Simplify 4 1/3+2 7/12

$4 \frac{1}{3} + 2 \frac{7}{12}$

Step 1

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

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

$4 + \frac{1}{3} + 2 \frac{7}{12}$

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

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

$4 \cdot \frac{3}{3} + \frac{1}{3} + 2 \frac{7}{12}$

Combine $4$ and $\frac{3}{3}$ .

$\frac{4 \cdot 3}{3} + \frac{1}{3} + 2 \frac{7}{12}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 1}{3} + 2 \frac{7}{12}$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{12 + 1}{3} + 2 \frac{7}{12}$

Add $12$ and $1$ .

$\frac{13}{3} + 2 \frac{7}{12}$

Step 2

Convert $2 \frac{7}{12}$ to an improper fraction.

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

$\frac{13}{3} + 2 + \frac{7}{12}$

Add $2$ and $\frac{7}{12}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{13}{3} + 2 \cdot \frac{12}{12} + \frac{7}{12}$

Combine $2$ and $\frac{12}{12}$ .

$\frac{13}{3} + \frac{2 \cdot 12}{12} + \frac{7}{12}$

Combine the numerators over the common denominator.

$\frac{13}{3} + \frac{2 \cdot 12 + 7}{12}$

Simplify the numerator.

Multiply $2$ by $12$ .

$\frac{13}{3} + \frac{24 + 7}{12}$

Add $24$ and $7$ .

$\frac{13}{3} + \frac{31}{12}$

Step 3

To write $\frac{13}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{13}{3} \cdot \frac{4}{4} + \frac{31}{12}$

Step 4

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

Multiply $\frac{13}{3}$ by $\frac{4}{4}$ .

$\frac{13 \cdot 4}{3 \cdot 4} + \frac{31}{12}$

Multiply $3$ by $4$ .

$\frac{13 \cdot 4}{12} + \frac{31}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{13 \cdot 4 + 31}{12}$

Step 6

Simplify the numerator.

Multiply $13$ by $4$ .

$\frac{52 + 31}{12}$

Add $52$ and $31$ .

$\frac{83}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{12}$

Decimal Form:

$6.91\overline{6}$

Mixed Number Form:

$6 \frac{11}{12}$

Simplify 4 1/3+2 7/12

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