Basic Math Examples

$99 \frac{77}{99} - y = \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $99 \frac{77}{99} - y$ .

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Step 1.1.1

Convert $99 \frac{77}{99}$ 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.

$99 + \frac{77}{99} - y = \frac{1}{2}$

Step 1.1.1.2

Add $99$ and $\frac{77}{99}$ .

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Step 1.1.1.2.1

To write $99$ as a fraction with a common denominator, multiply by $\frac{99}{99}$ .

$99 \cdot \frac{99}{99} + \frac{77}{99} - y = \frac{1}{2}$

Step 1.1.1.2.2

Combine $99$ and $\frac{99}{99}$ .

$\frac{99 \cdot 99}{99} + \frac{77}{99} - y = \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{99 \cdot 99 + 77}{99} - y = \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $99$ by $99$ .

$\frac{9801 + 77}{99} - y = \frac{1}{2}$

Step 1.1.1.2.4.2

Add $9801$ and $77$ .

$\frac{9878}{99} - y = \frac{1}{2}$

Step 1.1.2

Cancel the common factor of $9878$ and $99$ .

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Step 1.1.2.1

Factor $11$ out of $9878$ .

$\frac{11 (898)}{99} - y = \frac{1}{2}$

Step 1.1.2.2

Cancel the common factors.

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Step 1.1.2.2.1

Factor $11$ out of $99$ .

$\frac{11 \cdot 898}{11 \cdot 9} - y = \frac{1}{2}$

Step 1.1.2.2.2

Cancel the common factor.

$\frac{11 \cdot 898}{11 \cdot 9} - y = \frac{1}{2}$

Step 1.1.2.2.3

Rewrite the expression.

$\frac{898}{9} - y = \frac{1}{2}$

Step 2

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

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Step 2.1

Subtract $\frac{898}{9}$ from both sides of the equation.

$- y = \frac{1}{2} - \frac{898}{9}$

Step 2.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- y = \frac{1}{2} \cdot \frac{9}{9} - \frac{898}{9}$

Step 2.3

To write $- \frac{898}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- y = \frac{1}{2} \cdot \frac{9}{9} - \frac{898}{9} \cdot \frac{2}{2}$

Step 2.4

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

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Step 2.4.1

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$- y = \frac{9}{2 \cdot 9} - \frac{898}{9} \cdot \frac{2}{2}$

Step 2.4.2

Multiply $2$ by $9$ .

$- y = \frac{9}{18} - \frac{898}{9} \cdot \frac{2}{2}$

Step 2.4.3

Multiply $\frac{898}{9}$ by $\frac{2}{2}$ .

$- y = \frac{9}{18} - \frac{898 \cdot 2}{9 \cdot 2}$

Step 2.4.4

Multiply $9$ by $2$ .

$- y = \frac{9}{18} - \frac{898 \cdot 2}{18}$

Step 2.5

Combine the numerators over the common denominator.

$- y = \frac{9 - 898 \cdot 2}{18}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 898$ by $2$ .

$- y = \frac{9 - 1796}{18}$

Step 2.6.2

Subtract $1796$ from $9$ .

$- y = \frac{- 1787}{18}$

Step 2.7

Move the negative in front of the fraction.

$- y = - \frac{1787}{18}$

Step 3

Divide each term in $- y = - \frac{1787}{18}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = - \frac{1787}{18}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- \frac{1787}{18}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- \frac{1787}{18}}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{- \frac{1787}{18}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$y = \frac{\frac{1787}{18}}{1}$

Step 3.3.2

Divide $\frac{1787}{18}$ by $1$ .

$y = \frac{1787}{18}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1787}{18}$

Decimal Form:

$y = 99.2\overline{7}$

Mixed Number Form:

$y = 99 \frac{5}{18}$