Algebra Examples

$\frac{5}{6} a + 4 \frac{1}{4} a$

Step 1

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

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Step 1.1

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

$\frac{5}{6} a + (4 + \frac{1}{4}) a$

Step 1.2

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

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Step 1.2.1

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

$\frac{5}{6} a + (4 \cdot \frac{4}{4} + \frac{1}{4}) a$

Step 1.2.2

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

$\frac{5}{6} a + (\frac{4 \cdot 4}{4} + \frac{1}{4}) a$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5}{6} a + \frac{4 \cdot 4 + 1}{4} a$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $4$ .

$\frac{5}{6} a + \frac{16 + 1}{4} a$

Step 1.2.4.2

Add $16$ and $1$ .

$\frac{5}{6} a + \frac{17}{4} a$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{5}{6}$ and $a$ .

$\frac{5 a}{6} + \frac{17}{4} a$

Step 2.2

Combine $\frac{17}{4}$ and $a$ .

$\frac{5 a}{6} + \frac{17 a}{4}$

Step 3

To write $\frac{5 a}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 a}{6} \cdot \frac{2}{2} + \frac{17 a}{4}$

Step 4

To write $\frac{17 a}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 a}{6} \cdot \frac{2}{2} + \frac{17 a}{4} \cdot \frac{3}{3}$

Step 5

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

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Step 5.1

Multiply $\frac{5 a}{6}$ by $\frac{2}{2}$ .

$\frac{5 a \cdot 2}{6 \cdot 2} + \frac{17 a}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply $6$ by $2$ .

$\frac{5 a \cdot 2}{12} + \frac{17 a}{4} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{17 a}{4}$ by $\frac{3}{3}$ .

$\frac{5 a \cdot 2}{12} + \frac{17 a \cdot 3}{4 \cdot 3}$

Step 5.4

Multiply $4$ by $3$ .

$\frac{5 a \cdot 2}{12} + \frac{17 a \cdot 3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 a \cdot 2 + 17 a \cdot 3}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Factor $a$ out of $5 a \cdot 2 + 17 a \cdot 3$ .

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Step 7.1.1

Factor $a$ out of $5 a \cdot 2$ .

$\frac{a (5 \cdot 2) + 17 a \cdot 3}{12}$

Step 7.1.2

Factor $a$ out of $17 a \cdot 3$ .

$\frac{a (5 \cdot 2) + a (17 \cdot 3)}{12}$

Step 7.1.3

Factor $a$ out of $a (5 \cdot 2) + a (17 \cdot 3)$ .

$\frac{a (5 \cdot 2 + 17 \cdot 3)}{12}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{a (10 + 17 \cdot 3)}{12}$

Step 7.3

Multiply $17$ by $3$ .

$\frac{a (10 + 51)}{12}$

Step 7.4

Add $10$ and $51$ .

$\frac{a \cdot 61}{12}$

Step 8

Move $61$ to the left of $a$ .

$\frac{61 a}{12}$