110 practice questions covering Working with Fractions, organised into 3 topics.
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The four products are $12$, $16$, $18$ and $20$, so the smallest comes from the smallest fraction, $\frac{1}{2}$. The other three fractions are each closer to $1$, and the nearer a proper fraction is to $1$, the more of the $24$ is kept.
Q2
easy
A student says that $\frac{1}{2}$ of $30$ is $60$. Why must this be wrong?
AHalf of a number is always a whole number
BHalf of a number is always smaller than the number
C$30$ is an even number
DHalving and doubling give the same answer
Show answer and explanation
Correct answer: B - Half of a number is always smaller than the number
Taking half keeps only part of the quantity, so the answer has to be less than $30$, and $60$ is more. Whether the answer is a whole number is beside the point, as is the fact that $30$ is even. Halving and doubling move in opposite directions, which is exactly the mistake made here.
Q3
medium
Multiply $\frac{5}{6}$ by $\frac{3}{10}$ and give the answer in simplest form.
A$\frac{1}{4}$
B$\frac{8}{16}$
C$\frac{25}{9}$
D$\frac{34}{30}$
Show answer and explanation
Correct answer: A - $\frac{1}{4}$
The product is $\frac{15}{60}$, and dividing both parts by $15$ gives $\frac{1}{4}$. The value $\frac{25}{9}$ comes from dividing instead of multiplying, $\frac{8}{16}$ from adding numerators and denominators separately, and $\frac{34}{30}$ from adding the two fractions.
Q4
medium
How many pieces of size $\frac{2}{3}$ fit into $8$?
A$4$
B$\frac{3}{16}$
C$\frac{16}{3}$
D$12$
Show answer and explanation
Correct answer: D - $12$
Dividing means multiplying by the reciprocal, so $8 \times \frac{3}{2} = \frac{24}{2} = 12$. The value $\frac{16}{3}$ comes from multiplying by $\frac{2}{3}$ instead of dividing, $\frac{3}{16}$ turns that answer over, and $4$ comes from dividing by $2$ and forgetting the $3$.
Q5
medium
Which number has no reciprocal?
A$1$
B$0$
C$\frac{1}{2}$
D$7$
Show answer and explanation
Correct answer: B - $0$
A reciprocal must give $1$ when multiplied by the number, and nothing multiplied by $0$ ever reaches $1$, so $0$ has no reciprocal. The number $1$ is its own reciprocal, $\frac{1}{2}$ has the reciprocal $2$, and $7$ has the reciprocal $\frac{1}{7}$.
Q6
easy
What is the reciprocal of $\frac{3}{5}$?
A$\frac{3}{5}$
B$\frac{1}{15}$
C$\frac{5}{3}$
D$\frac{1}{3}$
Show answer and explanation
Correct answer: C - $\frac{5}{3}$
The reciprocal is found by swapping the numerator and the denominator, so $\frac{3}{5}$ becomes $\frac{5}{3}$, and $\frac{3}{5} \times \frac{5}{3} = 1$. Repeating $\frac{3}{5}$ changes nothing, $\frac{1}{3}$ writes $1$ over the numerator alone, and $\frac{1}{15}$ comes from multiplying the two parts together.
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