To determine which expressions and multiplication phrases have the same value, we will evaluate each expression step-by-step and then match the ones that produce the same result.
1. Evaluate the expression [tex]\( \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \)[/tex]:
[tex]\[
\frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5} \approx 0.600
\][/tex]
2. Evaluate [tex]\( \frac{1}{5} \times 3 \)[/tex]:
[tex]\[
\frac{1}{5} \times 3 = \frac{3}{5} \approx 0.600
\][/tex]
3. Evaluate [tex]\( 1 \times \frac{4}{7} \)[/tex]:
[tex]\[
1 \times \frac{4}{7} = \frac{4}{7} \approx 0.571
\][/tex]
4. Evaluate [tex]\( \frac{4}{7} \)[/tex]:
[tex]\[
\frac{4}{7} \approx 0.571
\][/tex]
5. Evaluate [tex]\( 13 \times 5 \)[/tex]:
[tex]\[
13 \times 5 = 65
\][/tex]
6. Evaluate [tex]\( 4 \times 17 \)[/tex]:
[tex]\[
4 \times 17 = 68
\][/tex]
7. Evaluate [tex]\( \frac{1}{3} \times 5 \)[/tex]:
[tex]\[
\frac{1}{3} \times 5 = \frac{5}{3} \approx 1.667
\][/tex]
8. Evaluate [tex]\( \frac{1}{7} \times 4 \)[/tex]:
[tex]\[
\frac{1}{7} \times 4 = \frac{4}{7} \approx 0.571
\][/tex]
Now, let's match the expressions that have the same value:
- [tex]\( \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \approx 0.600 \)[/tex] matches with [tex]\( \frac{1}{5} \times 3 \approx 0.600 \)[/tex]
- [tex]\( 1 \times \frac{4}{7} \approx 0.571 \)[/tex] matches with [tex]\( \frac{4}{7} \approx 0.571 \)[/tex]
- [tex]\( 13 \times 5 = 65 \)[/tex] does not match any other given expression.
- [tex]\( 4 \times 17 = 68 \)[/tex] does not match any other given expression.
- [tex]\( \frac{1}{3} \times 5 \approx 1.667 \)[/tex] does not match any other given expression.
- [tex]\( \frac{1}{7} \times 4 \approx 0.571 \)[/tex] matches with [tex]\( 1 \times \frac{4}{7} \approx 0.571 \)[/tex] (This pair, however, has been already matched.)
The matched expressions are:
1. [tex]\( \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \)[/tex] matches [tex]\( \frac{1}{5} \times 3 \)[/tex].
2. [tex]\( 1 \times \frac{4}{7} \)[/tex] matches [tex]\( \frac{4}{7} \)[/tex].
