Simplify 5 3/8-2 1/3

$5 \frac{3}{8} - 2 \frac{1}{3}$

Step 1

Convert $5 \frac{3}{8}$ to an improper fraction.

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

$5 + \frac{3}{8} - 2 \frac{1}{3}$

Add $5$ and $\frac{3}{8}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$5 \cdot \frac{8}{8} + \frac{3}{8} - 2 \frac{1}{3}$

Combine $5$ and $\frac{8}{8}$ .

$\frac{5 \cdot 8}{8} + \frac{3}{8} - 2 \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 8 + 3}{8} - 2 \frac{1}{3}$

Simplify the numerator.

Multiply $5$ by $8$ .

$\frac{40 + 3}{8} - 2 \frac{1}{3}$

Add $40$ and $3$ .

$\frac{43}{8} - 2 \frac{1}{3}$

Step 2

Convert $2 \frac{1}{3}$ to an improper fraction.

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

$\frac{43}{8} - (2 + \frac{1}{3})$

Add $2$ and $\frac{1}{3}$ .

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

$\frac{43}{8} - (2 \cdot \frac{3}{3} + \frac{1}{3})$

Combine $2$ and $\frac{3}{3}$ .

$\frac{43}{8} - (\frac{2 \cdot 3}{3} + \frac{1}{3})$

Combine the numerators over the common denominator.

$\frac{43}{8} - \frac{2 \cdot 3 + 1}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{43}{8} - \frac{6 + 1}{3}$

Add $6$ and $1$ .

$\frac{43}{8} - \frac{7}{3}$

Step 3

To write $\frac{43}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{43}{8} \cdot \frac{3}{3} - \frac{7}{3}$

Step 4

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{43}{8} \cdot \frac{3}{3} - \frac{7}{3} \cdot \frac{8}{8}$

Step 5

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{43}{8}$ by $\frac{3}{3}$ .

$\frac{43 \cdot 3}{8 \cdot 3} - \frac{7}{3} \cdot \frac{8}{8}$

Multiply $8$ by $3$ .

$\frac{43 \cdot 3}{24} - \frac{7}{3} \cdot \frac{8}{8}$

Multiply $\frac{7}{3}$ by $\frac{8}{8}$ .

$\frac{43 \cdot 3}{24} - \frac{7 \cdot 8}{3 \cdot 8}$

Multiply $3$ by $8$ .

$\frac{43 \cdot 3}{24} - \frac{7 \cdot 8}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{43 \cdot 3 - 7 \cdot 8}{24}$

Step 7

Simplify the numerator.

Multiply $43$ by $3$ .

$\frac{129 - 7 \cdot 8}{24}$

Multiply $- 7$ by $8$ .

$\frac{129 - 56}{24}$

Subtract $56$ from $129$ .

$\frac{73}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{73}{24}$

Decimal Form:

$3.041\overline{6}$

Mixed Number Form:

$3 \frac{1}{24}$

Simplify 5 3/8-2 1/3

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