Algebra Examples

$(1 \frac{2}{3} + 2 \frac{1}{6}) \cdot \frac{24}{23}$

Step 1

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

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Step 1.1

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

$(1 + \frac{2}{3} + 2 \frac{1}{6}) \cdot \frac{24}{23}$

Step 1.2

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

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Step 1.2.1

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

$(\frac{3}{3} + \frac{2}{3} + 2 \frac{1}{6}) \cdot \frac{24}{23}$

Step 1.2.2

Combine the numerators over the common denominator.

$(\frac{3 + 2}{3} + 2 \frac{1}{6}) \cdot \frac{24}{23}$

Step 1.2.3

Add $3$ and $2$ .

$(\frac{5}{3} + 2 \frac{1}{6}) \cdot \frac{24}{23}$

Step 2

Convert $2 \frac{1}{6}$ to an improper fraction.

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Step 2.1

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

$(\frac{5}{3} + 2 + \frac{1}{6}) \cdot \frac{24}{23}$

Step 2.2

Add $2$ and $\frac{1}{6}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(\frac{5}{3} + 2 \cdot \frac{6}{6} + \frac{1}{6}) \cdot \frac{24}{23}$

Step 2.2.2

Combine $2$ and $\frac{6}{6}$ .

$(\frac{5}{3} + \frac{2 \cdot 6}{6} + \frac{1}{6}) \cdot \frac{24}{23}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{5}{3} + \frac{2 \cdot 6 + 1}{6}) \cdot \frac{24}{23}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $6$ .

$(\frac{5}{3} + \frac{12 + 1}{6}) \cdot \frac{24}{23}$

Step 2.2.4.2

Add $12$ and $1$ .

$(\frac{5}{3} + \frac{13}{6}) \cdot \frac{24}{23}$

Step 3

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{5}{3} \cdot \frac{2}{2} + \frac{13}{6}) \cdot \frac{24}{23}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{3}$ by $\frac{2}{2}$ .

$(\frac{5 \cdot 2}{3 \cdot 2} + \frac{13}{6}) \cdot \frac{24}{23}$

Step 4.2

Multiply $3$ by $2$ .

$(\frac{5 \cdot 2}{6} + \frac{13}{6}) \cdot \frac{24}{23}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 13}{6} \cdot \frac{24}{23}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $2$ .

$\frac{10 + 13}{6} \cdot \frac{24}{23}$

Step 6.2

Add $10$ and $13$ .

$\frac{23}{6} \cdot \frac{24}{23}$

Step 7

Cancel the common factor of $23$ .

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Step 7.1

Cancel the common factor.

$\frac{23}{6} \cdot \frac{24}{23}$

Step 7.2

Rewrite the expression.

$\frac{1}{6} \cdot 24$

Step 8

Cancel the common factor of $6$ .

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Step 8.1

Factor $6$ out of $24$ .

$\frac{1}{6} \cdot (6 (4))$

Step 8.2

Cancel the common factor.

$\frac{1}{6} \cdot (6 \cdot 4)$

Step 8.3

Rewrite the expression.

$4$