Basic Math Examples

$8 \frac{3}{5} - 4 \frac{1}{2}$

Step 1

Convert $8 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{3}{5} - 4 \frac{1}{2}$

Step 1.2

Add $8$ and $\frac{3}{5}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 \cdot \frac{5}{5} + \frac{3}{5} - 4 \frac{1}{2}$

Step 1.2.2

Combine $8$ and $\frac{5}{5}$ .

$\frac{8 \cdot 5}{5} + \frac{3}{5} - 4 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 5 + 3}{5} - 4 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $5$ .

$\frac{40 + 3}{5} - 4 \frac{1}{2}$

Step 1.2.4.2

Add $40$ and $3$ .

$\frac{43}{5} - 4 \frac{1}{2}$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{43}{5} - (4 + \frac{1}{2})$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.2.1

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

$\frac{43}{5} - (4 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{43}{5} - (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{43}{5} - \frac{4 \cdot 2 + 1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$\frac{43}{5} - \frac{8 + 1}{2}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{43}{5} - \frac{9}{2}$

Step 3

To write $\frac{43}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{43}{5} \cdot \frac{2}{2} - \frac{9}{2}$

Step 4

To write $- \frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{43}{5} \cdot \frac{2}{2} - \frac{9}{2} \cdot \frac{5}{5}$

Step 5

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

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Step 5.1

Multiply $\frac{43}{5}$ by $\frac{2}{2}$ .

$\frac{43 \cdot 2}{5 \cdot 2} - \frac{9}{2} \cdot \frac{5}{5}$

Step 5.2

Multiply $5$ by $2$ .

$\frac{43 \cdot 2}{10} - \frac{9}{2} \cdot \frac{5}{5}$

Step 5.3

Multiply $\frac{9}{2}$ by $\frac{5}{5}$ .

$\frac{43 \cdot 2}{10} - \frac{9 \cdot 5}{2 \cdot 5}$

Step 5.4

Multiply $2$ by $5$ .

$\frac{43 \cdot 2}{10} - \frac{9 \cdot 5}{10}$

Step 6

Combine the numerators over the common denominator.

$\frac{43 \cdot 2 - 9 \cdot 5}{10}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $43$ by $2$ .

$\frac{86 - 9 \cdot 5}{10}$

Step 7.2

Multiply $- 9$ by $5$ .

$\frac{86 - 45}{10}$

Step 7.3

Subtract $45$ from $86$ .

$\frac{41}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{41}{10}$

Decimal Form:

$4.1$

Mixed Number Form:

$4 \frac{1}{10}$