Basic Math Examples

$\frac{9}{5} k + \frac{- 4}{3} k$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{9}{5}$ and $k$ .

$\frac{9 k}{5} + \frac{- 4}{3} k$

Step 1.2

Move the negative in front of the fraction.

$\frac{9 k}{5} - \frac{4}{3} k$

Step 1.3

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

$\frac{9 k}{5} - \frac{k \cdot 4}{3}$

Step 1.4

Move $4$ to the left of $k$ .

$\frac{9 k}{5} - \frac{4 k}{3}$

Step 2

To write $\frac{9 k}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9 k}{5} \cdot \frac{3}{3} - \frac{4 k}{3}$

Step 3

To write $- \frac{4 k}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9 k}{5} \cdot \frac{3}{3} - \frac{4 k}{3} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{9 k}{5}$ by $\frac{3}{3}$ .

$\frac{9 k \cdot 3}{5 \cdot 3} - \frac{4 k}{3} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $3$ .

$\frac{9 k \cdot 3}{15} - \frac{4 k}{3} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{4 k}{3}$ by $\frac{5}{5}$ .

$\frac{9 k \cdot 3}{15} - \frac{4 k \cdot 5}{3 \cdot 5}$

Step 4.4

Multiply $3$ by $5$ .

$\frac{9 k \cdot 3}{15} - \frac{4 k \cdot 5}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 k \cdot 3 - 4 k \cdot 5}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $k$ out of $9 k \cdot 3 - 4 k \cdot 5$ .

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Step 6.1.1

Factor $k$ out of $9 k \cdot 3$ .

$\frac{k (9 \cdot 3) - 4 k \cdot 5}{15}$

Step 6.1.2

Factor $k$ out of $- 4 k \cdot 5$ .

$\frac{k (9 \cdot 3) + k (- 4 \cdot 5)}{15}$

Step 6.1.3

Factor $k$ out of $k (9 \cdot 3) + k (- 4 \cdot 5)$ .

$\frac{k (9 \cdot 3 - 4 \cdot 5)}{15}$

Step 6.2

Multiply $9$ by $3$ .

$\frac{k (27 - 4 \cdot 5)}{15}$

Step 6.3

Multiply $- 4$ by $5$ .

$\frac{k (27 - 20)}{15}$

Step 6.4

Subtract $20$ from $27$ .

$\frac{k \cdot 7}{15}$

Step 7

Move $7$ to the left of $k$ .

$\frac{7 k}{15}$