Basic Math Examples

$3 \frac{1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1

Simplify the left side.

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Step 1.1

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

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

$3 + \frac{1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1.1.2

Add $3$ and $\frac{1}{2}$ .

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Step 1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 \cdot \frac{2}{2} + \frac{1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1.1.2.2

Combine $3$ and $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + \frac{1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $3$ by $2$ .

$\frac{6 + 1}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 1.1.2.4.2

Add $6$ and $1$ .

$\frac{7}{2} + \frac{7 y}{10} = \frac{13}{20}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{2}$ from both sides of the equation.

$\frac{7 y}{10} = \frac{13}{20} - \frac{7}{2}$

Step 2.2

To write $- \frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{7 y}{10} = \frac{13}{20} - \frac{7}{2} \cdot \frac{10}{10}$

Step 2.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{7}{2}$ by $\frac{10}{10}$ .

$\frac{7 y}{10} = \frac{13}{20} - \frac{7 \cdot 10}{2 \cdot 10}$

Step 2.3.2

Multiply $2$ by $10$ .

$\frac{7 y}{10} = \frac{13}{20} - \frac{7 \cdot 10}{20}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 y}{10} = \frac{13 - 7 \cdot 10}{20}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 7$ by $10$ .

$\frac{7 y}{10} = \frac{13 - 70}{20}$

Step 2.5.2

Subtract $70$ from $13$ .

$\frac{7 y}{10} = \frac{- 57}{20}$

Step 2.6

Move the negative in front of the fraction.

$\frac{7 y}{10} = - \frac{57}{20}$

Step 3

Multiply both sides of the equation by $\frac{10}{7}$ .

$\frac{10}{7} \cdot \frac{7 y}{10} = \frac{10}{7} (- \frac{57}{20})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{10}{7} \cdot \frac{7 y}{10}$ .

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Step 4.1.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{10}{7} \cdot \frac{7 y}{10} = \frac{10}{7} (- \frac{57}{20})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 y) = \frac{10}{7} (- \frac{57}{20})$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 y$ .

$\frac{1}{7} (7 (y)) = \frac{10}{7} (- \frac{57}{20})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 y) = \frac{10}{7} (- \frac{57}{20})$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{10}{7} (- \frac{57}{20})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{10}{7} (- \frac{57}{20})$ .

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Step 4.2.1.1

Cancel the common factor of $10$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{57}{20}$ into the numerator.

$y = \frac{10}{7} \cdot \frac{- 57}{20}$

Step 4.2.1.1.2

Factor $10$ out of $20$ .

$y = \frac{10}{7} \cdot \frac{- 57}{10 (2)}$

Step 4.2.1.1.3

Cancel the common factor.

$y = \frac{10}{7} \cdot \frac{- 57}{10 \cdot 2}$

Step 4.2.1.1.4

Rewrite the expression.

$y = \frac{1}{7} \cdot \frac{- 57}{2}$

Step 4.2.1.2

Multiply $\frac{1}{7}$ by $\frac{- 57}{2}$ .

$y = \frac{- 57}{7 \cdot 2}$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $7$ by $2$ .

$y = \frac{- 57}{14}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$y = - \frac{57}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{57}{14}$

Decimal Form:

$y = - 4.07142857 \dots$

Mixed Number Form:

$y = - 4 \frac{1}{14}$