Basic Math Examples

$(1 \frac{1}{4} - \frac{2}{5}) \div \frac{1}{10}$

Step 1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{1}{4} - \frac{2}{5}) \div \frac{1}{10}$

Step 1.2

Add $1$ and $\frac{1}{4}$ .

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Step 1.2.1

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

$(\frac{4}{4} + \frac{1}{4} - \frac{2}{5}) \div \frac{1}{10}$

Step 1.2.2

Combine the numerators over the common denominator.

$(\frac{4 + 1}{4} - \frac{2}{5}) \div \frac{1}{10}$

Step 1.2.3

Add $4$ and $1$ .

$(\frac{5}{4} - \frac{2}{5}) \div \frac{1}{10}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(\frac{5}{4} - \frac{2}{5}) \cdot 10$

Step 3

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{5}{4} \cdot \frac{5}{5} - \frac{2}{5}) \cdot 10$

Step 4

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{5}{4} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{4}{4}) \cdot 10$

Step 5

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

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Step 5.1

Multiply $\frac{5}{4}$ by $\frac{5}{5}$ .

$(\frac{5 \cdot 5}{4 \cdot 5} - \frac{2}{5} \cdot \frac{4}{4}) \cdot 10$

Step 5.2

Multiply $4$ by $5$ .

$(\frac{5 \cdot 5}{20} - \frac{2}{5} \cdot \frac{4}{4}) \cdot 10$

Step 5.3

Multiply $\frac{2}{5}$ by $\frac{4}{4}$ .

$(\frac{5 \cdot 5}{20} - \frac{2 \cdot 4}{5 \cdot 4}) \cdot 10$

Step 5.4

Multiply $5$ by $4$ .

$(\frac{5 \cdot 5}{20} - \frac{2 \cdot 4}{20}) \cdot 10$

Step 6

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 2 \cdot 4}{20} \cdot 10$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $5$ by $5$ .

$\frac{25 - 2 \cdot 4}{20} \cdot 10$

Step 7.2

Multiply $- 2$ by $4$ .

$\frac{25 - 8}{20} \cdot 10$

Step 7.3

Subtract $8$ from $25$ .

$\frac{17}{20} \cdot 10$

Step 8

Cancel the common factor of $10$ .

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Step 8.1

Factor $10$ out of $20$ .

$\frac{17}{10 (2)} \cdot 10$

Step 8.2

Cancel the common factor.

$\frac{17}{10 \cdot 2} \cdot 10$

Step 8.3

Rewrite the expression.

$\frac{17}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{2}$

Decimal Form:

$8.5$

Mixed Number Form:

$8 \frac{1}{2}$