Simplify 2/3+1 4/7+5 1/2-1/3

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

Step 1

Convert

$1 \frac{4}{7}$ to an improper fraction.

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

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

Add

$1$ and

$\frac{4}{7}$ .

Write

$1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add

$7$ and

$4$ .

$\frac{2}{3} + \frac{11}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 2

Convert

$5 \frac{1}{2}$ to an improper fraction.

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

$\frac{2}{3} + \frac{11}{7} + 5 + \frac{1}{2} - \frac{1}{3}$

Add

$5$ and

$\frac{1}{2}$ .

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{2}{3} + \frac{11}{7} + 5 \cdot \frac{2}{2} + \frac{1}{2} - \frac{1}{3}$

Combine

$5$ and

$\frac{2}{2}$ .

$\frac{2}{3} + \frac{11}{7} + \frac{5 \cdot 2}{2} + \frac{1}{2} - \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{2}{3} + \frac{11}{7} + \frac{5 \cdot 2 + 1}{2} - \frac{1}{3}$

Simplify the numerator.

Multiply

$5$ by

$2$ .

$\frac{2}{3} + \frac{11}{7} + \frac{10 + 1}{2} - \frac{1}{3}$

Add

$10$ and

$1$ .

$\frac{2}{3} + \frac{11}{7} + \frac{11}{2} - \frac{1}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 - 1}{3} + \frac{11}{7} + \frac{11}{2}$

Step 4

Subtract

$1$ from

$2$ .

$\frac{1}{3} + \frac{11}{7} + \frac{11}{2}$

Step 5

Find the common denominator.

Multiply

$\frac{1}{3}$ by

$\frac{14}{14}$ .

$\frac{1}{3} \cdot \frac{14}{14} + \frac{11}{7} + \frac{11}{2}$

Multiply

$\frac{1}{3}$ by

$\frac{14}{14}$ .

$\frac{14}{3 \cdot 14} + \frac{11}{7} + \frac{11}{2}$

Multiply

$\frac{11}{7}$ by

$\frac{6}{6}$ .

$\frac{14}{3 \cdot 14} + \frac{11}{7} \cdot \frac{6}{6} + \frac{11}{2}$

Multiply

$\frac{11}{7}$ by

$\frac{6}{6}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11}{2}$

Multiply

$\frac{11}{2}$ by

$\frac{21}{21}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11}{2} \cdot \frac{21}{21}$

Multiply

$\frac{11}{2}$ by

$\frac{21}{21}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11 \cdot 21}{2 \cdot 21}$

Multiply

$3$ by

$14$ .

$\frac{14}{42} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11 \cdot 21}{2 \cdot 21}$

Reorder the factors of

$7 \cdot 6$ .

$\frac{14}{42} + \frac{11 \cdot 6}{6 \cdot 7} + \frac{11 \cdot 21}{2 \cdot 21}$

Multiply

$6$ by

$7$ .

$\frac{14}{42} + \frac{11 \cdot 6}{42} + \frac{11 \cdot 21}{2 \cdot 21}$

Multiply

$2$ by

$21$ .

$\frac{14}{42} + \frac{11 \cdot 6}{42} + \frac{11 \cdot 21}{42}$

Step 6

Combine the numerators over the common denominator.

$\frac{14 + 11 \cdot 6 + 11 \cdot 21}{42}$

Step 7

Simplify each term.

Multiply

$11$ by

$6$ .

$\frac{14 + 66 + 11 \cdot 21}{42}$

Multiply

$11$ by

$21$ .

$\frac{14 + 66 + 231}{42}$

Step 8

Simplify by adding numbers.

Add

$14$ and

$66$ .

$\frac{80 + 231}{42}$

Add

$80$ and

$231$ .

$\frac{311}{42}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{311}{42}$

Decimal Form:

$7.40476190 \dots$

Mixed Number Form:

$7 \frac{17}{42}$

Simplify 2/3+1 4/7+5 1/2-1/3

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