Algebra Examples

$2 \frac{1}{4} = 1 \frac{2}{7} \div x$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

$2 + \frac{1}{4} = 1 \frac{2}{7} \div x$

Step 1.1.2

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

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Step 1.1.2.1

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

$2 \cdot \frac{4}{4} + \frac{1}{4} = 1 \frac{2}{7} \div x$

Step 1.1.2.2

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

$\frac{2 \cdot 4}{4} + \frac{1}{4} = 1 \frac{2}{7} \div x$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 1}{4} = 1 \frac{2}{7} \div x$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 1}{4} = 1 \frac{2}{7} \div x$

Step 1.1.2.4.2

Add $8$ and $1$ .

$\frac{9}{4} = 1 \frac{2}{7} \div x$

Step 2

Simplify the right side.

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Step 2.1

Simplify $1 \frac{2}{7} \div x$ .

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Step 2.1.1

Convert $1 \frac{2}{7}$ 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.

$\frac{9}{4} = (1 + \frac{2}{7}) \div x$

Step 2.1.1.2

Add $1$ and $\frac{2}{7}$ .

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Step 2.1.1.2.1

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

$\frac{9}{4} = (\frac{7}{7} + \frac{2}{7}) \div x$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{9}{4} = \frac{7 + 2}{7} \div x$

Step 2.1.1.2.3

Add $7$ and $2$ .

$\frac{9}{4} = \frac{9}{7} \div x$

Step 2.1.2

Rewrite the division as a fraction.

$\frac{9}{4} = \frac{\frac{9}{7}}{x}$

Step 2.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{9}{4} = \frac{9}{7} \cdot \frac{1}{x}$

Step 2.1.4

Multiply $\frac{9}{7}$ by $\frac{1}{x}$ .

$\frac{9}{4} = \frac{9}{7 x}$

Step 3

Rewrite the equation as $\frac{9}{7 x} = \frac{9}{4}$ .

$\frac{9}{7 x} = \frac{9}{4}$

Step 4

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$9 \cdot 4 = 7 x \cdot 9$

Step 5

Solve the equation for $x$ .

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Step 5.1

Rewrite the equation as $7 x \cdot 9 = 9 \cdot 4$ .

$7 x \cdot 9 = 9 \cdot 4$

Step 5.2

Simplify.

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Step 5.2.1

Multiply $9$ by $7$ .

$63 x = 9 \cdot 4$

Step 5.2.2

Multiply $9$ by $4$ .

$63 x = 36$

Step 5.3

Divide each term in $63 x = 36$ by $63$ and simplify.

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Step 5.3.1

Divide each term in $63 x = 36$ by $63$ .

$\frac{63 x}{63} = \frac{36}{63}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $63$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{63 x}{63} = \frac{36}{63}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{63}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Cancel the common factor of $36$ and $63$ .

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Step 5.3.3.1.1

Factor $9$ out of $36$ .

$x = \frac{9 (4)}{63}$

Step 5.3.3.1.2

Cancel the common factors.

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Step 5.3.3.1.2.1

Factor $9$ out of $63$ .

$x = \frac{9 \cdot 4}{9 \cdot 7}$

Step 5.3.3.1.2.2

Cancel the common factor.

$x = \frac{9 \cdot 4}{9 \cdot 7}$

Step 5.3.3.1.2.3

Rewrite the expression.

$x = \frac{4}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$