Basic Math Examples

$2 \frac{1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1

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

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Step 1.1

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

$2 + \frac{1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1.2

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

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Step 1.2.1

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

$2 \cdot \frac{2}{2} + \frac{1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1.2.2

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

$\frac{2 \cdot 2}{2} + \frac{1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} - \frac{7}{6} - 1 \frac{3}{4}$

Step 2

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

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Step 2.1

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

$\frac{5}{2} - \frac{7}{6} - (1 + \frac{3}{4})$

Step 2.2

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

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Step 2.2.1

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

$\frac{5}{2} - \frac{7}{6} - (\frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{5}{2} - \frac{7}{6} - \frac{4 + 3}{4}$

Step 2.2.3

Add $4$ and $3$ .

$\frac{5}{2} - \frac{7}{6} - \frac{7}{4}$

Step 3

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2} \cdot \frac{3}{3} - \frac{7}{6} - \frac{7}{4}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 \cdot 3} - \frac{7}{6} - \frac{7}{4}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6} - \frac{7}{6} - \frac{7}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 7}{6} - \frac{7}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$\frac{15 - 7}{6} - \frac{7}{4}$

Step 6.2

Subtract $7$ from $15$ .

$\frac{8}{6} - \frac{7}{4}$

Step 7

To write $\frac{8}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{8}{6} \cdot \frac{2}{2} - \frac{7}{4}$

Step 8

To write $- \frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{6} \cdot \frac{2}{2} - \frac{7}{4} \cdot \frac{3}{3}$

Step 9

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

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Step 9.1

Multiply $\frac{8}{6}$ by $\frac{2}{2}$ .

$\frac{8 \cdot 2}{6 \cdot 2} - \frac{7}{4} \cdot \frac{3}{3}$

Step 9.2

Multiply $6$ by $2$ .

$\frac{8 \cdot 2}{12} - \frac{7}{4} \cdot \frac{3}{3}$

Step 9.3

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{8 \cdot 2}{12} - \frac{7 \cdot 3}{4 \cdot 3}$

Step 9.4

Multiply $4$ by $3$ .

$\frac{8 \cdot 2}{12} - \frac{7 \cdot 3}{12}$

Step 10

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 - 7 \cdot 3}{12}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $8$ by $2$ .

$\frac{16 - 7 \cdot 3}{12}$

Step 11.2

Multiply $- 7$ by $3$ .

$\frac{16 - 21}{12}$

Step 11.3

Subtract $21$ from $16$ .

$\frac{- 5}{12}$

Step 12

Move the negative in front of the fraction.

$- \frac{5}{12}$