + \frac{1}{3}) \cdot x$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{75}{32} = \frac{3 + 1}{3} \cdot x$

Step 2.1.1.2.3

Add $3$ and $1$ .

$\frac{75}{32} = \frac{4}{3} \cdot x$

Step 2.1.2

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

$\frac{75}{32} = \frac{4 x}{3}$

Step 3

Rewrite the equation as $\frac{4 x}{3} = \frac{75}{32}$ .

$\frac{4 x}{3} = \frac{75}{32}$

Step 4

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{75}{32}$

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 $\frac{3}{4} \cdot \frac{4 x}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 x}{3} = \frac{3}{4} \cdot \frac{75}{32}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{75}{32}$

Step 5.1.1.2

Cancel the common factor of $4$ .

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Step 5.1.1.2.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{3}{4} \cdot \frac{75}{32}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{3}{4} \cdot \frac{75}{32}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{4} \cdot \frac{75}{32}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{3}{4} \cdot \frac{75}{32}$ .

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Step 5.2.1.1

Multiply $\frac{3}{4}$ by $\frac{75}{32}$ .

$x = \frac{3 \cdot 75}{4 \cdot 32}$

Step 5.2.1.2

Multiply $3$ by $75$ .

$x = \frac{225}{4 \cdot 32}$

Step 5.2.1.3

Multiply $4$ by $32$ .

$x = \frac{225}{128}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{225}{128}$

Decimal Form:

$x = 1.7578125$

Mixed Number Form:

$x = 1 \frac{97}{128}$