Basic Math Examples

$(3 \frac{3}{8} - 1 \frac{1}{5}) + 1 \frac{7}{8}$

Step 1

Convert $3 \frac{3}{8}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$3 + \frac{3}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 1.2

Add $3$ and $\frac{3}{8}$ .

Tap for more steps...

Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$3 \cdot \frac{8}{8} + \frac{3}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 1.2.2

Combine $3$ and $\frac{8}{8}$ .

$\frac{3 \cdot 8}{8} + \frac{3}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 8 + 3}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $3$ by $8$ .

$\frac{24 + 3}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 1.2.4.2

Add $24$ and $3$ .

$\frac{27}{8} - 1 \frac{1}{5} + 1 \frac{7}{8}$

Step 2

Convert $1 \frac{1}{5}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{27}{8} - (1 + \frac{1}{5}) + 1 \frac{7}{8}$

Step 2.2

Add $1$ and $\frac{1}{5}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{27}{8} - (\frac{5}{5} + \frac{1}{5}) + 1 \frac{7}{8}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{27}{8} - \frac{5 + 1}{5} + 1 \frac{7}{8}$

Step 2.2.3

Add $5$ and $1$ .

$\frac{27}{8} - \frac{6}{5} + 1 \frac{7}{8}$

Step 3

Convert $1 \frac{7}{8}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{27}{8} - \frac{6}{5} + 1 + \frac{7}{8}$

Step 3.2

Add $1$ and $\frac{7}{8}$ .

Tap for more steps...

Step 3.2.1

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

$\frac{27}{8} - \frac{6}{5} + \frac{8}{8} + \frac{7}{8}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{27}{8} - \frac{6}{5} + \frac{8 + 7}{8}$

Step 3.2.3

Add $8$ and $7$ .

$\frac{27}{8} - \frac{6}{5} + \frac{15}{8}$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Combine the numerators over the common denominator.

$\frac{27 + 15}{8} + \frac{- 6}{5}$

Step 4.2

Add $27$ and $15$ .

$\frac{42}{8} + \frac{- 6}{5}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Cancel the common factor of $42$ and $8$ .

Tap for more steps...

Step 5.1.1

Factor $2$ out of $42$ .

$\frac{2 (21)}{8} + \frac{- 6}{5}$

Step 5.1.2

Cancel the common factors.

Tap for more steps...

Step 5.1.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 21}{2 \cdot 4} + \frac{- 6}{5}$

Step 5.1.2.2

Cancel the common factor.

$\frac{2 \cdot 21}{2 \cdot 4} + \frac{- 6}{5}$

Step 5.1.2.3

Rewrite the expression.

$\frac{21}{4} + \frac{- 6}{5}$

Step 5.2

Move the negative in front of the fraction.

$\frac{21}{4} - \frac{6}{5}$

Step 6

To write $\frac{21}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{21}{4} \cdot \frac{5}{5} - \frac{6}{5}$

Step 7

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{21}{4} \cdot \frac{5}{5} - \frac{6}{5} \cdot \frac{4}{4}$

Step 8

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 8.1

Multiply $\frac{21}{4}$ by $\frac{5}{5}$ .

$\frac{21 \cdot 5}{4 \cdot 5} - \frac{6}{5} \cdot \frac{4}{4}$

Step 8.2

Multiply $4$ by $5$ .

$\frac{21 \cdot 5}{20} - \frac{6}{5} \cdot \frac{4}{4}$

Step 8.3

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$\frac{21 \cdot 5}{20} - \frac{6 \cdot 4}{5 \cdot 4}$

Step 8.4

Multiply $5$ by $4$ .

$\frac{21 \cdot 5}{20} - \frac{6 \cdot 4}{20}$

Step 9

Combine the numerators over the common denominator.

$\frac{21 \cdot 5 - 6 \cdot 4}{20}$

Step 10

Simplify the numerator.

Tap for more steps...

Step 10.1

Multiply $21$ by $5$ .

$\frac{105 - 6 \cdot 4}{20}$

Step 10.2

Multiply $- 6$ by $4$ .

$\frac{105 - 24}{20}$

Step 10.3

Subtract $24$ from $105$ .

$\frac{81}{20}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{20}$

Decimal Form:

$4.05$

Mixed Number Form:

$4 \frac{1}{20}$