MATHEMATICS - DIVIDING FRACTIONS

Dividing Fractions Worksheet

10 questions
Estimate, multiply and divide proper fractions.
Difficulty: Medium
Board: CAIE
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Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.
For $\frac{3}{4}\div\frac{2}{5}$ , which line shows the correct reciprocal method and simplified quotient?

A) Invert both fractions: $\frac{4}{3}\times\frac{5}{2}=\frac{10}{3}$
B) Multiply the fractions without inverting: $\frac{3}{4}\times\frac{2}{5}=\frac{3}{10}$
C) Keep the first fraction and invert the second: $\frac{3}{4}\times\frac{5}{2}=\frac{15}{8}$
D) Keep the first fraction and invert the second: $\frac{3}{4}\times\frac{2}{5}=\frac{3}{10}$

Q2.
Which is the best estimate of $\frac{7}{8}\div\frac{3}{10}$ ?

A) $\frac{1}{3}$
B) $8$
C) $3$
D) $1$

Q3.
Which proper fraction completes $\frac{2}{3}\div\square=\frac{8}{9}$ ?

A) $\frac{4}{5}$
B) $\frac{3}{4}$
C) $\frac{1}{2}$
D) $\frac{8}{9}$

Q4.
A student is finding $\frac{5}{6}\div\frac{2}{3}$ . Which explanation is correct?

A) Keep the first fraction and multiply by the reciprocal of the divisor: $\frac{5}{6}\times\frac{3}{2}=\frac{5}{4}$
B) Multiply by the divisor without changing it: $\frac{5}{6}\times\frac{2}{3}=\frac{5}{9}$
C) Invert the first fraction, then multiply: $\frac{6}{5}\times\frac{2}{3}=\frac{4}{5}$
D) Invert the divisor but subtract the numerators: $\frac{5-3}{6-2}=\frac{1}{2}$

Q5.
A container holds $\frac{3}{5}\,\mathrm{L}$ of juice. Each glass receives $\frac{3}{20}\,\mathrm{L}$ . How many glasses can be filled?

A) $4$ glasses
B) $5$ glasses
C) $3$ glasses
D) $6$ glasses

Q6.
Without calculating the exact quotient, which statement about $\frac{4}{7}\div\frac{2}{3}$ is correct?

A) The quotient is less than $\frac{4}{7}$ .
B) The quotient is equal to $\frac{4}{7}$ .
C) The quotient is greater than $\frac{4}{7}$ .
D) The quotient is equal to $\frac{2}{3}$ .

Q7.
Which statement correctly interprets $\frac{5}{8}\div\frac{1}{4}=2\frac{1}{2}$ ?

A) There are $\frac{5}{32}$ groups of size $\frac{1}{4}$ in $\frac{5}{8}$ .
B) There are $2\frac{1}{2}$ groups of size $\frac{1}{4}$ in $\frac{5}{8}$ .
C) Splitting $\frac{1}{4}$ into $\frac{5}{8}$ equal groups gives $2\frac{1}{2}$ in each group.
D) The fraction $\frac{5}{8}$ is $2\frac{1}{2}$ less than $\frac{1}{4}$ .

Q8.
Which quotient is equal to $\frac{7}{10}$ ?

A) $\frac{7}{20}\div\frac{1}{2}$
B) $\frac{3}{10}\div\frac{3}{5}$
C) $\frac{7}{20}\div\frac{2}{5}$
D) $\frac{4}{9}\div\frac{2}{3}$

Q9.
The diagram shows a ribbon and the required length of each piece. How many pieces of that length can be cut from the ribbon?

Diagram for question 9: The diagram shows a ribbon and the required length of each piece. How many pieces of that length can be cut…

A) $4$ pieces
B) $3$ pieces
C) $8$ pieces
D) $6$ pieces

Q10.
Which division expression finds how many groups of the size shown in the lower bar fit into the shaded amount in the upper bar?

Diagram for question 10: Which division expression finds how many groups of the size shown in the lower bar fit into the shaded…

A) $\frac{5}{6}\times\frac{1}{3}$
B) $\frac{1}{3}\div\frac{5}{6}$
C) $\frac{5}{6}\div\frac{2}{3}$
D) $\frac{5}{6}\div\frac{1}{3}$

What this assessment covers

Concepts Tested

dividing fractions
Estimate, multiply and divide proper fractions.

Question Mix

Medium questions included

Skills you build

Understand

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Assessment details

Total questions:: 10
Subject:: Mathematics
Topic:: Dividing Fractions
Difficulty:: Medium
Grade:: Grade 6
Board:: CAIE
Marks:: 10.00

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Q1. For 3/4 ÷ 2/5, which line shows the correct reciprocal method and simplified quotient?

Q2. Which is the best estimate of 7/8 ÷ 3/10?

Q3. Which proper fraction completes 2/3 ÷ square = 8/9?

Q4. A student is finding 5/6 ÷ 2/3. Which explanation is correct?

Q5. A container holds 3/5 L of juice. Each glass receives 3/20 L. How many glasses can be filled?

Q6. Without calculating the exact quotient, which statement about 4/7 ÷ 2/3 is correct?

Q7. Which statement correctly interprets 5/8 ÷ 1/4 = 21/2?

Q8. Which quotient is equal to 7/10?

Q9. The diagram shows a ribbon and the required length of each piece. How many pieces of that length can be cut from the ribbon?

Q10. Which division expression finds how many groups of the size shown in the lower bar fit into the shaded amount in the upper bar?