On this page
You stopped at:
ContinueRevision Mode is on. Questions and activities are hidden.
The linked question or activity is hidden by Revision Mode.
Count the same-sized parts across wholes
Task reminder
Count quarters across all the strips. How many wholes do they make?
The marked amount is two wholes and three quarters. Each full strip is one whole. Count the marked quarters across all three strips.
Keep the quarter-sized parts
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Strip A | marked; marked; marked; marked |
| Strip B | marked; marked; marked; marked |
| Strip C | marked; marked; marked; empty |
A mixed number separates whole units from a fractional part. An improper fraction counts the parts together; its numerator is at least its denominator.
Write 2 3/4 as an improper fraction. Use a slash, as in 1/4.
Show answerHide answer
Each whole contains 4 quarters. Two wholes contain 8 quarters. The extra three make 11 quarters:
The parts are still quarters. Changing the way we count does not change their size.
Explore: exchange the pieces
Select a whole and exchange it for four quarters. Repeat for the other whole. What stays the same?
What this checks
Exchange the starting pieces into the requested same-sized parts. Undo restores the earlier pieces.
The same amount
One whole
One whole
One quarter
One quarter
One quarter
The same amount: 11/4 whole.
Show solutionHide answer
Keep the quarter-sized parts
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Strip A | marked; marked; marked; marked |
| Strip B | marked; marked; marked; marked |
| Strip C | marked; marked; marked; empty |
Both wholes become eight quarters. With the three extra quarters, 2 3/4 = 11/4.
Make whole groups again
Write 17/5 as a mixed number. Make groups of five fifths. How many whole groups can you make? What is left?
Use a space between the whole and fraction, as in 1 1/4.
Show the regroupingHide answer
Seventeen fifths, grouped into wholes
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Strip A | marked; marked; marked; marked; marked |
| Strip B | marked; marked; marked; marked; marked |
| Strip C | marked; marked; marked; marked; marked |
| Strip D | marked; marked; empty; empty; empty |
17 = 3 × 5 + 2, so 17/5 = 3 2/5. The remainder gives the fractional numerator. The denominator stays 5.
Make whole groups with nothing left
Write 20/5 as a whole number. Make groups of five fifths. Does any fractional part remain?
Show answerHide answer
20/5 = 4. There are no fifths left over. Do not add an extra whole.
Check your understanding 1
Move between the two forms
Check your understanding 1
Move between the two forms
Choose how to count the parts
Write 4 1/6 as an improper fraction. Write 23/6 as a mixed number. Make or draw groups of sixths if you need them.
Show answerHide answer
4 1/6 = 25/6 because 4 × 6 + 1 = 25.
23/6 = 3 5/6 because 23 = 3 × 6 + 5. Count the same sixth-sized parts in both directions.
Changing form and simplifying are separate decisions: 2 2/4 = 10/4 = 5/2. Simplify the fraction when the question asks for simplest form.
Task reminder
Do both ways of writing the fraction show the same amount?
Check your understanding 2
Check every whole
Check your understanding 2
Check every whole
One record is wrong. Choose its row and write the correct answer.
| Row | Given task | Written answer |
|---|---|---|
A | 3 1/4 as an improper fraction | 4/4 |
B | 2 2/3 as an improper fraction | 8/3 |
Show the checksHide answer
A: 3 × 4 + 1 = 13, so 3 1/4 = 13/4.
B: 2 × 3 + 2 = 8, so 2 2/3 = 8/3. Keep this record.
Check your understanding 3
Keep all the leftover parts
Check your understanding 3
Keep all the leftover parts
One record is wrong. Choose its row and write the correct answer.
| Row | Given task | Written answer |
|---|---|---|
A | 19/4 as a mixed or whole number | 4 3/4 |
B | 23/5 as a mixed or whole number | 4 2/5 |
Show the checksHide answer
A: 19 = 4 × 4 + 3, so 19/4 = 4 3/4.
B: 23 = 4 × 5 + 3, so 23/5 = 4 3/5. Two fifths would lose one fifth.
Task reminder
Which counters make the whole set?
A set can be the whole
Find 3/8 of 24 counters. All 24 counters form the whole set. Share them into 8 equal groups, then select 3 groups.
Select groups, not single counters
Each row is an equal group. The selected and other groups together form the original set.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Counters |
|---|---|
| Selected groups | counter; counter; counter; counter; counter; counter; counter; counter; counter |
| Other groups | counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter |
Show answerHide answer
One eighth is 24 ÷ 8 = 3 counters. Three eighths is 3 × 3 = 9 counters. Here the denominator counts equal groups; the numerator counts selected groups. Counting individual counters instead gives 9/24 = 3/8: the same selected part of the same whole.
Selecting only three counters would not select three eighths of this set.
Check your understanding 4
Name a fraction from the selected count
Check your understanding 4
Name a fraction from the selected count
Keep the whole tray
A tray holds 18 counters. 6 are marked. What fraction of the whole tray is marked? What fraction is unmarked? Write each as a fraction; equivalent forms are welcome. Treat each counter as one equal part of the tray.
Both parts belong to the whole
The marked and unmarked counters are separate parts of the same tray. Include both parts when identifying the whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Counters |
|---|---|
| Marked | counter; counter; counter; counter; counter; counter |
| Unmarked | counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter |
Show answerHide answer
Marked: 6/18 = 1/3. Unmarked: 12/18 = 2/3. The two parts together make one whole tray.
6/12 compares the marked count with the unmarked count. It does not describe the marked part of the whole tray.
Check your understanding 5
Identify the whole set
Check your understanding 5
Identify the whole set
Find a part without a picture
A box holds 35 beads. Two fifths are green. How many beads are green?
Help: find one fifth first
Show answerHide answer
14 beads: one fifth contains 35 ÷ 5 = 7 beads; two fifths contain 2 × 7 = 14. The 35 beads, including all colours, form the whole set.
Task reminder
How many stickers does one equal part stand for?
Let a bar stand for a large set
A shop has 240 stickers. 3/8 of them are star stickers. The rest are heart stickers. The shop then sells 45 heart stickers. How many heart stickers are left?
Use a bar to stand for all 240 stickers. Split it into 8 equal parts. Mark 3 parts for the star stickers.
One bar for all 240 stickers
Each full strip is one equal-sized whole.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| All 240 stickers | marked; marked; marked; empty; empty; empty; empty; empty |
Now use the second fact in the story. The 45 stickers sold are all heart stickers.
Two ways to find the heart stickersHide answer
One eighth is 240÷8 = 30 stickers.
Stars first: 3 × 30 = 90 star stickers, so 240-90 = 150 heart stickers.
Hearts straight from the bar: the heart stickers fill the other 5 parts, so 5 × 30 = 150.
Both ways give 150. Then 150-45 = 105 heart stickers are left.
Check: 90 + 150 = 240, and 105 + 45 = 150.
The 45 is not part of the fraction. Find the heart stickers first, then take away the 45 sold.
Check your understanding 6
Plan two steps with your own bar
Check your understanding 6
Plan two steps with your own bar
A class collects 360 cans. 5/12 of them are drink cans. The rest are food cans. 70 food cans are dented. How many food cans are not dented?
Sketch a bar for all 360 cans before you calculate.
Help: use the bar one step at a time
Show answerHide answer
One twelfth is 360÷12 = 30 cans. Drink cans: 5 × 30 = 150. Food cans: 360-150 = 210, or 7 × 30 = 210. Food cans not dented: 210-70 = 140.
Check: 150 + 70 + 140 = 360 cans.
360-70 = 290 takes the dented cans from every can. The 70 dented cans are only food cans.
Task reminder
Are you finding a fraction of one group or the whole box?
Check which whole the fraction uses
Check your understanding 7
The same selected objects can name different fractions
Check your understanding 7
The same selected objects can name different fractions
A box holds 35 beads. 14 are green. 7 of the green beads have a star. The labelled mats show the parts of this one box.
Keep the selected seven; change the whole
The two green mats show all the green beads. All three mats show the whole box. The starred beads belong to both these groups.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Counters |
|---|---|
| Green, with a star | counter; counter; counter; counter; counter; counter; counter |
| Green, no star | counter; counter; counter; counter; counter; counter; counter |
| Other beads | counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter; counter |
Show answerHide answer
Of the 14 green beads, 7/14 = 1/2 have a star. Of all 35 beads, 7/35 = 1/5 have a star.
The selected seven beads stay the same. The reference whole changes. Neither fraction means that only seven beads are in the box.
Check your understanding 8
Check the reference whole
Check your understanding 8
Check the reference whole
One record is wrong. Choose its row and write the correct answer.
| Row | Given task | Written answer |
|---|---|---|
A | 9 marked; 27 objects in all. Fraction marked | 9/18 |
B | 8 marked; 40 objects in all. Fraction marked | 1/5 |
Show the checksHide answer
A: Nine marked objects belong to a whole set of 27: 9/27 = 1/3. The other 18 are only the unmarked part.
B: 8/40 = 1/5. Both marked and unmarked objects belong in the whole.
Check your understanding 9
Check the objects in the selected groups
Check your understanding 9
Check the objects in the selected groups
One record is wrong. Choose its row and write the correct answer.
| Row | Given task | Written answer |
|---|---|---|
A | Number of objects in 3/8 of a set of 48 | 18 |
B | Number of objects in 2/7 of a set of 35 | 2 |
Show the checksHide answer
A: 48÷8 = 6 in each group, then 3 × 6 = 18 objects.
B: 35÷7 = 5 in each group, then 2 × 5 = 10 objects. The numerator 2 counts groups, not the objects in them.
Can the groups overlap?
A class has 30 pupils. Half are in a choir. One third of the whole class plays an instrument. How many are in each group? Is there enough information to find how many do neither?
Show answerHide answer
There are 15 choir pupils and 10 instrument players. We do not know how many belong to both groups, so we cannot find how many do neither.
If the groups are separate, 5 pupils do neither. If all ten instrument players are in the choir, 15 pupils do neither. Both fit what you know. You cannot choose one exact answer.
Before adding groups, check that the story says nobody belongs to both.
For a grown-up
Pip’s synthetic voice uses the University of Edinburgh’s Alba speech dataset, via Piper’s Alba voice, under CC BY 4.0. Audio is optional.
Loading reading progress…
Lesson done
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday
Checking learning on this device…
Change goal
Progress options
Loading questions…
Syllabus and review details
- Primary 4 Mathematics 2024 · 2021-updated-2025-10
- Primary 5 Foundation Mathematics 2025 · 2021-updated-2025-10
Last reviewed: