Simplify 7 1/3t-(10 2/3t-6)

$7 \frac{1}{3} t - (10 \frac{2}{3} t - 6)$

Step 1

Convert $7 \frac{1}{3}$ to an improper fraction.

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

$(7 + \frac{1}{3}) t - (10 \frac{2}{3} t - 6)$

Add $7$ and $\frac{1}{3}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(7 \cdot \frac{3}{3} + \frac{1}{3}) t - (10 \frac{2}{3} t - 6)$

Combine $7$ and $\frac{3}{3}$ .

$(\frac{7 \cdot 3}{3} + \frac{1}{3}) t - (10 \frac{2}{3} t - 6)$

Combine the numerators over the common denominator.

$\frac{7 \cdot 3 + 1}{3} t - (10 \frac{2}{3} t - 6)$

Simplify the numerator.

Multiply $7$ by $3$ .

$\frac{21 + 1}{3} t - (10 \frac{2}{3} t - 6)$

Add $21$ and $1$ .

$\frac{22}{3} t - (10 \frac{2}{3} t - 6)$

Step 2

Convert $10 \frac{2}{3}$ to an improper fraction.

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

$\frac{22}{3} t - ((10 + \frac{2}{3}) t - 6)$

Add $10$ and $\frac{2}{3}$ .

To write $10$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{22}{3} t - ((10 \cdot \frac{3}{3} + \frac{2}{3}) t - 6)$

Combine $10$ and $\frac{3}{3}$ .

$\frac{22}{3} t - ((\frac{10 \cdot 3}{3} + \frac{2}{3}) t - 6)$

Combine the numerators over the common denominator.

$\frac{22}{3} t - (\frac{10 \cdot 3 + 2}{3} t - 6)$

Simplify the numerator.

Multiply $10$ by $3$ .

$\frac{22}{3} t - (\frac{30 + 2}{3} t - 6)$

Add $30$ and $2$ .

$\frac{22}{3} t - (\frac{32}{3} t - 6)$

Step 3

Simplify each term.

Combine $\frac{22}{3}$ and $t$ .

$\frac{22 t}{3} - (\frac{32}{3} t - 6)$

Combine $\frac{32}{3}$ and $t$ .

$\frac{22 t}{3} - (\frac{32 t}{3} - 6)$

Apply the distributive property.

$\frac{22 t}{3} - \frac{32 t}{3} - - 6$

Multiply $- 1$ by $- 6$ .

$\frac{22 t}{3} - \frac{32 t}{3} + 6$

Step 4

Simplify terms.

Combine the numerators over the common denominator.

$6 + \frac{22 t - 32 t}{3}$

Subtract $32 t$ from $22 t$ .

$6 + \frac{- 10 t}{3}$

Step 5

Move the negative in front of the fraction.

$6 - \frac{10 t}{3}$

Simplify 7 1/3t-(10 2/3t-6)

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