Question

Which of these choices is the best estimate for the answer of 3 1/4 + (-2 2/3)?

Answer 1

3 1/4 = 3.25
-2 2/3 = -2.6667
3.25 + (- 2.6667)
= 3.25 - 2.6667
= ~0.58
therefore best estimate is 0

Answer 2

Answer:  0

Step-by-step explanation:

Conversion of Mixed fraction to improper :

$a\dfrac{b}{c}=\dfrac{a\timesc+b}{c}$ , where a, b, c are integers and not equal to zero.

The given expression : $3\dfrac{1}{4}+(-2\dfrac{2}{3})$    ..(i)

Here , $3\dfrac{1}{4}=\dfrac{3\times4+1}{4}=\dfrac{13}{4}$     ..(ii)

$-2\dfrac{2}{3}=-\dfrac{2\times3+2}{3}=-\dfrac{6+2}{3}=-\dfrac{8}{3}$    ...(iii)

Now substitute (ii) and (iii) in (i) , we get

$\dfrac{13}{4}-\dfrac{8}{3}=\dfrac{13\times3-8\times4}{4\times3}\\\\=\dfrac{39-34}{12}\\\\=\dfrac{7}{12}=0.583333333333\approx0 [\text{Nearest given option}]$

Hence the best estimate for the give expression would be 0.