Basic Math Examples

126 \frac{1}{4} - 78 \frac{2}{3}

$126 \frac{1}{4} - 78 \frac{2}{3}$

Step 1

Convert

126 \frac{1}{4}

$126 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

126 + \frac{1}{4} - 78 \frac{2}{3}

$126 + \frac{1}{4} - 78 \frac{2}{3}$

Step 1.2

Add

126

$126$ and

\frac{1}{4}

$\frac{1}{4}$ .

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Step 1.2.1

To write

126

$126$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

126 \cdot \frac{4}{4} + \frac{1}{4} - 78 \frac{2}{3}

$126 \cdot \frac{4}{4} + \frac{1}{4} - 78 \frac{2}{3}$

Step 1.2.2

Combine

126

$126$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{126 \cdot 4}{4} + \frac{1}{4} - 78 \frac{2}{3}

$\frac{126 \cdot 4}{4} + \frac{1}{4} - 78 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{126 \cdot 4 + 1}{4} - 78 \frac{2}{3}

$\frac{126 \cdot 4 + 1}{4} - 78 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

126

$126$ by

4

$4$ .

\frac{504 + 1}{4} - 78 \frac{2}{3}

$\frac{504 + 1}{4} - 78 \frac{2}{3}$

Step 1.2.4.2

Add

504

$504$ and

1

$1$ .

\frac{505}{4} - 78 \frac{2}{3}

$\frac{505}{4} - 78 \frac{2}{3}$

\frac{505}{4} - 78 \frac{2}{3}

$\frac{505}{4} - 78 \frac{2}{3}$

\frac{505}{4} - 78 \frac{2}{3}

$\frac{505}{4} - 78 \frac{2}{3}$

\frac{505}{4} - 78 \frac{2}{3}

$\frac{505}{4} - 78 \frac{2}{3}$

Step 2

Convert

78 \frac{2}{3}

$78 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

\frac{505}{4} - (78 + \frac{2}{3})

$\frac{505}{4} - (78 + \frac{2}{3})$

Step 2.2

Add

78

$78$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

78

$78$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{505}{4} - (78 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{505}{4} - (78 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

78

$78$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{505}{4} - (\frac{78 \cdot 3}{3} + \frac{2}{3})

$\frac{505}{4} - (\frac{78 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{505}{4} - \frac{78 \cdot 3 + 2}{3}

$\frac{505}{4} - \frac{78 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

78

$78$ by

3

$3$ .

\frac{505}{4} - \frac{234 + 2}{3}

$\frac{505}{4} - \frac{234 + 2}{3}$

Step 2.2.4.2

Add

234

$234$ and

2

$2$ .

\frac{505}{4} - \frac{236}{3}

$\frac{505}{4} - \frac{236}{3}$

\frac{505}{4} - \frac{236}{3}

$\frac{505}{4} - \frac{236}{3}$

\frac{505}{4} - \frac{236}{3}

$\frac{505}{4} - \frac{236}{3}$

\frac{505}{4} - \frac{236}{3}

$\frac{505}{4} - \frac{236}{3}$

Step 3

To write

\frac{505}{4}

$\frac{505}{4}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{505}{4} \cdot \frac{3}{3} - \frac{236}{3}

$\frac{505}{4} \cdot \frac{3}{3} - \frac{236}{3}$

Step 4

To write

- \frac{236}{3}

$- \frac{236}{3}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{505}{4} \cdot \frac{3}{3} - \frac{236}{3} \cdot \frac{4}{4}

$\frac{505}{4} \cdot \frac{3}{3} - \frac{236}{3} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

12

$12$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{505}{4}

$\frac{505}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{505 \cdot 3}{4 \cdot 3} - \frac{236}{3} \cdot \frac{4}{4}

$\frac{505 \cdot 3}{4 \cdot 3} - \frac{236}{3} \cdot \frac{4}{4}$

Step 5.2

Multiply

4

$4$ by

3

$3$ .

\frac{505 \cdot 3}{12} - \frac{236}{3} \cdot \frac{4}{4}

$\frac{505 \cdot 3}{12} - \frac{236}{3} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{236}{3}

$\frac{236}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{3 \cdot 4}

$\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{3 \cdot 4}$

Step 5.4

Multiply

3

$3$ by

4

$4$ .

\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{12}

$\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{12}$

\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{12}

$\frac{505 \cdot 3}{12} - \frac{236 \cdot 4}{12}$

Step 6

Combine the numerators over the common denominator.

\frac{505 \cdot 3 - 236 \cdot 4}{12}

$\frac{505 \cdot 3 - 236 \cdot 4}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

505

$505$ by

3

$3$ .

\frac{1515 - 236 \cdot 4}{12}

$\frac{1515 - 236 \cdot 4}{12}$

Step 7.2

Multiply

- 236

$- 236$ by

4

$4$ .

\frac{1515 - 944}{12}

$\frac{1515 - 944}{12}$

Step 7.3

Subtract

944

$944$ from

1515

$1515$ .

\frac{571}{12}

$\frac{571}{12}$

\frac{571}{12}

$\frac{571}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{571}{12}

$\frac{571}{12}$

Decimal Form:

47.58 ¯ 3

$47.58\overline{3}$

Mixed Number Form:

47 \frac{7}{12}

$47 \frac{7}{12}$