Basic Math Examples

$\frac{4}{3} - (1 \frac{11}{12} - \frac{5}{4})$

Step 1

Convert $1 \frac{11}{12}$ to an improper fraction.

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Step 1.1

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

$\frac{4}{3} - (1 + \frac{11}{12} - \frac{5}{4})$

Step 1.2

Add $1$ and $\frac{11}{12}$ .

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Step 1.2.1

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

$\frac{4}{3} - (\frac{12}{12} + \frac{11}{12} - \frac{5}{4})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4}{3} - (\frac{12 + 11}{12} - \frac{5}{4})$

Step 1.2.3

Add $12$ and $11$ .

$\frac{4}{3} - (\frac{23}{12} - \frac{5}{4})$

Step 2

To write $- \frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{3} - (\frac{23}{12} - \frac{5}{4} \cdot \frac{3}{3})$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$\frac{4}{3} - (\frac{23}{12} - \frac{5 \cdot 3}{4 \cdot 3})$

Step 3.2

Multiply $4$ by $3$ .

$\frac{4}{3} - (\frac{23}{12} - \frac{5 \cdot 3}{12})$

Step 4

Combine the numerators over the common denominator.

$\frac{4}{3} - \frac{23 - 5 \cdot 3}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 5$ by $3$ .

$\frac{4}{3} - \frac{23 - 15}{12}$

Step 5.2

Subtract $15$ from $23$ .

$\frac{4}{3} - \frac{8}{12}$

Step 6

Cancel the common factor of $8$ and $12$ .

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Step 6.1

Factor $4$ out of $8$ .

$\frac{4}{3} - \frac{4 (2)}{12}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $12$ .

$\frac{4}{3} - \frac{4 \cdot 2}{4 \cdot 3}$

Step 6.2.2

Cancel the common factor.

$\frac{4}{3} - \frac{4 \cdot 2}{4 \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{4}{3} - \frac{2}{3}$

Step 7

Combine the numerators over the common denominator.

$\frac{4 - 2}{3}$

Step 8

Subtract $2$ from $4$ .

$\frac{2}{3}$