Basic Math Examples

$4 \frac{2}{15} - 2 \frac{11}{45}$

Step 1

Convert

$4 \frac{2}{15}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{2}{15} - 2 \frac{11}{45}$

Step 1.2

Add

$4$ and

$\frac{2}{15}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{15}{15}$ .

$4 \cdot \frac{15}{15} + \frac{2}{15} - 2 \frac{11}{45}$

Step 1.2.2

Combine

$4$ and

$\frac{15}{15}$ .

$\frac{4 \cdot 15}{15} + \frac{2}{15} - 2 \frac{11}{45}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 15 + 2}{15} - 2 \frac{11}{45}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$15$ .

$\frac{60 + 2}{15} - 2 \frac{11}{45}$

Step 1.2.4.2

Add

$60$ and

$2$ .

$\frac{62}{15} - 2 \frac{11}{45}$

Step 2

Convert

$2 \frac{11}{45}$ to an improper fraction.

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Step 2.1

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

$\frac{62}{15} - (2 + \frac{11}{45})$

Step 2.2

Add

$2$ and

$\frac{11}{45}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{45}{45}$ .

$\frac{62}{15} - (2 \cdot \frac{45}{45} + \frac{11}{45})$

Step 2.2.2

Combine

$2$ and

$\frac{45}{45}$ .

$\frac{62}{15} - (\frac{2 \cdot 45}{45} + \frac{11}{45})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{62}{15} - \frac{2 \cdot 45 + 11}{45}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$45$ .

$\frac{62}{15} - \frac{90 + 11}{45}$

Step 2.2.4.2

Add

$90$ and

$11$ .

$\frac{62}{15} - \frac{101}{45}$

Step 3

To write

$\frac{62}{15}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{62}{15} \cdot \frac{3}{3} - \frac{101}{45}$

Step 4

Write each expression with a common denominator of

$45$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{62}{15}$ by

$\frac{3}{3}$ .

$\frac{62 \cdot 3}{15 \cdot 3} - \frac{101}{45}$

Step 4.2

Multiply

$15$ by

$3$ .

$\frac{62 \cdot 3}{45} - \frac{101}{45}$

Step 5

Combine the numerators over the common denominator.

$\frac{62 \cdot 3 - 101}{45}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$62$ by

$3$ .

$\frac{186 - 101}{45}$

Step 6.2

Subtract

$101$ from

$186$ .

$\frac{85}{45}$

Step 7

Cancel the common factor of

$85$ and

$45$ .

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Step 7.1

Factor

$5$ out of

$85$ .

$\frac{5 (17)}{45}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

$5$ out of

$45$ .

$\frac{5 \cdot 17}{5 \cdot 9}$

Step 7.2.2

Cancel the common factor.

$\frac{5 \cdot 17}{5 \cdot 9}$

Step 7.2.3

Rewrite the expression.

$\frac{17}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{9}$

Decimal Form:

$1.\overline{8}$

Mixed Number Form:

$1 \frac{8}{9}$