Fraction Practice: Equivalent Parts, Addition and Division
A denominator describes the size of the parts; a numerator counts them. You cannot add counts of different-sized pieces until you express them in a common unit. Start with this picture before using an arithmetic rule.
Original foundation practice · choose by prerequisite skill.
Start here if this is where you get stuck
Start here if you add denominators, cannot explain equivalent fractions, or stall when an algebra problem contains fractions. A younger learner meeting fractions and an older learner repairing this prerequisite can use the same model.
Before opening a solution, find 1/2 + 1/3 and explain why the denominator is not 5.
Before you start
You will need: Multiplication tables, factors and equal sharing.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
Three ideas to keep in view
Equivalent fractions describe the same amount using different-sized equal parts. Multiply or divide numerator and denominator by the same non-zero number.
To add unlike fractions, rewrite both with a common denominator and then add the numerators. The common part size stays unchanged.
Dividing by a fraction asks how many of those fractional units fit. For example, dividing by one-half counts halves rather than whole units.
Three of four equal parts are shaded: 3/4 of one whole. If each quarter is split in two, the same shaded amount is 6/8; the whole has not changed.
Try the worked example first
F-FRAC-W1Common partsFocused practice
Find 1/3 + 1/4. Explain why adding top and bottom separately is incorrect.
Show your working
Need a starting hint?
Use pieces small enough to fit exactly into both thirds and quarters.
Still stuck? Reveal the setup
Twelfths work: 1/3=4/12 and 1/4=3/12.
Show worked solution+
1
Rename the parts
Both fractions now count twelfths.
2
Add counts
Four twelfths plus three twelfths is seven twelfths.
Answer: 7/12
Before moving on: can you explain why your method works, as well as give the answer?
Your turn: three different checks
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
F-FRAC-Q1Equivalent fractionsFocused practice
Fill the blank: 3/5 = ?/20.
Show your working
Need a starting hint?
How did 5 become 20?
Still stuck? Reveal the setup
Multiply both numerator and denominator by 4.
Show worked solution+
1
Scale the part count
3 × 4=12.
2
Verify
12/20 reduces to 3/5.
Answer: 12
Before moving on: can you explain why your method works, as well as give the answer?
F-FRAC-Q2SubtractFocused practice
Find 5/6 − 1/4.
Show your working
Need a starting hint?
Use a common denominator of 12.
Still stuck? Reveal the setup
5/6=10/12 and 1/4=3/12.
Show worked solution+
1
Rename
Both quantities are now in twelfths.
2
Subtract
10−3=7 twelfths.
Answer: 7/12
Before moving on: can you explain why your method works, as well as give the answer?
F-FRAC-Q3Count halvesFocused practice
How many half-cup portions fit into 3 cups?
Show your working
Need a starting hint?
Each cup contains two half-cups.
Still stuck? Reveal the setup
3 ÷ 1/2 counts the number of halves.
Show worked solution+
1
Interpret
Two portions fit in each cup.
2
Count
Three cups contain 3 × 2 portions.
Answer: 6 portions
Before moving on: can you explain why your method works, as well as give the answer?
Catch a likely mistake
A tempting claim: “Add fractions by adding both numerators and denominators.”
The denominator is the part size, not another count to add.
Close the examples and try again
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
F-FRAC-R1Changed sumIndependent retest
Find 2/3 + 1/6.
Show your working
Need a starting hint?
Express both in sixths.
Still stuck? Reveal the setup
2/3=4/6.
Show worked solution+
1
Rename
Four sixths plus one sixth.
2
Add
5/6.
Answer: 5/6
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
F-FRAC-R2Changed portionsIndependent retest
How many quarter-metre pieces can be cut from 2 metres with no waste?
Show your working
Need a starting hint?
Count quarters in each metre.
Still stuck? Reveal the setup
2 ÷ 1/4.
Show worked solution+
1
Per metre
There are four quarter-metres.
2
Total
Two metres contain eight.
Answer: 8 pieces
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Use the repair in your next task
Try the two retests with examples closed. If the same error returns, correct that step and retry later; this short practice is not a diagnostic score or a grade assessment.
Ask the learner to point to one whole and one part in the drawing. An arithmetic answer alone does not show whether they understand the part size.
If the retests are independent, return to the problem that brought you here. The linked Class 10 application is optional for learners already studying that topic; younger learners should use their current school exercise.
No. It is a prerequisite-focused foundation lesson. Teachers and parents can use the listed skills to decide whether it fits the learner's current work.
Can I print the questions and worked solutions separately?+
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
PERSONAL SUPPORT
Does the same mistake keep returning?
Bring one attempted question and the step that caused difficulty. Discuss suitable TutorMax support for the learner's current level.
