Question

problem 3b
select all the fractions that are equivalent to \\(\frac{10}{4}\\).
\\(\frac{5}{2}\\) \\(10\frac{1}{4}\\) \\(\frac{20}{8}\\) \\(\frac{8}{2}\\) \\(2\frac{1}{2}\\)

Explanation:

Step1: Simplify \(\frac{10}{4}\)

Simplify \(\frac{10}{4}\) by dividing numerator and denominator by 2: \(\frac{10\div2}{4\div2}=\frac{5}{2}\).

Step2: Check \(\frac{5}{2}\)

We just found \(\frac{10}{4}=\frac{5}{2}\), so \(\frac{5}{2}\) is equivalent.

Step3: Check \(10\frac{1}{4}\)

\(10\frac{1}{4}=\frac{41}{4}\), which is not equal to \(\frac{10}{4}\), so it's not equivalent.

Step4: Check \(\frac{20}{8}\)

Simplify \(\frac{20}{8}\) by dividing numerator and denominator by 4: \(\frac{20\div4}{8\div4}=\frac{5}{2}\), and \(\frac{10}{4}=\frac{5}{2}\), so \(\frac{20}{8}\) is equivalent.

Step5: Check \(\frac{8}{2}\)

\(\frac{8}{2} = 4\), and \(\frac{10}{4}=2.5\), so they are not equal, not equivalent.

Step6: Check \(2\frac{1}{2}\)

Convert \(2\frac{1}{2}\) to improper fraction: \(2\frac{1}{2}=\frac{5}{2}\), and \(\frac{10}{4}=\frac{5}{2}\), so \(2\frac{1}{2}\) is equivalent.

Answer:

\(\frac{5}{2}\), \(\frac{20}{8}\), \(2\frac{1}{2}\)