Functional Skills: Fraction Basics

a) $dfrac{2}{5}=2div5=0.4$

b) $dfrac{7}{10}=7div10=0.7$

c) $dfrac{4}{5}=4div 5=0.8$

d) $dfrac{2}{3}=2div 3 =0.6666…$

The answer to part d) is different because it does not stop.

a) $dfrac{2}{3}times600=2div3times600=400$

b) $dfrac{1}{3}times 36 =1div 3times36=12$

c) $dfrac{3}{4}times540=3div4times540=405$

d) $dfrac{12}{5}times 290=12div5times 290=696$

a) These are equivalent because we multiply the top and the bottom by $3$ to go from $dfrac{1}{2}$ to $dfrac{3}{6}$.

b) These are not equivalent because the top has been multiplied by $3$ while the bottom has been multiplied by $4$.

c) These are equivalent because we multiply the top and the bottom by $12$ to go from $dfrac{2}{5}$ to $dfrac{12}{60}$.

d) These are not equivalent because the top has been multiplied by $2$ but the new bottom is $18$ while $10times2=20$

e) There is no obvious multiplier for either top or bottom here, so to check we have to turn them into decimals.

$dfrac{2}{10}=2div10=0.2$ and $dfrac{5}{25}=5div25=0.2$, so they are the same, so they are equivalent.

For $dfrac{12}{20}$, both the top and the bottom have been multiplied by $4$, so this is equivalent.

For $dfrac{6}{10}$, both the top and the bottom have been multiplied by $2$, so this is equivalent.

For $dfrac{24}{35}$, the top has been multiplied by $8$, but $5times8=40$ so the bottom has not been multiplied by $8$. So, this is not equivalent.

For $dfrac{9}{15}$, both the top and the bottom have been multiplied by $3$, so this is equivalent.

For $dfrac{150}{250}$, both the top and the bottom have been multiplied by $50$, so this is equivalent.

Therefore, the only non-equivalent fraction is $dfrac{24}{35}$.