Algebra Examples

$8 \frac{7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $8 \frac{7}{18} - (1 \frac{5}{6} + y)$ .

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Step 1.1.1

Convert $8 \frac{7}{18}$ 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.

$8 + \frac{7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.1.2

Add $8$ and $\frac{7}{18}$ .

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Step 1.1.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$8 \cdot \frac{18}{18} + \frac{7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.1.2.2

Combine $8$ and $\frac{18}{18}$ .

$\frac{8 \cdot 18}{18} + \frac{7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 18 + 7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $8$ by $18$ .

$\frac{144 + 7}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.1.2.4.2

Add $144$ and $7$ .

$\frac{151}{18} - (1 \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.2

Convert $1 \frac{5}{6}$ 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.

$\frac{151}{18} - (1 + \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.2.2

Add $1$ and $\frac{5}{6}$ .

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Step 1.1.2.2.1

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

$\frac{151}{18} - (\frac{6}{6} + \frac{5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{151}{18} - (\frac{6 + 5}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.2.2.3

Add $6$ and $5$ .

$\frac{151}{18} - (\frac{11}{6} + y) = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.3

Apply the distributive property.

$\frac{151}{18} - \frac{11}{6} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.4

To write $- \frac{11}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{151}{18} - \frac{11}{6} \cdot \frac{3}{3} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{11}{6}$ by $\frac{3}{3}$ .

$\frac{151}{18} - \frac{11 \cdot 3}{6 \cdot 3} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.5.2

Multiply $6$ by $3$ .

$\frac{151}{18} - \frac{11 \cdot 3}{18} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{151 - 11 \cdot 3}{18} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $- 11$ by $3$ .

$\frac{151 - 33}{18} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.7.2

Subtract $33$ from $151$ .

$\frac{118}{18} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.8

Cancel the common factor of $118$ and $18$ .

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Step 1.1.8.1

Factor $2$ out of $118$ .

$\frac{2 (59)}{18} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.8.2

Cancel the common factors.

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Step 1.1.8.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 59}{2 \cdot 9} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.8.2.2

Cancel the common factor.

$\frac{2 \cdot 59}{2 \cdot 9} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 1.1.8.2.3

Rewrite the expression.

$\frac{59}{9} - y = 3 \frac{4}{15} + 2 \frac{13}{45}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $3 \frac{4}{15} + 2 \frac{13}{45}$ .

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Step 2.1.1

Convert $3 \frac{4}{15}$ 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.

$\frac{59}{9} - y = 3 + \frac{4}{15} + 2 \frac{13}{45}$

Step 2.1.1.2

Add $3$ and $\frac{4}{15}$ .

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Step 2.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{59}{9} - y = 3 \cdot \frac{15}{15} + \frac{4}{15} + 2 \frac{13}{45}$

Step 2.1.1.2.2

Combine $3$ and $\frac{15}{15}$ .

$\frac{59}{9} - y = \frac{3 \cdot 15}{15} + \frac{4}{15} + 2 \frac{13}{45}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{59}{9} - y = \frac{3 \cdot 15 + 4}{15} + 2 \frac{13}{45}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $3$ by $15$ .

$\frac{59}{9} - y = \frac{45 + 4}{15} + 2 \frac{13}{45}$

Step 2.1.1.2.4.2

Add $45$ and $4$ .

$\frac{59}{9} - y = \frac{49}{15} + 2 \frac{13}{45}$

Step 2.1.2

Convert $2 \frac{13}{45}$ to an improper fraction.

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Step 2.1.2.1

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

$\frac{59}{9} - y = \frac{49}{15} + 2 + \frac{13}{45}$

Step 2.1.2.2

Add $2$ and $\frac{13}{45}$ .

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Step 2.1.2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{45}{45}$ .

$\frac{59}{9} - y = \frac{49}{15} + 2 \cdot \frac{45}{45} + \frac{13}{45}$

Step 2.1.2.2.2

Combine $2$ and $\frac{45}{45}$ .

$\frac{59}{9} - y = \frac{49}{15} + \frac{2 \cdot 45}{45} + \frac{13}{45}$

Step 2.1.2.2.3

Combine the numerators over the common denominator.

$\frac{59}{9} - y = \frac{49}{15} + \frac{2 \cdot 45 + 13}{45}$

Step 2.1.2.2.4

Simplify the numerator.

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Step 2.1.2.2.4.1

Multiply $2$ by $45$ .

$\frac{59}{9} - y = \frac{49}{15} + \frac{90 + 13}{45}$

Step 2.1.2.2.4.2

Add $90$ and $13$ .

$\frac{59}{9} - y = \frac{49}{15} + \frac{103}{45}$

Step 2.1.3

To write $\frac{49}{15}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{59}{9} - y = \frac{49}{15} \cdot \frac{3}{3} + \frac{103}{45}$

Step 2.1.4

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.4.1

Multiply $\frac{49}{15}$ by $\frac{3}{3}$ .

$\frac{59}{9} - y = \frac{49 \cdot 3}{15 \cdot 3} + \frac{103}{45}$

Step 2.1.4.2

Multiply $15$ by $3$ .

$\frac{59}{9} - y = \frac{49 \cdot 3}{45} + \frac{103}{45}$

Step 2.1.5

Combine the numerators over the common denominator.

$\frac{59}{9} - y = \frac{49 \cdot 3 + 103}{45}$

Step 2.1.6

Simplify the numerator.

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Step 2.1.6.1

Multiply $49$ by $3$ .

$\frac{59}{9} - y = \frac{147 + 103}{45}$

Step 2.1.6.2

Add $147$ and $103$ .

$\frac{59}{9} - y = \frac{250}{45}$

Step 2.1.7

Cancel the common factor of $250$ and $45$ .

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Step 2.1.7.1

Factor $5$ out of $250$ .

$\frac{59}{9} - y = \frac{5 (50)}{45}$

Step 2.1.7.2

Cancel the common factors.

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Step 2.1.7.2.1

Factor $5$ out of $45$ .

$\frac{59}{9} - y = \frac{5 \cdot 50}{5 \cdot 9}$

Step 2.1.7.2.2

Cancel the common factor.

$\frac{59}{9} - y = \frac{5 \cdot 50}{5 \cdot 9}$

Step 2.1.7.2.3

Rewrite the expression.

$\frac{59}{9} - y = \frac{50}{9}$

Step 3

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

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Step 3.1

Subtract $\frac{59}{9}$ from both sides of the equation.

$- y = \frac{50}{9} - \frac{59}{9}$

Step 3.2

Combine the numerators over the common denominator.

$- y = \frac{50 - 59}{9}$

Step 3.3

Subtract $59$ from $50$ .

$- y = \frac{- 9}{9}$

Step 3.4

Divide $- 9$ by $9$ .

$- y = - 1$

Step 4

Divide each term in $- y = - 1$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y = - 1$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 1}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 1}{- 1}$

Step 4.2.2

Divide $y$ by $1$ .

$y = \frac{- 1}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 1$ by $- 1$ .

$y = 1$