Answer:
5/6, 30/36, 50/60
Step-by-step explanation:
remember, when changing the denominator via a multiplication factor, we need to multiply the numerator with the same factor to keep the actual value of the fraction unchanged, and only the optical appearance is changed, so that we can compare it more easily.
and what factor are we multiplying the denominator (and therefore also the numerator) with ?
whatever we need to change it to a denominator value that allows us then to compare the numerators.
so, 10/12 is the reference.
please notice, that this is also the same as 5/6 (after dividing numerator and denominator by 2).
we need to compare this with
2/3
what do I need to multiply 3 (the denominator) with to get 12 (or 6) ?
3x = 12
x = 12/3 = 4
or
3x = 6
x = 2
so, we need to multiply 2/3 by 4/4 or by 2/2 to compare it to our reference.
2/3 × 4/4 = (2×4) / (3×4) = 8/12
so, as 8/12 is not 10/12, this is not an equivalent answer option.
5/6
hey, this is the same as our simplified reference. so, this is correct.
just to be formally complete :
6x = 12
x = 2
5/6 × 2/2 = (5×2) / (6×2) = 10/12
=> again, correct
12/24 (= 1/2 => not correct)
again to be formally complete :
24x = 12
x = 12/24 = 1/2
12/24 × (1/2)/(1/2) = (12 × 1/2) / (24 × 1/2) = 6/12
6/12 is not 10/12
30/36
36x = 12
x = 12/36 = 1/3
30/36 × (1/3)/(1/3) = (30 × 1/3) / (36 × 1/3) = 10/12
correct.
50/60
60x = 12
x = 12/60 = 1/5
50/60 × (1/5)/(1/5) = (50 × 1/5) / (60 × 1/5) = 10/12
correct.
60/84
84x = 12
x = 12/84 = 1/7
60/84 × (1/7)/(1/7) = (60 × 1/7) / (84 × 1/7) = (60/7)/12
60/7 is not 10, so the fraction is not 10/12.
so, not equivalent.
