Basic Math Examples

$3 \frac{1}{15} - 1 \frac{3}{20}$

Step 1

Convert $3 \frac{1}{15}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{1}{15} - 1 \frac{3}{20}$

Step 1.2

Add $3$ and $\frac{1}{15}$ .

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Step 1.2.1

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

$3 \cdot \frac{15}{15} + \frac{1}{15} - 1 \frac{3}{20}$

Step 1.2.2

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

$\frac{3 \cdot 15}{15} + \frac{1}{15} - 1 \frac{3}{20}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 15 + 1}{15} - 1 \frac{3}{20}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $15$ .

$\frac{45 + 1}{15} - 1 \frac{3}{20}$

Step 1.2.4.2

Add $45$ and $1$ .

$\frac{46}{15} - 1 \frac{3}{20}$

Step 2

Convert $1 \frac{3}{20}$ to an improper fraction.

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Step 2.1

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

$\frac{46}{15} - (1 + \frac{3}{20})$

Step 2.2

Add $1$ and $\frac{3}{20}$ .

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Step 2.2.1

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

$\frac{46}{15} - (\frac{20}{20} + \frac{3}{20})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{46}{15} - \frac{20 + 3}{20}$

Step 2.2.3

Add $20$ and $3$ .

$\frac{46}{15} - \frac{23}{20}$

Step 3

To write $\frac{46}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{46}{15} \cdot \frac{4}{4} - \frac{23}{20}$

Step 4

To write $- \frac{23}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{46}{15} \cdot \frac{4}{4} - \frac{23}{20} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{46}{15}$ by $\frac{4}{4}$ .

$\frac{46 \cdot 4}{15 \cdot 4} - \frac{23}{20} \cdot \frac{3}{3}$

Step 5.2

Multiply $15$ by $4$ .

$\frac{46 \cdot 4}{60} - \frac{23}{20} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{23}{20}$ by $\frac{3}{3}$ .

$\frac{46 \cdot 4}{60} - \frac{23 \cdot 3}{20 \cdot 3}$

Step 5.4

Multiply $20$ by $3$ .

$\frac{46 \cdot 4}{60} - \frac{23 \cdot 3}{60}$

Step 6

Combine the numerators over the common denominator.

$\frac{46 \cdot 4 - 23 \cdot 3}{60}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $46$ by $4$ .

$\frac{184 - 23 \cdot 3}{60}$

Step 7.2

Multiply $- 23$ by $3$ .

$\frac{184 - 69}{60}$

Step 7.3

Subtract $69$ from $184$ .

$\frac{115}{60}$

Step 8

Cancel the common factor of $115$ and $60$ .

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Step 8.1

Factor $5$ out of $115$ .

$\frac{5 (23)}{60}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $60$ .

$\frac{5 \cdot 23}{5 \cdot 12}$

Step 8.2.2

Cancel the common factor.

$\frac{5 \cdot 23}{5 \cdot 12}$

Step 8.2.3

Rewrite the expression.

$\frac{23}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{12}$

Decimal Form:

$1.91\overline{6}$

Mixed Number Form:

$1 \frac{11}{12}$