Question

Suki rode her bike 4/5 mile. Claire rode her bike 1/3 mile. they want to compare how far they each rode their bikes using the Benchmark 1/2

Answer 1

Suki rode her bike a longer distance than Claire because when comparing each of their distances to the benchmark of 1/2 mile, Suki's distance (4/5 mile) is greater than the benchmark (1/2 mile), while Claire's distance (1/3 mile) is less than the benchmark. Therefore, Suki rode a longer distance than Claire in relation to the benchmark.

Suki's Distance with Benchmark (1/2):

Suki rode her bike for 4/5 miles.

The benchmark is 1/2 mile.

Comparison:
`(4)/(5) > (1)/(2)`

Interpretation: Suki's distance ( 4/5 miles) is greater than the benchmark 1/2 mile.

Claire's Distance with Benchmark (1/2):

Claire rode her bike for 1/3 mile.

The benchmark is 1/2 mile.

Comparison:
`(1)/(3) < (1)/(2)`

Interpretation: Claire's distance ( 1/3 mile) is less than the benchmark 1/2 mile.

Overall Comparison:

Suki's distance (4/5) is greater than Claire's distance (1/3).

Interpretation: Suki rode her bike a longer distance than Claire.

In summary, both Suki and Claire are comparing their distances to the benchmark of 1/2 mile. Suki's distance is greater than the benchmark, while Claire's distance is less than the benchmark. Therefore, Suki rode a longer distance than Claire.

Answer 2

(a)
`(4)/(5) > (1)/(2)`

(b)
`(1)/(3) < (1)/(2)`

(c) Suki rode her bike a longer distance than Clarie

Explanation:

Suki's distance is 4/5 miles

Now compare with bechmark 1/2

compare
`(4)/(5) and (1)/(2)`

To compare , we make the denominators same

`(4*2)/(5*2) ----- (1*5)/(2*5)`

`(8)/(10) ----- (5)/(10)`

8/10 is greater than 5/10

`(8)/(10) > (5)/(10)`

Clarie distance is 1/3 miles

Now compare with bechmark 1/2

compare
`(1)/(3) and (1)/(2)`

To compare , we make the denominators same

`(1*2)/(3*2) ----- (1*3)/(2*3)`

`(2)/(6) ----- (3)/(6)`

2/6 is less than 3/6

`(2)/(6) < (3)/(6)`

Now we compare Suki's distance with Clarie

compare
`(4)/(5) and (1)/(3)`

Make the denominators same

`(4*3)/(5*3) and (1*5)/(3*5)`

`(12)/(15) and (5)/(15)`

`(12)/(15) > (5)/(15)`

Suki rode her bike a longer distance than Clarie