Question

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

Answer 1

`-3 (1)/(3)t+6`

Explanation:

Given expression:

`\sf 7(1)/(3)t-\left(10 (2)/(3)t-6\right)`

Remove the parentheses:

`\implies \sf 7(1)/(3)t-10 (2)/(3)t+6`

Factor out the common term t:

`\implies \sf \left(7(1)/(3)-10 (2)/(3)\right)t+6`

Change the mixed numbers into improper fractions:

`\implies \sf \left((7 \cdot 3+1)/(3)-(10 \cdot 3+2)/(3)\right)t+6`

`\implies \sf \left((22)/(3)-(32)/(3)\right)t+6`

Subtract the fractions:

`\implies \sf \left((22-32)/(3)\right)t+6`

`\implies \sf \left((-10)/(3)\right)t+6`

Convert the improper fraction back into a mixed number:

`\implies -3 (1)/(3)t+6`