Simplify 2/24+1 7/5+1/6

$\frac{2}{24} + 1 \frac{7}{5} + \frac{1}{6}$

Step 1

Convert $1 \frac{7}{5}$ to an improper fraction.

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

$\frac{2}{24} + 1 + \frac{7}{5} + \frac{1}{6}$

Add $1$ and $\frac{7}{5}$ .

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

$\frac{2}{24} + \frac{5}{5} + \frac{7}{5} + \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{2}{24} + \frac{5 + 7}{5} + \frac{1}{6}$

Add $5$ and $7$ .

$\frac{2}{24} + \frac{12}{5} + \frac{1}{6}$

Step 2

Find the common denominator.

Multiply $\frac{2}{24}$ by $\frac{5}{5}$ .

$\frac{2}{24} \cdot \frac{5}{5} + \frac{12}{5} + \frac{1}{6}$

Multiply $\frac{2}{24}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 5}{24 \cdot 5} + \frac{12}{5} + \frac{1}{6}$

Multiply $\frac{12}{5}$ by $\frac{24}{24}$ .

$\frac{2 \cdot 5}{24 \cdot 5} + \frac{12}{5} \cdot \frac{24}{24} + \frac{1}{6}$

Multiply $\frac{12}{5}$ by $\frac{24}{24}$ .

$\frac{2 \cdot 5}{24 \cdot 5} + \frac{12 \cdot 24}{5 \cdot 24} + \frac{1}{6}$

Multiply $\frac{1}{6}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 5}{24 \cdot 5} + \frac{12 \cdot 24}{5 \cdot 24} + \frac{1}{6} \cdot \frac{20}{20}$

Multiply $\frac{1}{6}$ by $\frac{20}{20}$ .

$\frac{2 \cdot 5}{24 \cdot 5} + \frac{12 \cdot 24}{5 \cdot 24} + \frac{20}{6 \cdot 20}$

Reorder the factors of $24 \cdot 5$ .

$\frac{2 \cdot 5}{5 \cdot 24} + \frac{12 \cdot 24}{5 \cdot 24} + \frac{20}{6 \cdot 20}$

Multiply $5$ by $24$ .

$\frac{2 \cdot 5}{120} + \frac{12 \cdot 24}{5 \cdot 24} + \frac{20}{6 \cdot 20}$

Multiply $5$ by $24$ .

$\frac{2 \cdot 5}{120} + \frac{12 \cdot 24}{120} + \frac{20}{6 \cdot 20}$

Multiply $6$ by $20$ .

$\frac{2 \cdot 5}{120} + \frac{12 \cdot 24}{120} + \frac{20}{120}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + 12 \cdot 24 + 20}{120}$

Step 4

Simplify each term.

Multiply $2$ by $5$ .

$\frac{10 + 12 \cdot 24 + 20}{120}$

Multiply $12$ by $24$ .

$\frac{10 + 288 + 20}{120}$

Step 5

Reduce the expression by cancelling the common factors.

Add $10$ and $288$ .

$\frac{298 + 20}{120}$

Add $298$ and $20$ .

$\frac{318}{120}$

Cancel the common factor of $318$ and $120$ .

Factor $6$ out of $318$ .

$\frac{6 (53)}{120}$

Cancel the common factors.

Factor $6$ out of $120$ .

$\frac{6 \cdot 53}{6 \cdot 20}$

Cancel the common factor.

$\frac{6 \cdot 53}{6 \cdot 20}$

Rewrite the expression.

$\frac{53}{20}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{53}{20}$

Decimal Form:

$2.65$

Mixed Number Form:

$2 \frac{13}{20}$

Simplify 2/24+1 7/5+1/6

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