Basic Math Examples

$3 \frac{1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{5} - 1 \frac{3}{10}$ .

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Step 1.1.1

Convert $3 \frac{1}{5}$ 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.

$3 + \frac{1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.1.2

Add $3$ and $\frac{1}{5}$ .

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Step 1.1.1.2.1

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

$3 \cdot \frac{5}{5} + \frac{1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.1.2.2

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

$\frac{3 \cdot 5}{5} + \frac{1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 + 1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $5$ .

$\frac{15 + 1}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.1.2.4.2

Add $15$ and $1$ .

$\frac{16}{5} - 1 \frac{3}{10} = y + \frac{5}{6}$

Step 1.1.2

Convert $1 \frac{3}{10}$ 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.

$\frac{16}{5} - (1 + \frac{3}{10}) = y + \frac{5}{6}$

Step 1.1.2.2

Add $1$ and $\frac{3}{10}$ .

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Step 1.1.2.2.1

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

$\frac{16}{5} - (\frac{10}{10} + \frac{3}{10}) = y + \frac{5}{6}$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{16}{5} - \frac{10 + 3}{10} = y + \frac{5}{6}$

Step 1.1.2.2.3

Add $10$ and $3$ .

$\frac{16}{5} - \frac{13}{10} = y + \frac{5}{6}$

Step 1.1.3

To write $\frac{16}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{16}{5} \cdot \frac{2}{2} - \frac{13}{10} = y + \frac{5}{6}$

Step 1.1.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.4.1

Multiply $\frac{16}{5}$ by $\frac{2}{2}$ .

$\frac{16 \cdot 2}{5 \cdot 2} - \frac{13}{10} = y + \frac{5}{6}$

Step 1.1.4.2

Multiply $5$ by $2$ .

$\frac{16 \cdot 2}{10} - \frac{13}{10} = y + \frac{5}{6}$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 - 13}{10} = y + \frac{5}{6}$

Step 1.1.6

Simplify the numerator.

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Step 1.1.6.1

Multiply $16$ by $2$ .

$\frac{32 - 13}{10} = y + \frac{5}{6}$

Step 1.1.6.2

Subtract $13$ from $32$ .

$\frac{19}{10} = y + \frac{5}{6}$

Step 2

Rewrite the equation as $y + \frac{5}{6} = \frac{19}{10}$ .

$y + \frac{5}{6} = \frac{19}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{5}{6}$ from both sides of the equation.

$y = \frac{19}{10} - \frac{5}{6}$

Step 3.2

To write $\frac{19}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{19}{10} \cdot \frac{3}{3} - \frac{5}{6}$

Step 3.3

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{19}{10} \cdot \frac{3}{3} - \frac{5}{6} \cdot \frac{5}{5}$

Step 3.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{19}{10}$ by $\frac{3}{3}$ .

$y = \frac{19 \cdot 3}{10 \cdot 3} - \frac{5}{6} \cdot \frac{5}{5}$

Step 3.4.2

Multiply $10$ by $3$ .

$y = \frac{19 \cdot 3}{30} - \frac{5}{6} \cdot \frac{5}{5}$

Step 3.4.3

Multiply $\frac{5}{6}$ by $\frac{5}{5}$ .

$y = \frac{19 \cdot 3}{30} - \frac{5 \cdot 5}{6 \cdot 5}$

Step 3.4.4

Multiply $6$ by $5$ .

$y = \frac{19 \cdot 3}{30} - \frac{5 \cdot 5}{30}$

Step 3.5

Combine the numerators over the common denominator.

$y = \frac{19 \cdot 3 - 5 \cdot 5}{30}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $19$ by $3$ .

$y = \frac{57 - 5 \cdot 5}{30}$

Step 3.6.2

Multiply $- 5$ by $5$ .

$y = \frac{57 - 25}{30}$

Step 3.6.3

Subtract $25$ from $57$ .

$y = \frac{32}{30}$

Step 3.7

Cancel the common factor of $32$ and $30$ .

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Step 3.7.1

Factor $2$ out of $32$ .

$y = \frac{2 (16)}{30}$

Step 3.7.2

Cancel the common factors.

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Step 3.7.2.1

Factor $2$ out of $30$ .

$y = \frac{2 \cdot 16}{2 \cdot 15}$

Step 3.7.2.2

Cancel the common factor.

$y = \frac{2 \cdot 16}{2 \cdot 15}$

Step 3.7.2.3

Rewrite the expression.

$y = \frac{16}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{16}{15}$

Decimal Form:

$y = 1.0\overline{6}$

Mixed Number Form:

$y = 1 \frac{1}{15}$