Question

< Sparx 5: Item B

Bookwork code: G24
second chance! Review your workings and see if you can correct your mistake
a) Which is larger, 2/3 or 4/7?
b) Work out how much larger it is.
Give your answers as fractions in their simplest form.

Answer 1

Explanation:

to compare fractions we need to bring them to the same denominator (bottom number).

we can transform any fraction by multiplying it by n/n.

simply because this means we are multiplying it by 1 and therefore not changing anything about the value of the fraction.

but we can use that to change the denominator.

the useful approach is to find the LCM (least common multiple) of both denominators (3 and 7).

as they are both prime numbers, the LCM is simply the product of both : 3×7 = 21.

so, what is the n in n/n that we need to multiply 2/3 with to get x/21 ? 7. so, we multiply by 7/7 :

2/3 × 7/7 = 14/21

and what is the n for 4/7 ? 3. so, we multiply by 3/3 :

4/7 × 3/3 = 12/21

a)

2/3 is larger than 4/7, because 14/21 is larger than 12/21.

b)

2/3 is larger than 4/7 by

14/21 - 12/21 = 2/21