Basic Math Examples

$7 \frac{1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1

Convert $7 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$7 + \frac{1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1.2

Add $7$ and $\frac{1}{5}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$7 \cdot \frac{5}{5} + \frac{1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{7 \cdot 5}{5} + \frac{1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 5 + 1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $5$ .

$\frac{35 + 1}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 1.2.4.2

Add $35$ and $1$ .

$\frac{36}{5} - 4 \frac{1}{8} \div 1 \frac{1}{4}$

Step 2

Convert $4 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{36}{5} - (4 + \frac{1}{8}) \div 1 \frac{1}{4}$

Step 2.2

Add $4$ and $\frac{1}{8}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{36}{5} - (4 \cdot \frac{8}{8} + \frac{1}{8}) \div 1 \frac{1}{4}$

Step 2.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{36}{5} - (\frac{4 \cdot 8}{8} + \frac{1}{8}) \div 1 \frac{1}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{36}{5} - \frac{4 \cdot 8 + 1}{8} \div 1 \frac{1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $8$ .

$\frac{36}{5} - \frac{32 + 1}{8} \div 1 \frac{1}{4}$

Step 2.2.4.2

Add $32$ and $1$ .

$\frac{36}{5} - \frac{33}{8} \div 1 \frac{1}{4}$

Step 3

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

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Step 3.1

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

$\frac{36}{5} - \frac{33}{8} \div (1 + \frac{1}{4})$

Step 3.2

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

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Step 3.2.1

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

$\frac{36}{5} - \frac{33}{8} \div (\frac{4}{4} + \frac{1}{4})$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{36}{5} - \frac{33}{8} \div \frac{4 + 1}{4}$

Step 3.2.3

Add $4$ and $1$ .

$\frac{36}{5} - \frac{33}{8} \div \frac{5}{4}$

Step 4

Simplify each term.

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Step 4.1

To divide by a fraction, multiply by its reciprocal.

$\frac{36}{5} - (\frac{33}{8} \cdot \frac{4}{5})$

Step 4.2

Cancel the common factor of $4$ .

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Step 4.2.1

Factor $4$ out of $8$ .

$\frac{36}{5} - (\frac{33}{4 (2)} \cdot \frac{4}{5})$

Step 4.2.2

Cancel the common factor.

$\frac{36}{5} - (\frac{33}{4 \cdot 2} \cdot \frac{4}{5})$

Step 4.2.3

Rewrite the expression.

$\frac{36}{5} - (\frac{33}{2} \cdot \frac{1}{5})$

Step 4.3

Multiply $\frac{33}{2}$ by $\frac{1}{5}$ .

$\frac{36}{5} - \frac{33}{2 \cdot 5}$

Step 4.4

Multiply $2$ by $5$ .

$\frac{36}{5} - \frac{33}{10}$

Step 5

To write $\frac{36}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{36}{5} \cdot \frac{2}{2} - \frac{33}{10}$

Step 6

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

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Step 6.1

Multiply $\frac{36}{5}$ by $\frac{2}{2}$ .

$\frac{36 \cdot 2}{5 \cdot 2} - \frac{33}{10}$

Step 6.2

Multiply $5$ by $2$ .

$\frac{36 \cdot 2}{10} - \frac{33}{10}$

Step 7

Combine the numerators over the common denominator.

$\frac{36 \cdot 2 - 33}{10}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $36$ by $2$ .

$\frac{72 - 33}{10}$

Step 8.2

Subtract $33$ from $72$ .

$\frac{39}{10}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{39}{10}$

Decimal Form:

$3.9$

Mixed Number Form:

$3 \frac{9}{10}$