Basic Math Examples

$- \frac{4}{3} d - 1 = \frac{1}{5} d - \frac{5}{3}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{d \cdot 4}{3} - 1 = \frac{1}{5} d - \frac{5}{3}$

Step 1.2

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

$- \frac{4 d}{3} - 1 = \frac{1}{5} d - \frac{5}{3}$

Step 2

Combine $\frac{1}{5}$ and $d$ .

$- \frac{4 d}{3} - 1 = \frac{d}{5} - \frac{5}{3}$

Step 3

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

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Step 3.1

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

$- \frac{4 d}{3} - 1 - \frac{d}{5} = - \frac{5}{3}$

Step 3.2

To write $- \frac{4 d}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4 d}{3} \cdot \frac{5}{5} - \frac{d}{5} - 1 = - \frac{5}{3}$

Step 3.3

To write $- \frac{d}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 d}{3} \cdot \frac{5}{5} - \frac{d}{5} \cdot \frac{3}{3} - 1 = - \frac{5}{3}$

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{4 d}{3}$ by $\frac{5}{5}$ .

$- \frac{4 d \cdot 5}{3 \cdot 5} - \frac{d}{5} \cdot \frac{3}{3} - 1 = - \frac{5}{3}$

Step 3.4.2

Multiply $3$ by $5$ .

$- \frac{4 d \cdot 5}{15} - \frac{d}{5} \cdot \frac{3}{3} - 1 = - \frac{5}{3}$

Step 3.4.3

Multiply $\frac{d}{5}$ by $\frac{3}{3}$ .

$- \frac{4 d \cdot 5}{15} - \frac{d \cdot 3}{5 \cdot 3} - 1 = - \frac{5}{3}$

Step 3.4.4

Multiply $5$ by $3$ .

$- \frac{4 d \cdot 5}{15} - \frac{d \cdot 3}{15} - 1 = - \frac{5}{3}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 4 d \cdot 5 - d \cdot 3}{15} - 1 = - \frac{5}{3}$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $d$ out of $- 4 d \cdot 5 - d \cdot 3$ .

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Step 3.6.1.1.1

Factor $d$ out of $- 4 d \cdot 5$ .

$\frac{d (- 4 \cdot 5) - d \cdot 3}{15} - 1 = - \frac{5}{3}$

Step 3.6.1.1.2

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

$\frac{d (- 4 \cdot 5) + d (- 1 \cdot 3)}{15} - 1 = - \frac{5}{3}$

Step 3.6.1.1.3

Factor $d$ out of $d (- 4 \cdot 5) + d (- 1 \cdot 3)$ .

$\frac{d (- 4 \cdot 5 - 1 \cdot 3)}{15} - 1 = - \frac{5}{3}$

Step 3.6.1.2

Multiply $- 4$ by $5$ .

$\frac{d (- 20 - 1 \cdot 3)}{15} - 1 = - \frac{5}{3}$

Step 3.6.1.3

Multiply $- 1$ by $3$ .

$\frac{d (- 20 - 3)}{15} - 1 = - \frac{5}{3}$

Step 3.6.1.4

Subtract $3$ from $- 20$ .

$\frac{d \cdot - 23}{15} - 1 = - \frac{5}{3}$

Step 3.6.2

Move $- 23$ to the left of $d$ .

$\frac{- 23 \cdot d}{15} - 1 = - \frac{5}{3}$

Step 3.6.3

Move the negative in front of the fraction.

$- \frac{23 d}{15} - 1 = - \frac{5}{3}$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$- \frac{23 d}{15} = - \frac{5}{3} + 1$

Step 4.2

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

$- \frac{23 d}{15} = - \frac{5}{3} + \frac{3}{3}$

Step 4.3

Combine the numerators over the common denominator.

$- \frac{23 d}{15} = \frac{- 5 + 3}{3}$

Step 4.4

Add $- 5$ and $3$ .

$- \frac{23 d}{15} = \frac{- 2}{3}$

Step 4.5

Move the negative in front of the fraction.

$- \frac{23 d}{15} = - \frac{2}{3}$

Step 5

Multiply both sides of the equation by $- \frac{15}{23}$ .

$- \frac{15}{23} (- \frac{23 d}{15}) = - \frac{15}{23} (- \frac{2}{3})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- \frac{15}{23} (- \frac{23 d}{15})$ .

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Step 6.1.1.1

Cancel the common factor of $15$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{15}{23}$ into the numerator.

$\frac{- 15}{23} (- \frac{23 d}{15}) = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.1.2

Move the leading negative in $- \frac{23 d}{15}$ into the numerator.

$\frac{- 15}{23} \cdot \frac{- 23 d}{15} = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.1.3

Factor $15$ out of $- 15$ .

$\frac{15 (- 1)}{23} \cdot \frac{- 23 d}{15} = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{15 \cdot - 1}{23} \cdot \frac{- 23 d}{15} = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{23} (- 23 d) = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.2

Cancel the common factor of $23$ .

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Step 6.1.1.2.1

Factor $23$ out of $- 23 d$ .

$\frac{- 1}{23} (23 (- d)) = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{23} (23 (- d)) = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.2.3

Rewrite the expression.

$- - d = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{15}{23} (- \frac{2}{3})$

Step 6.1.1.3.2

Multiply $d$ by $1$ .

$d = - \frac{15}{23} (- \frac{2}{3})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{15}{23} (- \frac{2}{3})$ .

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Step 6.2.1.1

Cancel the common factor of $3$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{15}{23}$ into the numerator.

$d = \frac{- 15}{23} (- \frac{2}{3})$

Step 6.2.1.1.2

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$d = \frac{- 15}{23} \cdot \frac{- 2}{3}$

Step 6.2.1.1.3

Factor $3$ out of $- 15$ .

$d = \frac{3 (- 5)}{23} \cdot \frac{- 2}{3}$

Step 6.2.1.1.4

Cancel the common factor.

$d = \frac{3 \cdot - 5}{23} \cdot \frac{- 2}{3}$

Step 6.2.1.1.5

Rewrite the expression.

$d = \frac{- 5}{23} \cdot - 2$

Step 6.2.1.2

Combine $\frac{- 5}{23}$ and $- 2$ .

$d = \frac{- 5 \cdot - 2}{23}$

Step 6.2.1.3

Multiply $- 5$ by $- 2$ .

$d = \frac{10}{23}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$d = \frac{10}{23}$

Decimal Form:

$d = 0.43478260 \dots$