Basic Math Examples

$1 \frac{1}{4} - \frac{19}{28} - 2$

Step 1

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

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Step 1.1

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

$1 + \frac{1}{4} - \frac{19}{28} - 2$

Step 1.2

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

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Step 1.2.1

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

$\frac{4}{4} + \frac{1}{4} - \frac{19}{28} - 2$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 1}{4} - \frac{19}{28} - 2$

Step 1.2.3

Add $4$ and $1$ .

$\frac{5}{4} - \frac{19}{28} - 2$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{5}{4}$ by $\frac{7}{7}$ .

$\frac{5}{4} \cdot \frac{7}{7} - \frac{19}{28} - 2$

Step 2.2

Multiply $\frac{5}{4}$ by $\frac{7}{7}$ .

$\frac{5 \cdot 7}{4 \cdot 7} - \frac{19}{28} - 2$

Step 2.3

Write $- 2$ as a fraction with denominator $1$ .

$\frac{5 \cdot 7}{4 \cdot 7} - \frac{19}{28} + \frac{- 2}{1}$

Step 2.4

Multiply $\frac{- 2}{1}$ by $\frac{28}{28}$ .

$\frac{5 \cdot 7}{4 \cdot 7} - \frac{19}{28} + \frac{- 2}{1} \cdot \frac{28}{28}$

Step 2.5

Multiply $\frac{- 2}{1}$ by $\frac{28}{28}$ .

$\frac{5 \cdot 7}{4 \cdot 7} - \frac{19}{28} + \frac{- 2 \cdot 28}{28}$

Step 2.6

Multiply $4$ by $7$ .

$\frac{5 \cdot 7}{28} - \frac{19}{28} + \frac{- 2 \cdot 28}{28}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 - 19 - 2 \cdot 28}{28}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $7$ .

$\frac{35 - 19 - 2 \cdot 28}{28}$

Step 4.2

Multiply $- 2$ by $28$ .

$\frac{35 - 19 - 56}{28}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $19$ from $35$ .

$\frac{16 - 56}{28}$

Step 5.2

Subtract $56$ from $16$ .

$\frac{- 40}{28}$

Step 5.3

Cancel the common factor of $- 40$ and $28$ .

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Step 5.3.1

Factor $4$ out of $- 40$ .

$\frac{4 (- 10)}{28}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $4$ out of $28$ .

$\frac{4 \cdot - 10}{4 \cdot 7}$

Step 5.3.2.2

Cancel the common factor.

$\frac{4 \cdot - 10}{4 \cdot 7}$

Step 5.3.2.3

Rewrite the expression.

$\frac{- 10}{7}$

Step 5.4

Move the negative in front of the fraction.

$- \frac{10}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{10}{7}$

Decimal Form:

$- 1.\overline{428571}$

Mixed Number Form:

$- 1 \frac{3}{7}$