Question 1
LEVEL 3
Find \dfrac{1}{6} of 42
Select your answer from the list below:
A: 7
B: 6
C: \dfrac{1}{7}
D: \dfrac{7}{6}
CORRECT ANSWER: A: 7
WORKED SOLUTION:
When we multiply fractions, we just need to multiply the numerators and multiply the denominators.
\dfrac{1}{6}\times\dfrac{42}{1}=\dfrac{42}{6}=7
Question 2
LEVEL 3
Work out the value of \dfrac{2}{9}\times\dfrac{7}{4} in its simplest form.
Select the correct answer from the list below:
A: \dfrac{14}{36}
B: \dfrac{9}{13}
C: \dfrac{7}{18}
D: \dfrac{8}{63}
CORRECT ANSWER: C: \dfrac{7}{18}
WORKED SOLUTION:
When we multiply fractions, we just need to multiply the numerators and multiply the denominators.
\dfrac{2}{9}\times\dfrac{7}{4}=\dfrac{2\times7}{9\times4}=\dfrac{14}{36}
And now we need to simplify the fraction by dividing the top and bottom by common factors until we can’t simplify anymore; this is most easily done by using the highest common factor.
\dfrac{14}{36}=\dfrac{14\div2}{36\div2}=\dfrac{7}{18}
We can’t simplify any further.
Question 3
LEVEL 3
Work out \dfrac{5}{6}-\dfrac{3}{8} in its simplest form.
Select the correct answer from the list below:
A: 1
B: \dfrac{1}{24}
C: \dfrac{11}{24}
D: \dfrac{29}{24}
CORRECT ANSWER: C: \dfrac{11}{24}
WORKED SOLUTION:
When adding fractions we need to make the denominators the same, this is done most easily by multiplying each fraction by the other’s denominator.
\dfrac{5}{\textcolor{green}{6}}-\dfrac{3}{\textcolor{red}{8}} =\dfrac{5\times\textcolor{red}{8}}{\textcolor{green}{6}\times\textcolor{red}{8}}-\dfrac{3\times\textcolor{green}{6}}{\textcolor{red}{8}\times\textcolor{green}{6}} =\dfrac{40}{48}-\dfrac{18}{48} =\dfrac{22}{48}
And now we need to simplify the fraction by dividing the top and bottom by common factors until we can’t simplify anymore; this is most easily done by using the highest common factor.
\dfrac{22}{48}=\dfrac{22\div2}{48\div2}=\dfrac{11}{24}
We can’t simplify any further.
Question 4
LEVEL 3
Work out \dfrac{3}{7}+\dfrac{3}{11} in its simplest form.
Select the correct answer from the list below:
A: \dfrac{6}{77}
B: \dfrac{12}{77}
C: \dfrac{6}{77}
D: \dfrac{54}{77}
CORRECT ANSWER: D: \dfrac{54}{77}
WORKED SOLUTION:
When adding fractions we need to make the denominators the same, this is done most easily by multiplying each fraction by the other’s denominator.
\dfrac{3}{\textcolor{green}{7}}+\dfrac{3}{\textcolor{red}{11}} =\dfrac{3\times\textcolor{red}{11}}{\textcolor{green}{7}\times\textcolor{red}{11}}-\dfrac{3\times\textcolor{green}{7}}{\textcolor{red}{11}\times\textcolor{green}{7}} =\dfrac{33}{77}+\dfrac{21}{77} =\dfrac{54}{77}
And now we need to simplify the fraction by dividing the top and bottom by common factors until we can’t simplify anymore; this is most easily done by using the highest common factor. (Luckily though, we can’t simplify this one, so we don’t need to do anything else!)
Question 5
LEVEL 3
Work out \dfrac{5}{12}\div\dfrac{7}{6} in its simplest form.
Select the correct answer from the list below:
A: \dfrac{35}{72}
B: \dfrac{5}{14}
C: \dfrac{19}{12}
D: -\dfrac{3}{4}
CORRECT ANSWER: B: \dfrac{5}{14}
WORKED SOLUTION:
To divide fractions we need to Keep, Change, and Flip. We Keep the first fraction the same, Change the division into a multiplication, and Flip the second fraction.
\dfrac{5}{12}\textcolor{blue}{\div}\dfrac{\textcolor{green}{7}}{\textcolor{red}{6}}=\dfrac{5}{12}\textcolor{blue}{\times}\dfrac{\textcolor{red}{6}}{\textcolor{green}{7}} =\dfrac{5\textcolor{blue}{\times}\textcolor{red}{6}}{12\textcolor{blue}{\times}\textcolor{green}{7}}=\dfrac{30}{84}
And now we need to simplify the fraction by dividing the top and bottom by common factors until we can’t simplify anymore; this is most easily done by using the highest common factor.
\dfrac{30}{84}=\dfrac{30\div2}{84\div2}=\dfrac{15}{42}=\dfrac{15\div3}{42\div3}=\dfrac{5}{14}
We can’t simplify any further.
Question 6
LEVEL 3
Work out \dfrac{9}{11}\div\dfrac{5}{3} in its simplest form.
Select the correct answer from the list below:
A: \dfrac{28}{33}
B: \dfrac{82}{33}
C: \dfrac{15}{11}
D: \dfrac{27}{55}
CORRECT ANSWER: D: \dfrac{27}{55}
WORKED SOLUTION:
To divide fractions we need to Keep, Change, and Flip. We Keep the first fraction the same, Change the division into a multiplication, and Flip the second fraction.
\dfrac{9}{11}\textcolor{blue}{\div}\dfrac{\textcolor{green}{5}}{\textcolor{red}{3}}=\dfrac{9}{11}\textcolor{blue}{\times}\dfrac{\textcolor{red}{3}}{\textcolor{green}{5}} =\dfrac{9\textcolor{blue}{\times}\textcolor{red}{3}}{11\textcolor{blue}{\times}\textcolor{green}{5}}=\dfrac{27}{55}
And now we need to simplify the fraction by dividing the top and bottom by common factors until we can’t simplify anymore; this is most easily done by using the highest common factor. (Luckily though, we can’t simplify this one, so we don’t need to do anything else!)