Basic Math Examples

$2 \frac{3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{3}{5} + w - 4 \frac{1}{3}$ .

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Step 1.1.1

Convert $2 \frac{3}{5}$ 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.

$2 + \frac{3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.1.2

Add $2$ and $\frac{3}{5}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 \cdot \frac{5}{5} + \frac{3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.1.2.2

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

$\frac{2 \cdot 5}{5} + \frac{3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $5$ .

$\frac{10 + 3}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.1.2.4.2

Add $10$ and $3$ .

$\frac{13}{5} + w - 4 \frac{1}{3} = 7 \frac{8}{15}$

Step 1.1.2

Convert $4 \frac{1}{3}$ 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.

$\frac{13}{5} + w - (4 + \frac{1}{3}) = 7 \frac{8}{15}$

Step 1.1.2.2

Add $4$ and $\frac{1}{3}$ .

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Step 1.1.2.2.1

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

$\frac{13}{5} + w - (4 \cdot \frac{3}{3} + \frac{1}{3}) = 7 \frac{8}{15}$

Step 1.1.2.2.2

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

$\frac{13}{5} + w - (\frac{4 \cdot 3}{3} + \frac{1}{3}) = 7 \frac{8}{15}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{13}{5} + w - \frac{4 \cdot 3 + 1}{3} = 7 \frac{8}{15}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $4$ by $3$ .

$\frac{13}{5} + w - \frac{12 + 1}{3} = 7 \frac{8}{15}$

Step 1.1.2.2.4.2

Add $12$ and $1$ .

$\frac{13}{5} + w - \frac{13}{3} = 7 \frac{8}{15}$

Step 1.1.3

To write $\frac{13}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$w + \frac{13}{5} \cdot \frac{3}{3} - \frac{13}{3} = 7 \frac{8}{15}$

Step 1.1.4

To write $- \frac{13}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$w + \frac{13}{5} \cdot \frac{3}{3} - \frac{13}{3} \cdot \frac{5}{5} = 7 \frac{8}{15}$

Step 1.1.5

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

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Step 1.1.5.1

Multiply $\frac{13}{5}$ by $\frac{3}{3}$ .

$w + \frac{13 \cdot 3}{5 \cdot 3} - \frac{13}{3} \cdot \frac{5}{5} = 7 \frac{8}{15}$

Step 1.1.5.2

Multiply $5$ by $3$ .

$w + \frac{13 \cdot 3}{15} - \frac{13}{3} \cdot \frac{5}{5} = 7 \frac{8}{15}$

Step 1.1.5.3

Multiply $\frac{13}{3}$ by $\frac{5}{5}$ .

$w + \frac{13 \cdot 3}{15} - \frac{13 \cdot 5}{3 \cdot 5} = 7 \frac{8}{15}$

Step 1.1.5.4

Multiply $3$ by $5$ .

$w + \frac{13 \cdot 3}{15} - \frac{13 \cdot 5}{15} = 7 \frac{8}{15}$

Step 1.1.6

Combine the numerators over the common denominator.

$w + \frac{13 \cdot 3 - 13 \cdot 5}{15} = 7 \frac{8}{15}$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $13$ by $3$ .

$w + \frac{39 - 13 \cdot 5}{15} = 7 \frac{8}{15}$

Step 1.1.7.2

Multiply $- 13$ by $5$ .

$w + \frac{39 - 65}{15} = 7 \frac{8}{15}$

Step 1.1.7.3

Subtract $65$ from $39$ .

$w + \frac{- 26}{15} = 7 \frac{8}{15}$

Step 1.1.8

Move the negative in front of the fraction.

$w - \frac{26}{15} = 7 \frac{8}{15}$

Step 2

Simplify the right side.

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Step 2.1

Convert $7 \frac{8}{15}$ to an improper fraction.

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Step 2.1.1

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

$w - \frac{26}{15} = 7 + \frac{8}{15}$

Step 2.1.2

Add $7$ and $\frac{8}{15}$ .

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Step 2.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$w - \frac{26}{15} = 7 \cdot \frac{15}{15} + \frac{8}{15}$

Step 2.1.2.2

Combine $7$ and $\frac{15}{15}$ .

$w - \frac{26}{15} = \frac{7 \cdot 15}{15} + \frac{8}{15}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$w - \frac{26}{15} = \frac{7 \cdot 15 + 8}{15}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $7$ by $15$ .

$w - \frac{26}{15} = \frac{105 + 8}{15}$

Step 2.1.2.4.2

Add $105$ and $8$ .

$w - \frac{26}{15} = \frac{113}{15}$

Step 3

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

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Step 3.1

Add $\frac{26}{15}$ to both sides of the equation.

$w = \frac{113}{15} + \frac{26}{15}$

Step 3.2

Combine the numerators over the common denominator.

$w = \frac{113 + 26}{15}$

Step 3.3

Add $113$ and $26$ .

$w = \frac{139}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = \frac{139}{15}$

Decimal Form:

$w = 9.2\overline{6}$

Mixed Number Form:

$w = 9 \frac{4}{15}$