Basic Math Examples

$\frac{5}{12} - (- 3 \frac{1}{4}) - 6 \frac{1}{2} - 3$

Step 1

Convert $3 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$\frac{5}{12} - - (3 + \frac{1}{4}) - 6 \frac{1}{2} - 3$

Step 1.2

Add $3$ and $\frac{1}{4}$ .

Tap for more steps...

Step 1.2.1

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

$\frac{5}{12} - - (3 \cdot \frac{4}{4} + \frac{1}{4}) - 6 \frac{1}{2} - 3$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{5}{12} - - (\frac{3 \cdot 4}{4} + \frac{1}{4}) - 6 \frac{1}{2} - 3$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5}{12} - - \frac{3 \cdot 4 + 1}{4} - 6 \frac{1}{2} - 3$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $3$ by $4$ .

$\frac{5}{12} - - \frac{12 + 1}{4} - 6 \frac{1}{2} - 3$

Step 1.2.4.2

Add $12$ and $1$ .

$\frac{5}{12} - - \frac{13}{4} - 6 \frac{1}{2} - 3$

Step 2

Convert $6 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{5}{12} - - \frac{13}{4} - (6 + \frac{1}{2}) - 3$

Step 2.2

Add $6$ and $\frac{1}{2}$ .

Tap for more steps...

Step 2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{12} - - \frac{13}{4} - (6 \cdot \frac{2}{2} + \frac{1}{2}) - 3$

Step 2.2.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{5}{12} - - \frac{13}{4} - (\frac{6 \cdot 2}{2} + \frac{1}{2}) - 3$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{5}{12} - - \frac{13}{4} - \frac{6 \cdot 2 + 1}{2} - 3$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $6$ by $2$ .

$\frac{5}{12} - - \frac{13}{4} - \frac{12 + 1}{2} - 3$

Step 2.2.4.2

Add $12$ and $1$ .

$\frac{5}{12} - - \frac{13}{4} - \frac{13}{2} - 3$

Step 3

Multiply $- - \frac{13}{4}$ .

Tap for more steps...

Step 3.1

Multiply $- 1$ by $- 1$ .

$\frac{5}{12} + 1 (\frac{13}{4}) - \frac{13}{2} - 3$

Step 3.2

Multiply $\frac{13}{4}$ by $1$ .

$\frac{5}{12} + \frac{13}{4} - \frac{13}{2} - 3$

Step 4

Find the common denominator.

Tap for more steps...

Step 4.1

Multiply $\frac{13}{4}$ by $\frac{3}{3}$ .

$\frac{5}{12} + \frac{13}{4} \cdot \frac{3}{3} - \frac{13}{2} - 3$

Step 4.2

Multiply $\frac{13}{4}$ by $\frac{3}{3}$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - \frac{13}{2} - 3$

Step 4.3

Multiply $\frac{13}{2}$ by $\frac{6}{6}$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - (\frac{13}{2} \cdot \frac{6}{6}) - 3$

Step 4.4

Multiply $\frac{13}{2}$ by $\frac{6}{6}$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - \frac{13 \cdot 6}{2 \cdot 6} - 3$

Step 4.5

Write $- 3$ as a fraction with denominator $1$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - \frac{13 \cdot 6}{2 \cdot 6} + \frac{- 3}{1}$

Step 4.6

Multiply $\frac{- 3}{1}$ by $\frac{12}{12}$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - \frac{13 \cdot 6}{2 \cdot 6} + \frac{- 3}{1} \cdot \frac{12}{12}$

Step 4.7

Multiply $\frac{- 3}{1}$ by $\frac{12}{12}$ .

$\frac{5}{12} + \frac{13 \cdot 3}{4 \cdot 3} - \frac{13 \cdot 6}{2 \cdot 6} + \frac{- 3 \cdot 12}{12}$

Step 4.8

Reorder the factors of $4 \cdot 3$ .

$\frac{5}{12} + \frac{13 \cdot 3}{3 \cdot 4} - \frac{13 \cdot 6}{2 \cdot 6} + \frac{- 3 \cdot 12}{12}$

Step 4.9

Multiply $3$ by $4$ .

$\frac{5}{12} + \frac{13 \cdot 3}{12} - \frac{13 \cdot 6}{2 \cdot 6} + \frac{- 3 \cdot 12}{12}$

Step 4.10

Multiply $2$ by $6$ .

$\frac{5}{12} + \frac{13 \cdot 3}{12} - \frac{13 \cdot 6}{12} + \frac{- 3 \cdot 12}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 + 13 \cdot 3 - 13 \cdot 6 - 3 \cdot 12}{12}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply $13$ by $3$ .

$\frac{5 + 39 - 13 \cdot 6 - 3 \cdot 12}{12}$

Step 6.2

Multiply $- 13$ by $6$ .

$\frac{5 + 39 - 78 - 3 \cdot 12}{12}$

Step 6.3

Multiply $- 3$ by $12$ .

$\frac{5 + 39 - 78 - 36}{12}$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

Add $5$ and $39$ .

$\frac{44 - 78 - 36}{12}$

Step 7.2

Simplify by subtracting numbers.

Tap for more steps...

Step 7.2.1

Subtract $78$ from $44$ .

$\frac{- 34 - 36}{12}$

Step 7.2.2

Subtract $36$ from $- 34$ .

$\frac{- 70}{12}$

Step 7.3

Cancel the common factor of $- 70$ and $12$ .

Tap for more steps...

Step 7.3.1

Factor $2$ out of $- 70$ .

$\frac{2 (- 35)}{12}$

Step 7.3.2

Cancel the common factors.

Tap for more steps...

Step 7.3.2.1

Factor $2$ out of $12$ .

$\frac{2 \cdot - 35}{2 \cdot 6}$

Step 7.3.2.2

Cancel the common factor.

$\frac{2 \cdot - 35}{2 \cdot 6}$

Step 7.3.2.3

Rewrite the expression.

$\frac{- 35}{6}$

Step 7.4

Move the negative in front of the fraction.

$- \frac{35}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{35}{6}$

Decimal Form:

$- 5.8\overline{3}$

Mixed Number Form:

$- 5 \frac{5}{6}$