Question

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below. StartFraction 42 m divided by 7 over 24 m divided by 7 EndFraction = StartFraction 6 over 4 EndFraction Which is Abel’s error? Abel should have written the ratio as StartFraction 24 meters over 7 meters EndFraction. Abel should have written the ratio as StartFraction 24 meters over 42 meters EndFraction. Abel should have divided both numbers by 6. Abel should have divided both numbers by 4.

Answer 1

C

bel should have divided both numbers by 6.

Answer 2

Question:

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.

`(42m)/(7)/{(24m)/(7) = (6)/(4)`

Which is Abel’s error?

Abel should have written the ratio as
`24 metres/7 metres`

Abel should have written the ratio as
`24 metres/42 metres`

Abel should have divided both numbers by 6.

Abel should have divided both numbers by 4.

Answer:

Abel should have divided both numbers by 6.

Explanation:

Given

Measured Length of backyard = 42m

Actual Length of backyard = 24m

Measured Ratio:
`(42m)/(7)/{(24m)/(7) = (6)/(4)`

Required

Error in calculation of measured ratio

From Abel's calculation:

It can be observed that He divided both numbers by 7

Though 42/7 = 6 but that's not so for 24/7

24/7≠4;

Instead 24/7 = 3.43 (Approximated)

To get the actual ration, he has to divide both numbers by the highest common factor

The common factors of 42 and 24 include 2,3,6 of which the highest is 6

Hence; HCF of 42 and 24 = 6

So, we can conclude that the error in his calculation is having not dividing both numbers by 6