Basic Math Examples

$\frac{3}{8} d - \frac{4}{9} d = \frac{5}{8} d + 11$

Step 1

Simplify $\frac{3}{8} d - \frac{4}{9} d$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{3 d}{8} - \frac{4}{9} d = \frac{5}{8} d + 11$

Step 1.1.2

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

$\frac{3 d}{8} - \frac{d \cdot 4}{9} = \frac{5}{8} d + 11$

Step 1.1.3

Move $4$ to the left of $d$ .

$\frac{3 d}{8} - \frac{4 d}{9} = \frac{5}{8} d + 11$

Step 1.2

To write $\frac{3 d}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{3 d}{8} \cdot \frac{9}{9} - \frac{4 d}{9} = \frac{5}{8} d + 11$

Step 1.3

To write $- \frac{4 d}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3 d}{8} \cdot \frac{9}{9} - \frac{4 d}{9} \cdot \frac{8}{8} = \frac{5}{8} d + 11$

Step 1.4

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 d}{8}$ by $\frac{9}{9}$ .

$\frac{3 d \cdot 9}{8 \cdot 9} - \frac{4 d}{9} \cdot \frac{8}{8} = \frac{5}{8} d + 11$

Step 1.4.2

Multiply $8$ by $9$ .

$\frac{3 d \cdot 9}{72} - \frac{4 d}{9} \cdot \frac{8}{8} = \frac{5}{8} d + 11$

Step 1.4.3

Multiply $\frac{4 d}{9}$ by $\frac{8}{8}$ .

$\frac{3 d \cdot 9}{72} - \frac{4 d \cdot 8}{9 \cdot 8} = \frac{5}{8} d + 11$

Step 1.4.4

Multiply $9$ by $8$ .

$\frac{3 d \cdot 9}{72} - \frac{4 d \cdot 8}{72} = \frac{5}{8} d + 11$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 d \cdot 9 - 4 d \cdot 8}{72} = \frac{5}{8} d + 11$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $d$ out of $3 d \cdot 9 - 4 d \cdot 8$ .

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Step 1.6.1.1

Factor $d$ out of $3 d \cdot 9$ .

$\frac{d (3 \cdot 9) - 4 d \cdot 8}{72} = \frac{5}{8} d + 11$

Step 1.6.1.2

Factor $d$ out of $- 4 d \cdot 8$ .

$\frac{d (3 \cdot 9) + d (- 4 \cdot 8)}{72} = \frac{5}{8} d + 11$

Step 1.6.1.3

Factor $d$ out of $d (3 \cdot 9) + d (- 4 \cdot 8)$ .

$\frac{d (3 \cdot 9 - 4 \cdot 8)}{72} = \frac{5}{8} d + 11$

Step 1.6.2

Multiply $3$ by $9$ .

$\frac{d (27 - 4 \cdot 8)}{72} = \frac{5}{8} d + 11$

Step 1.6.3

Multiply $- 4$ by $8$ .

$\frac{d (27 - 32)}{72} = \frac{5}{8} d + 11$

Step 1.6.4

Subtract $32$ from $27$ .

$\frac{d \cdot - 5}{72} = \frac{5}{8} d + 11$

Step 1.7

Simplify the expression.

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Step 1.7.1

Move $- 5$ to the left of $d$ .

$\frac{- 5 \cdot d}{72} = \frac{5}{8} d + 11$

Step 1.7.2

Move the negative in front of the fraction.

$- \frac{5 d}{72} = \frac{5}{8} d + 11$

Step 2

Combine $\frac{5}{8}$ and $d$ .

$- \frac{5 d}{72} = \frac{5 d}{8} + 11$

Step 3

Move all terms containing $d$ to the left side of the equation.

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Step 3.1

Subtract $\frac{5 d}{8}$ from both sides of the equation.

$- \frac{5 d}{72} - \frac{5 d}{8} = 11$

Step 3.2

To write $- \frac{5 d}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{5 d}{72} - \frac{5 d}{8} \cdot \frac{9}{9} = 11$

Step 3.3

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{5 d}{8}$ by $\frac{9}{9}$ .

$- \frac{5 d}{72} - \frac{5 d \cdot 9}{8 \cdot 9} = 11$

Step 3.3.2

Multiply $8$ by $9$ .

$- \frac{5 d}{72} - \frac{5 d \cdot 9}{72} = 11$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- 5 d - 5 d \cdot 9}{72} = 11$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $5 d$ out of $- 5 d - 5 d \cdot 9$ .

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Step 3.5.1.1

Factor $5 d$ out of $- 5 d$ .

$\frac{5 d (- 1) - 5 d \cdot 9}{72} = 11$

Step 3.5.1.2

Factor $5 d$ out of $- 5 d \cdot 9$ .

$\frac{5 d (- 1) + 5 d (- 1 \cdot 9)}{72} = 11$

Step 3.5.1.3

Factor $5 d$ out of $5 d (- 1) + 5 d (- 1 \cdot 9)$ .

$\frac{5 d (- 1 - 1 \cdot 9)}{72} = 11$

Step 3.5.2

Multiply $- 1$ by $9$ .

$\frac{5 d (- 1 - 9)}{72} = 11$

Step 3.5.3

Subtract $9$ from $- 1$ .

$\frac{5 d \cdot - 10}{72} = 11$

Step 3.5.4

Multiply $- 10$ by $5$ .

$\frac{- 50 d}{72} = 11$

Step 3.6

Cancel the common factor of $- 50$ and $72$ .

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Step 3.6.1

Factor $2$ out of $- 50 d$ .

$\frac{2 (- 25 d)}{72} = 11$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $2$ out of $72$ .

$\frac{2 (- 25 d)}{2 (36)} = 11$

Step 3.6.2.2

Cancel the common factor.

$\frac{2 (- 25 d)}{2 \cdot 36} = 11$

Step 3.6.2.3

Rewrite the expression.

$\frac{- 25 d}{36} = 11$

Step 3.7

Move the negative in front of the fraction.

$- \frac{25 d}{36} = 11$

Step 4

Multiply both sides of the equation by $- \frac{36}{25}$ .

$- \frac{36}{25} (- \frac{25 d}{36}) = - \frac{36}{25} \cdot 11$

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 $- \frac{36}{25} (- \frac{25 d}{36})$ .

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Step 5.1.1.1

Cancel the common factor of $36$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{36}{25}$ into the numerator.

$\frac{- 36}{25} (- \frac{25 d}{36}) = - \frac{36}{25} \cdot 11$

Step 5.1.1.1.2

Move the leading negative in $- \frac{25 d}{36}$ into the numerator.

$\frac{- 36}{25} \cdot \frac{- 25 d}{36} = - \frac{36}{25} \cdot 11$

Step 5.1.1.1.3

Factor $36$ out of $- 36$ .

$\frac{36 (- 1)}{25} \cdot \frac{- 25 d}{36} = - \frac{36}{25} \cdot 11$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{36 \cdot - 1}{25} \cdot \frac{- 25 d}{36} = - \frac{36}{25} \cdot 11$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{25} (- 25 d) = - \frac{36}{25} \cdot 11$

Step 5.1.1.2

Cancel the common factor of $25$ .

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Step 5.1.1.2.1

Factor $25$ out of $- 25 d$ .

$\frac{- 1}{25} (25 (- d)) = - \frac{36}{25} \cdot 11$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{25} (25 (- d)) = - \frac{36}{25} \cdot 11$

Step 5.1.1.2.3

Rewrite the expression.

$- - d = - \frac{36}{25} \cdot 11$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{36}{25} \cdot 11$

Step 5.1.1.3.2

Multiply $d$ by $1$ .

$d = - \frac{36}{25} \cdot 11$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{36}{25} \cdot 11$ .

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Step 5.2.1.1

Multiply $- \frac{36}{25} \cdot 11$ .

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Step 5.2.1.1.1

Multiply $11$ by $- 1$ .

$d = - 11 (\frac{36}{25})$

Step 5.2.1.1.2

Combine $- 11$ and $\frac{36}{25}$ .

$d = \frac{- 11 \cdot 36}{25}$

Step 5.2.1.1.3

Multiply $- 11$ by $36$ .

$d = \frac{- 396}{25}$

Step 5.2.1.2

Move the negative in front of the fraction.

$d = - \frac{396}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{396}{25}$

Decimal Form:

$d = - 15.84$

Mixed Number Form:

$d = - 15 \frac{21}{25}$