Algebra Examples

$8 \frac{6}{10} - 4 \frac{7}{12}$

Step 1

Convert $8 \frac{6}{10}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{6}{10} - 4 \frac{7}{12}$

Step 1.2

Add $8$ and $\frac{6}{10}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$8 \cdot \frac{10}{10} + \frac{6}{10} - 4 \frac{7}{12}$

Step 1.2.2

Combine $8$ and $\frac{10}{10}$ .

$\frac{8 \cdot 10}{10} + \frac{6}{10} - 4 \frac{7}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 10 + 6}{10} - 4 \frac{7}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $10$ .

$\frac{80 + 6}{10} - 4 \frac{7}{12}$

Step 1.2.4.2

Add $80$ and $6$ .

$\frac{86}{10} - 4 \frac{7}{12}$

Step 2

Convert $4 \frac{7}{12}$ to an improper fraction.

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Step 2.1

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

$\frac{86}{10} - (4 + \frac{7}{12})$

Step 2.2

Add $4$ and $\frac{7}{12}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{86}{10} - (4 \cdot \frac{12}{12} + \frac{7}{12})$

Step 2.2.2

Combine $4$ and $\frac{12}{12}$ .

$\frac{86}{10} - (\frac{4 \cdot 12}{12} + \frac{7}{12})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{86}{10} - \frac{4 \cdot 12 + 7}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $12$ .

$\frac{86}{10} - \frac{48 + 7}{12}$

Step 2.2.4.2

Add $48$ and $7$ .

$\frac{86}{10} - \frac{55}{12}$

Step 3

Cancel the common factor of $86$ and $10$ .

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Step 3.1

Factor $2$ out of $86$ .

$\frac{2 (43)}{10} - \frac{55}{12}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot 43}{2 \cdot 5} - \frac{55}{12}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \cdot 43}{2 \cdot 5} - \frac{55}{12}$

Step 3.2.3

Rewrite the expression.

$\frac{43}{5} - \frac{55}{12}$

Step 4

To write $\frac{43}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{43}{5} \cdot \frac{12}{12} - \frac{55}{12}$

Step 5

To write $- \frac{55}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{43}{5} \cdot \frac{12}{12} - \frac{55}{12} \cdot \frac{5}{5}$

Step 6

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

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Step 6.1

Multiply $\frac{43}{5}$ by $\frac{12}{12}$ .

$\frac{43 \cdot 12}{5 \cdot 12} - \frac{55}{12} \cdot \frac{5}{5}$

Step 6.2

Multiply $5$ by $12$ .

$\frac{43 \cdot 12}{60} - \frac{55}{12} \cdot \frac{5}{5}$

Step 6.3

Multiply $\frac{55}{12}$ by $\frac{5}{5}$ .

$\frac{43 \cdot 12}{60} - \frac{55 \cdot 5}{12 \cdot 5}$

Step 6.4

Multiply $12$ by $5$ .

$\frac{43 \cdot 12}{60} - \frac{55 \cdot 5}{60}$

Step 7

Combine the numerators over the common denominator.

$\frac{43 \cdot 12 - 55 \cdot 5}{60}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $43$ by $12$ .

$\frac{516 - 55 \cdot 5}{60}$

Step 8.2

Multiply $- 55$ by $5$ .

$\frac{516 - 275}{60}$

Step 8.3

Subtract $275$ from $516$ .

$\frac{241}{60}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{241}{60}$

Decimal Form:

$4.01\overline{6}$

Mixed Number Form:

$4 \frac{1}{60}$