Simplify 6 1/5-2 1/4

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

Step 1

Convert $6 \frac{1}{5}$ to an improper fraction.

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

$6 + \frac{1}{5} - 2 \frac{1}{4}$

Add $6$ and $\frac{1}{5}$ .

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

$6 \cdot \frac{5}{5} + \frac{1}{5} - 2 \frac{1}{4}$

Combine $6$ and $\frac{5}{5}$ .

$\frac{6 \cdot 5}{5} + \frac{1}{5} - 2 \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 + 1}{5} - 2 \frac{1}{4}$

Simplify the numerator.

Multiply $6$ by $5$ .

$\frac{30 + 1}{5} - 2 \frac{1}{4}$

Add $30$ and $1$ .

$\frac{31}{5} - 2 \frac{1}{4}$

Step 2

Convert $2 \frac{1}{4}$ to an improper fraction.

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

$\frac{31}{5} - (2 + \frac{1}{4})$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{31}{5} - (2 \cdot \frac{4}{4} + \frac{1}{4})$

Combine $2$ and $\frac{4}{4}$ .

$\frac{31}{5} - (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$\frac{31}{5} - \frac{2 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{31}{5} - \frac{8 + 1}{4}$

Add $8$ and $1$ .

$\frac{31}{5} - \frac{9}{4}$

Step 3

To write $\frac{31}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{31}{5} \cdot \frac{4}{4} - \frac{9}{4}$

Step 4

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{31}{5} \cdot \frac{4}{4} - \frac{9}{4} \cdot \frac{5}{5}$

Step 5

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

Multiply $\frac{31}{5}$ by $\frac{4}{4}$ .

$\frac{31 \cdot 4}{5 \cdot 4} - \frac{9}{4} \cdot \frac{5}{5}$

Multiply $5$ by $4$ .

$\frac{31 \cdot 4}{20} - \frac{9}{4} \cdot \frac{5}{5}$

Multiply $\frac{9}{4}$ by $\frac{5}{5}$ .

$\frac{31 \cdot 4}{20} - \frac{9 \cdot 5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$\frac{31 \cdot 4}{20} - \frac{9 \cdot 5}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{31 \cdot 4 - 9 \cdot 5}{20}$

Step 7

Simplify the numerator.

Multiply $31$ by $4$ .

$\frac{124 - 9 \cdot 5}{20}$

Multiply $- 9$ by $5$ .

$\frac{124 - 45}{20}$

Subtract $45$ from $124$ .

$\frac{79}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{79}{20}$

Decimal Form:

$3.95$

Mixed Number Form:

$3 \frac{19}{20}$

Simplify 6 1/5-2 1/4

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