Question

item #1
estimate \\(\frac{5}{8} - \frac{1}{10}\\)
(1 point)
\\(\bigcirc\\) 0
\\(\bigcirc\\) \\(\frac{1}{2}\\)
\\(\bigcirc\\) 1
\\(\bigcirc\\) \\(1\frac{1}{2}\\)
item #2
which is a common denominator of \\(\frac{1}{4}\\) and \\(\frac{3}{5}\\)
(1 point)
\\(\bigcirc\\) 9
\\(\bigcirc\\) 15
\\(\bigcirc\\) 16
\\(\bigcirc\\) 20

Explanation:

Item #1

Step1: Approximate $\frac{5}{8}$

$\frac{5}{8}$ is close to $\frac{1}{2}$ (since $\frac{4}{8}=\frac{1}{2}$ and 5 is close to 4) or we can also note that $\frac{5}{8} = 0.625$.

Step2: Approximate $\frac{1}{10}$

$\frac{1}{10}=0.1$.

Step3: Subtract the approximations

$0.625 - 0.1 = 0.525$, which is close to $\frac{1}{2}$.

Step1: Recall common denominator definition

A common denominator of two fractions is a common multiple of their denominators. The denominators here are 4 and 5.

Step2: Find LCM of 4 and 5

The prime factorization of 4 is $2\times2$ and of 5 is $5$. The LCM is $2\times2\times5 = 20$. Also, 20 is a multiple of both 4 (since $20\div4 = 5$) and 5 (since $20\div5 = 4$).

Answer:

$\frac{1}{2}$ (the option with $\frac{1}{2}$)

Item #2