1 | FRACTIONS 02 – OPERATIONS ×& ÷ - PRACTICE VERSION 2 LEARNING RESOURCE DEVELOPMENT PROGRAM
Fractions 02 – Operations with Fractions: × and ÷ PRACTICE QUESTIONS & WORKED SOLUTIONS
QUESTIONS
Multiplication
1. !!× !!
2. 2 !!×1 !
!
3. !!"× !!
4. !!"×6
Division
1. !!÷ !
!
2. 4÷ !!
3. !!÷ !
!
4. 3 !!÷ 1 !
!
Challenge yourself: Word Problems1
1. A cupcake recipe asks for !! of a cup of butter. Rob wants to make !
! of the original recipe. How many cups of butter will
Rob need?
2. At the candy store, Sophie filled a bag with 2 !! kilograms of candy. !
! of the weight of the candy was from chocolate
covered pretzels. How much did the chocolate covered pretzels in Sophie’s bag weigh?
3. Vera is using her phone. Its battery life is down to !!, and it drains another !
! every hour. How many hours will her battery
last?
4. Sara decides to bottle !! of her milk. She pours the milk evenly among 5 bottles. What fraction of her milk will she put in
each bottle?
NOTE:
If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through reception: phone (02) 4221 3977, or Level 2 (top floor), Building 11, or through your campus.
Alternatively, if you have not been working with fractions in a while, do refer to the resource “Fractions 01 – An Introduction” for a quick revision.
REFERENCES
1. Questions from Khan Academy <https://www.khanacademy.org/math/arithmetic/fraction-arithmetic>
2 | FRACTIONS 02 – OPERATIONS ×& ÷ - PRACTICE VERSION 2 LEARNING RESOURCE DEVELOPMENT PROGRAM
WORKED SOLUTIONS
Multiplication
1. !!
× !!
= !×!!×!
= !"!"
2. 2 !!
× 1 !!
= !!
× !!
= !×!!×!
= !"!"
= 4 !!"
3. !!"
× !!
= !×!!"×!
= !!"
= ! ÷!!" ÷!
= !!"
4. !!"
× 6 = !!"
× !!
= !×!!"×!
= !"!"
= !" ÷!!" ÷!
= !"!
= 2 !!
Division
1. !!
÷ !!
= !!
× !!
= !×!!×!
= !"!
= 5 !!
2. 4 ÷ !!
= !!
× !!
= !×!!×!
= !"!
= 14
3. !!
÷ !!
= !!
× !!
= !×!!×!
= !!"
4. 3 !!
÷ 1 !!
= !!
÷ !!
= !!
× !!
= !×!!×!
= !" ÷!!" ÷!
= !"!
= 2 !!
Challenge yourself: Word Problems 1. Rob needs !
! of !
! of a cup of butter. To find what fractions is equal to !
! of !
! , we can change the word “of” to “times”
and multiply: 13
of 34
= 13
× 34
= 1×33×4
= 312
= 3 ÷ 312 ÷ 3
= 14
Therefore, Rob needs !! of a cup of butter.
2. The chocolate covered pretzels weighted !
! of 2 !
! kilograms. To find out what amount is equal to !
! of 2 !
!, we change the
word “of” to “times” and multiply:
14
of 223
= 14
× 223
= 14
× 83
= 812
= 8 ÷ 412 ÷ 4
= 23
Therefore, the chocolate covered pretzels in Sophie’s bag of candy weighed !! of a kilogram.
3. We can think about this problem like this:
Number of hours = remaining battery life ÷ amount used per hour So,
Number of hours =12÷18=12×81=82= 4 hours
Therefore, her battery will last 4 hours.
4. We need to divide the fraction of her milk !!
by the number of bottles she will fill 5 . So !!÷ 5 will be the answer:
13÷ 5 =
13÷51=13×15=1×13×5
=115
Therefore, Sara will put !!"
of her milk in each bottle.