Basic Math Examples

$\frac{7 d}{4} - \frac{3 d}{8} = 1$

Step 1

Simplify $\frac{7 d}{4} - \frac{3 d}{8}$ .

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Step 1.1

To write $\frac{7 d}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 d}{4} \cdot \frac{2}{2} - \frac{3 d}{8} = 1$

Step 1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{7 d}{4}$ by $\frac{2}{2}$ .

$\frac{7 d \cdot 2}{4 \cdot 2} - \frac{3 d}{8} = 1$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{7 d \cdot 2}{8} - \frac{3 d}{8} = 1$

Step 1.3

Combine the numerators over the common denominator.

$\frac{7 d \cdot 2 - 3 d}{8} = 1$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $d$ out of $7 d \cdot 2 - 3 d$ .

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Step 1.4.1.1

Factor $d$ out of $7 d \cdot 2$ .

$\frac{d (7 \cdot 2) - 3 d}{8} = 1$

Step 1.4.1.2

Factor $d$ out of $- 3 d$ .

$\frac{d (7 \cdot 2) + d \cdot - 3}{8} = 1$

Step 1.4.1.3

Factor $d$ out of $d (7 \cdot 2) + d \cdot - 3$ .

$\frac{d (7 \cdot 2 - 3)}{8} = 1$

Step 1.4.2

Multiply $7$ by $2$ .

$\frac{d (14 - 3)}{8} = 1$

Step 1.4.3

Subtract $3$ from $14$ .

$\frac{d \cdot 11}{8} = 1$

Step 1.5

Move $11$ to the left of $d$ .

$\frac{11 d}{8} = 1$

Step 2

Multiply both sides of the equation by $\frac{8}{11}$ .

$\frac{8}{11} \cdot \frac{11 d}{8} = \frac{8}{11} \cdot 1$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8}{11} \cdot \frac{11 d}{8}$ .

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Step 3.1.1.1

Cancel the common factor of $8$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{8}{11} \cdot \frac{11 d}{8} = \frac{8}{11} \cdot 1$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 d) = \frac{8}{11} \cdot 1$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $11 d$ .

$\frac{1}{11} (11 (d)) = \frac{8}{11} \cdot 1$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 d) = \frac{8}{11} \cdot 1$

Step 3.1.1.2.3

Rewrite the expression.

$d = \frac{8}{11} \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{8}{11}$ by $1$ .

$d = \frac{8}{11}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = \frac{8}{11}$

Decimal Form:

$d = 0.\overline{72}$