Pre-Algebra Examples

$(- \frac{4}{5} t + \frac{5}{3} s)$ and $(- 3 - \frac{7}{5} s + 2 t)$

Step 1

Add the expressions.

$- \frac{4}{5} t + \frac{5}{3} s - 3 - \frac{7}{5} s + 2 t$

Step 2

Remove parentheses.

$- \frac{4}{5} t + \frac{5}{3} s - 3 - \frac{7}{5} s + 2 t$

Step 3

Simplify each term.

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Step 3.1

Combine $t$ and $\frac{4}{5}$ .

$- \frac{t \cdot 4}{5} + \frac{5}{3} s - 3 - \frac{7}{5} s + 2 t$

Step 3.2

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

$- \frac{4 \cdot t}{5} + \frac{5}{3} s - 3 - \frac{7}{5} s + 2 t$

Step 3.3

Combine $\frac{5}{3}$ and $s$ .

$- \frac{4 t}{5} + \frac{5 s}{3} - 3 - \frac{7}{5} s + 2 t$

Step 3.4

Combine $s$ and $\frac{7}{5}$ .

$- \frac{4 t}{5} + \frac{5 s}{3} - 3 - \frac{s \cdot 7}{5} + 2 t$

Step 3.5

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

$- \frac{4 t}{5} + \frac{5 s}{3} - 3 - \frac{7 s}{5} + 2 t$

Step 4

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

$\frac{5 s}{3} - 3 - \frac{7 s}{5} - \frac{4 t}{5} + 2 t \cdot \frac{5}{5}$

Step 5

Combine $2 t$ and $\frac{5}{5}$ .

$\frac{5 s}{3} - 3 - \frac{7 s}{5} - \frac{4 t}{5} + \frac{2 t \cdot 5}{5}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 s}{3} - 3 - \frac{7 s}{5} + \frac{- 4 t + 2 t \cdot 5}{5}$

Step 7

Combine the numerators over the common denominator.

$- 3 + \frac{5 s}{3} + \frac{- 7 s - 4 t + 2 t \cdot 5}{5}$

Step 8

Multiply $5$ by $2$ .

$- 3 + \frac{5 s}{3} + \frac{- 7 s - 4 t + 10 t}{5}$

Step 9

Add $- 4 t$ and $10 t$ .

$- 3 + \frac{5 s}{3} + \frac{- 7 s + 6 t}{5}$

Step 10

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

$\frac{5 s}{3} - 3 \cdot \frac{5}{5} + \frac{- 7 s + 6 t}{5}$

Step 11

Combine $- 3$ and $\frac{5}{5}$ .

$\frac{5 s}{3} + \frac{- 3 \cdot 5}{5} + \frac{- 7 s + 6 t}{5}$

Step 12

Combine the numerators over the common denominator.

$\frac{5 s}{3} + \frac{- 3 \cdot 5 - 7 s + 6 t}{5}$

Step 13

Multiply $- 3$ by $5$ .

$\frac{5 s}{3} + \frac{- 15 - 7 s + 6 t}{5}$

Step 14

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

$\frac{5 s}{3} \cdot \frac{5}{5} + \frac{- 15 - 7 s + 6 t}{5}$

Step 15

To write $\frac{- 15 - 7 s + 6 t}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 s}{3} \cdot \frac{5}{5} + \frac{- 15 - 7 s + 6 t}{5} \cdot \frac{3}{3}$

Step 16

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

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Step 16.1

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

$\frac{5 s \cdot 5}{3 \cdot 5} + \frac{- 15 - 7 s + 6 t}{5} \cdot \frac{3}{3}$

Step 16.2

Multiply $3$ by $5$ .

$\frac{5 s \cdot 5}{15} + \frac{- 15 - 7 s + 6 t}{5} \cdot \frac{3}{3}$

Step 16.3

Multiply $\frac{- 15 - 7 s + 6 t}{5}$ by $\frac{3}{3}$ .

$\frac{5 s \cdot 5}{15} + \frac{(- 15 - 7 s + 6 t) \cdot 3}{5 \cdot 3}$

Step 16.4

Multiply $5$ by $3$ .

$\frac{5 s \cdot 5}{15} + \frac{(- 15 - 7 s + 6 t) \cdot 3}{15}$

Step 17

Combine the numerators over the common denominator.

$\frac{5 s \cdot 5 + (- 15 - 7 s + 6 t) \cdot 3}{15}$

Step 18

Simplify the numerator.

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Step 18.1

Multiply $5$ by $5$ .

$\frac{25 s + (- 15 - 7 s + 6 t) \cdot 3}{15}$

Step 18.2

Apply the distributive property.

$\frac{25 s - 15 \cdot 3 - 7 s \cdot 3 + 6 t \cdot 3}{15}$

Step 18.3

Simplify.

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Step 18.3.1

Multiply $- 15$ by $3$ .

$\frac{25 s - 45 - 7 s \cdot 3 + 6 t \cdot 3}{15}$

Step 18.3.2

Multiply $3$ by $- 7$ .

$\frac{25 s - 45 - 21 s + 6 t \cdot 3}{15}$

Step 18.3.3

Multiply $3$ by $6$ .

$\frac{25 s - 45 - 21 s + 18 t}{15}$

Step 18.4

Subtract $21 s$ from $25 s$ .

$\frac{4 s - 45 + 18 t}{15}$