Algebra Examples

$3 \frac{1}{3} (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{3} (y + 1 \frac{1}{8})$ .

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Step 1.1.1

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

$(3 + \frac{1}{3}) (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

$(3 \cdot \frac{3}{3} + \frac{1}{3}) (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.1.2.2

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

$(\frac{3 \cdot 3}{3} + \frac{1}{3}) (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 1}{3} (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 1}{3} (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.1.2.4.2

Add $9$ and $1$ .

$\frac{10}{3} (y + 1 \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.2

Convert $1 \frac{1}{8}$ 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.

$\frac{10}{3} (y + 1 + \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.2.2

Add $1$ and $\frac{1}{8}$ .

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Step 1.1.2.2.1

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

$\frac{10}{3} (y + \frac{8}{8} + \frac{1}{8}) = 6 \frac{11}{12}$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{10}{3} (y + \frac{8 + 1}{8}) = 6 \frac{11}{12}$

Step 1.1.2.2.3

Add $8$ and $1$ .

$\frac{10}{3} (y + \frac{9}{8}) = 6 \frac{11}{12}$

Step 1.1.3

Apply the distributive property.

$\frac{10}{3} y + \frac{10}{3} \cdot \frac{9}{8} = 6 \frac{11}{12}$

Step 1.1.4

Combine $\frac{10}{3}$ and $y$ .

$\frac{10 y}{3} + \frac{10}{3} \cdot \frac{9}{8} = 6 \frac{11}{12}$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

Factor $2$ out of $10$ .

$\frac{10 y}{3} + \frac{2 (5)}{3} \cdot \frac{9}{8} = 6 \frac{11}{12}$

Step 1.1.5.2

Factor $2$ out of $8$ .

$\frac{10 y}{3} + \frac{2 \cdot 5}{3} \cdot \frac{9}{2 \cdot 4} = 6 \frac{11}{12}$

Step 1.1.5.3

Cancel the common factor.

$\frac{10 y}{3} + \frac{2 \cdot 5}{3} \cdot \frac{9}{2 \cdot 4} = 6 \frac{11}{12}$

Step 1.1.5.4

Rewrite the expression.

$\frac{10 y}{3} + \frac{5}{3} \cdot \frac{9}{4} = 6 \frac{11}{12}$

Step 1.1.6

Cancel the common factor of $3$ .

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Step 1.1.6.1

Factor $3$ out of $9$ .

$\frac{10 y}{3} + \frac{5}{3} \cdot \frac{3 (3)}{4} = 6 \frac{11}{12}$

Step 1.1.6.2

Cancel the common factor.

$\frac{10 y}{3} + \frac{5}{3} \cdot \frac{3 \cdot 3}{4} = 6 \frac{11}{12}$

Step 1.1.6.3

Rewrite the expression.

$\frac{10 y}{3} + 5 (\frac{3}{4}) = 6 \frac{11}{12}$

Step 1.1.7

Combine $5$ and $\frac{3}{4}$ .

$\frac{10 y}{3} + \frac{5 \cdot 3}{4} = 6 \frac{11}{12}$

Step 1.1.8

Multiply $5$ by $3$ .

$\frac{10 y}{3} + \frac{15}{4} = 6 \frac{11}{12}$

Step 2

Simplify the right side.

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Step 2.1

Convert $6 \frac{11}{12}$ to an improper fraction.

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Step 2.1.1

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

$\frac{10 y}{3} + \frac{15}{4} = 6 + \frac{11}{12}$

Step 2.1.2

Add $6$ and $\frac{11}{12}$ .

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Step 2.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{10 y}{3} + \frac{15}{4} = 6 \cdot \frac{12}{12} + \frac{11}{12}$

Step 2.1.2.2

Combine $6$ and $\frac{12}{12}$ .

$\frac{10 y}{3} + \frac{15}{4} = \frac{6 \cdot 12}{12} + \frac{11}{12}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{10 y}{3} + \frac{15}{4} = \frac{6 \cdot 12 + 11}{12}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $6$ by $12$ .

$\frac{10 y}{3} + \frac{15}{4} = \frac{72 + 11}{12}$

Step 2.1.2.4.2

Add $72$ and $11$ .

$\frac{10 y}{3} + \frac{15}{4} = \frac{83}{12}$

Step 3

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

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Step 3.1

Subtract $\frac{15}{4}$ from both sides of the equation.

$\frac{10 y}{3} = \frac{83}{12} - \frac{15}{4}$

Step 3.2

To write $- \frac{15}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10 y}{3} = \frac{83}{12} - \frac{15}{4} \cdot \frac{3}{3}$

Step 3.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{15}{4}$ by $\frac{3}{3}$ .

$\frac{10 y}{3} = \frac{83}{12} - \frac{15 \cdot 3}{4 \cdot 3}$

Step 3.3.2

Multiply $4$ by $3$ .

$\frac{10 y}{3} = \frac{83}{12} - \frac{15 \cdot 3}{12}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{10 y}{3} = \frac{83 - 15 \cdot 3}{12}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 15$ by $3$ .

$\frac{10 y}{3} = \frac{83 - 45}{12}$

Step 3.5.2

Subtract $45$ from $83$ .

$\frac{10 y}{3} = \frac{38}{12}$

Step 3.6

Cancel the common factor of $38$ and $12$ .

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Step 3.6.1

Factor $2$ out of $38$ .

$\frac{10 y}{3} = \frac{2 (19)}{12}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $2$ out of $12$ .

$\frac{10 y}{3} = \frac{2 \cdot 19}{2 \cdot 6}$

Step 3.6.2.2

Cancel the common factor.

$\frac{10 y}{3} = \frac{2 \cdot 19}{2 \cdot 6}$

Step 3.6.2.3

Rewrite the expression.

$\frac{10 y}{3} = \frac{19}{6}$

Step 4

Multiply both sides of the equation by $\frac{3}{10}$ .

$\frac{3}{10} \cdot \frac{10 y}{3} = \frac{3}{10} \cdot \frac{19}{6}$

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 $\frac{3}{10} \cdot \frac{10 y}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{10} \cdot \frac{10 y}{3} = \frac{3}{10} \cdot \frac{19}{6}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 y) = \frac{3}{10} \cdot \frac{19}{6}$

Step 5.1.1.2

Cancel the common factor of $10$ .

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Step 5.1.1.2.1

Factor $10$ out of $10 y$ .

$\frac{1}{10} (10 (y)) = \frac{3}{10} \cdot \frac{19}{6}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 y) = \frac{3}{10} \cdot \frac{19}{6}$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{3}{10} \cdot \frac{19}{6}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{10} \cdot \frac{19}{6}$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $6$ .

$y = \frac{3}{10} \cdot \frac{19}{3 (2)}$

Step 5.2.1.1.2

Cancel the common factor.

$y = \frac{3}{10} \cdot \frac{19}{3 \cdot 2}$

Step 5.2.1.1.3

Rewrite the expression.

$y = \frac{1}{10} \cdot \frac{19}{2}$

Step 5.2.1.2

Multiply $\frac{1}{10}$ by $\frac{19}{2}$ .

$y = \frac{19}{10 \cdot 2}$

Step 5.2.1.3

Multiply $10$ by $2$ .

$y = \frac{19}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{19}{20}$

Decimal Form:

$y = 0.95$