Question

What is the answer to 16 1/9 + (-4 2/3)?
a. 131/3
b. 103/9
c. 103/3
d. 131/9

Answer 1

b.
`\sf (103)/(9)`

Explanation:

To find the answer to
`\sf 16 (1)/(9)+ \left(-4 (2)/(3)\right)` , we first need to convert the mixed numbers to fractions.

`\sf 16 (1)/(9) = (16\cdot 9 + 1)/(9) = (145)/(9)`

`\sf - 4 (2)/(3) =- (4\cdot 3+2)/(3)=-(14)/(3)`

Now we can add the two fractions:

`\sf (145)/(9) + \left(-(14)/(3)\right)`

`\sf (145)/(9) -(14)/(3)`

To subtract fractions, we must first get them over a common denominator. In this case, the common denominator is the least common multiple of 9 and 3, which is 9.

We can get
`\sf (14)/(3)` over 9 by multiplying the top and bottom by 3.

`\sf (14)/(3) * (3)/(3) = (42)/(9)` Therefore, our problem becomes

`\sf (145)/(9) - (42)/(9)`

Now, we can simply subtract the numerators and keep the denominator the same.

`\sf (145)/(9) - (42)/(9) = (145-42)/(9) \\\\ = (103)/(9)`

Therefore, the answer is.

b.
`\sf (103)/(9)`