Certainly! To find which expressions are equivalent to [tex]\(2 \times \frac{10}{3}\)[/tex], we'll calculate each expression step-by-step.
First, let's calculate the given expression:
[tex]\[ 2 \times \frac{10}{3} = \frac{20}{3} \][/tex]
Now, we will evaluate each choice and compare it to [tex]\(\frac{20}{3}\)[/tex].
Option (A): [tex]\( 12 \times \frac{1}{3} \)[/tex]
[tex]\[ 12 \times \frac{1}{3} = \frac{12 \times 1}{3} = \frac{12}{3} = 4 \][/tex]
Option (B): [tex]\( \frac{5}{3} \times 4 \)[/tex]
[tex]\[ \frac{5}{3} \times 4 = \frac{5 \times 4}{3} = \frac{20}{3} \][/tex]
Option (C): [tex]\( \frac{3}{10} \times 2 \)[/tex]
[tex]\[ \frac{3}{10} \times 2 = \frac{3 \times 2}{10} = \frac{6}{10} = \frac{3}{5} \][/tex]
Option (D): [tex]\( 20 \times \frac{1}{3} \)[/tex]
[tex]\[ 20 \times \frac{1}{3} = \frac{20 \times 1}{3} = \frac{20}{3} \][/tex]
Now let's compare each result to [tex]\(\frac{20}{3}\)[/tex]:
- [tex]\(12 \times \frac{1}{3} = 4\)[/tex] which is not equal to [tex]\(\frac{20}{3}\)[/tex].
- [tex]\(\frac{5}{3} \times 4 = \frac{20}{3}\)[/tex] which is equal to [tex]\(\frac{20}{3}\)[/tex].
- [tex]\(\frac{3}{10} \times 2 = \frac{3}{5}\)[/tex] which is not equal to [tex]\(\frac{20}{3}\)[/tex].
- [tex]\(20 \times \frac{1}{3} = \frac{20}{3}\)[/tex] which is equal to [tex]\(\frac{20}{3}\)[/tex].
Therefore, the two expressions that are equivalent to [tex]\(2 \times \frac{10}{3}\)[/tex] are:
(B) [tex]\(\frac{5}{3} \times 4\)[/tex] and (D) [tex]\(20 \times \frac{1}{3}\)[/tex].
