Basic Math Examples

6 \frac{5}{12} - 4 \frac{1}{9}

$6 \frac{5}{12} - 4 \frac{1}{9}$

Step 1

Convert

6 \frac{5}{12}

$6 \frac{5}{12}$ to an improper fraction.

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Step 1.1

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

6 + \frac{5}{12} - 4 \frac{1}{9}

$6 + \frac{5}{12} - 4 \frac{1}{9}$

Step 1.2

Add

6

$6$ and

\frac{5}{12}

$\frac{5}{12}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{12}{12}

$\frac{12}{12}$ .

6 \cdot \frac{12}{12} + \frac{5}{12} - 4 \frac{1}{9}

$6 \cdot \frac{12}{12} + \frac{5}{12} - 4 \frac{1}{9}$

Step 1.2.2

Combine

6

$6$ and

\frac{12}{12}

$\frac{12}{12}$ .

\frac{6 \cdot 12}{12} + \frac{5}{12} - 4 \frac{1}{9}

$\frac{6 \cdot 12}{12} + \frac{5}{12} - 4 \frac{1}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 12 + 5}{12} - 4 \frac{1}{9}

$\frac{6 \cdot 12 + 5}{12} - 4 \frac{1}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

12

$12$ .

\frac{72 + 5}{12} - 4 \frac{1}{9}

$\frac{72 + 5}{12} - 4 \frac{1}{9}$

Step 1.2.4.2

Add

72

$72$ and

5

$5$ .

\frac{77}{12} - 4 \frac{1}{9}

$\frac{77}{12} - 4 \frac{1}{9}$

\frac{77}{12} - 4 \frac{1}{9}

$\frac{77}{12} - 4 \frac{1}{9}$

\frac{77}{12} - 4 \frac{1}{9}

$\frac{77}{12} - 4 \frac{1}{9}$

\frac{77}{12} - 4 \frac{1}{9}

$\frac{77}{12} - 4 \frac{1}{9}$

Step 2

Convert

4 \frac{1}{9}

$4 \frac{1}{9}$ to an improper fraction.

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Step 2.1

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

\frac{77}{12} - (4 + \frac{1}{9})

$\frac{77}{12} - (4 + \frac{1}{9})$

Step 2.2

Add

4

$4$ and

\frac{1}{9}

$\frac{1}{9}$ .

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Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

\frac{77}{12} - (4 \cdot \frac{9}{9} + \frac{1}{9})

$\frac{77}{12} - (4 \cdot \frac{9}{9} + \frac{1}{9})$

Step 2.2.2

Combine

4

$4$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{77}{12} - (\frac{4 \cdot 9}{9} + \frac{1}{9})

$\frac{77}{12} - (\frac{4 \cdot 9}{9} + \frac{1}{9})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{77}{12} - \frac{4 \cdot 9 + 1}{9}

$\frac{77}{12} - \frac{4 \cdot 9 + 1}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

4

$4$ by

9

$9$ .

\frac{77}{12} - \frac{36 + 1}{9}

$\frac{77}{12} - \frac{36 + 1}{9}$

Step 2.2.4.2

Add

36

$36$ and

1

$1$ .

\frac{77}{12} - \frac{37}{9}

$\frac{77}{12} - \frac{37}{9}$

\frac{77}{12} - \frac{37}{9}

$\frac{77}{12} - \frac{37}{9}$

\frac{77}{12} - \frac{37}{9}

$\frac{77}{12} - \frac{37}{9}$

\frac{77}{12} - \frac{37}{9}

$\frac{77}{12} - \frac{37}{9}$

Step 3

To write

\frac{77}{12}

$\frac{77}{12}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{77}{12} \cdot \frac{3}{3} - \frac{37}{9}

$\frac{77}{12} \cdot \frac{3}{3} - \frac{37}{9}$

Step 4

To write

- \frac{37}{9}

$- \frac{37}{9}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{77}{12} \cdot \frac{3}{3} - \frac{37}{9} \cdot \frac{4}{4}

$\frac{77}{12} \cdot \frac{3}{3} - \frac{37}{9} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

36

$36$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{77}{12}

$\frac{77}{12}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{77 \cdot 3}{12 \cdot 3} - \frac{37}{9} \cdot \frac{4}{4}

$\frac{77 \cdot 3}{12 \cdot 3} - \frac{37}{9} \cdot \frac{4}{4}$

Step 5.2

Multiply

12

$12$ by

3

$3$ .

\frac{77 \cdot 3}{36} - \frac{37}{9} \cdot \frac{4}{4}

$\frac{77 \cdot 3}{36} - \frac{37}{9} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{37}{9}

$\frac{37}{9}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{9 \cdot 4}

$\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{9 \cdot 4}$

Step 5.4

Multiply

9

$9$ by

4

$4$ .

\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{36}

$\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{36}$

\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{36}

$\frac{77 \cdot 3}{36} - \frac{37 \cdot 4}{36}$

Step 6

Combine the numerators over the common denominator.

\frac{77 \cdot 3 - 37 \cdot 4}{36}

$\frac{77 \cdot 3 - 37 \cdot 4}{36}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

77

$77$ by

3

$3$ .

\frac{231 - 37 \cdot 4}{36}

$\frac{231 - 37 \cdot 4}{36}$

Step 7.2

Multiply

- 37

$- 37$ by

4

$4$ .

\frac{231 - 148}{36}

$\frac{231 - 148}{36}$

Step 7.3

Subtract

148

$148$ from

231

$231$ .

\frac{83}{36}

$\frac{83}{36}$

\frac{83}{36}

$\frac{83}{36}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{83}{36}

$\frac{83}{36}$

Decimal Form:

2.30\overline{5}

$2.30\overline{5}$

Mixed Number Form:

2 \frac{11}{36}

$2 \frac{11}{36}$