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Cut each half in two
Task reminder
Cut every piece in two. Does the amount change?
The marked amount stays the same
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Halves | marked; empty |
| Quarters | marked; marked; empty; empty |
One half becomes two quarters. The marked lengths match: 1/2 = 2/4.
The numerator is the top number. The denominator is the bottom number. Cut every old part into equal pieces. Multiply both counts by the same whole number above zero. Split each third in two: 2/3 = 4/6. Split each third in four instead: 2/3 = 8/12.
Changing only the numerator changes the amount. Two thirds is not four thirds.
Rename two thirds
Check your understanding 1
Change the pieces, keep the amount
Check your understanding 1
Change the pieces, keep the amount
Rename this amount
Each full strip is one equal-sized whole.
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Figure data
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| Whole | Parts in order |
|---|---|
| Thirds | marked; marked; empty |
Write a fraction equal to 2/3 with a different denominator. Use a slash, as in 1/5. More than one answer works.
Explain how both counts change, aloud or on paper.
Show some answersHide answer
One way to cut new pieces
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Thirds | marked; marked; empty |
| Sixths | marked; marked; marked; marked; empty; empty |
4/6 works: multiply both counts by two. 6/9 works too: multiply both by three. Copying 2/3 keeps the value. But you have not changed the pieces.
Group pieces to simplify
Group smaller parts into larger parts
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Twelfths | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
| Thirds | marked; marked; empty |
The 12 small parts make 3 groups of four. The 8 marked parts make 2 of those groups. So 8/12 = 2/3.
In simplest form, no whole number above one divides both counts exactly. To simplify, divide both counts by the same factor.
Check the fraction names
Check your understanding 2
Same amount, different name
Check your understanding 2
Same amount, different name
One record is wrong. Choose its row and write the correct answer.
| Row | Given task | Written answer |
|---|---|---|
A | A fraction equal to 3/5, using a different denominator | 3/5 |
B | A fraction equal to 2/7, using a different denominator | 6/21 |
Show one correctionHide answer
A needs a different name. For example, 3/5 = 6/10. Split every fifth into two tenths; both counts double.
Different pieces, the same marked length
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Fifths | marked; marked; marked; empty; empty |
| Tenths | marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
Other answers, such as 9/15, work too. Copying 3/5 does not change the denominator. B already works: 2/7 = 6/21.
Use the top or bottom number shown
For 3/5 = Box/10, five doubles to ten. Double three too: the missing numerator is 6.
For 2/3 = 6/(Box), two triples to six. Triple three too: the missing denominator is 9.
Check your understanding 3
Which number is already there?
Check your understanding 3
Which number is already there?
Write each complete fraction. Keep its value. Use the top or bottom number shown.
Show answerHide answer
3/4 = 9/12: multiply both counts by three.
1/2 = 4/8: multiply both counts by four.
3/4 has the right value for the first task. But its top number does not match the question. Check both the value and the number shown.
Compare equal-sized pieces
Task reminder
How can you compare different-sized pieces?
Compare the marked amounts
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Thirds | marked; marked; empty |
| Quarters | marked; marked; marked; empty |
What sign belongs between 2/3 and 3/4? Write <, > or =. You can also write less than, greater than or equal to.
Show the common unitHide answer
Now the pieces match
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| First amount | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
| Second amount | marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty |
2/3 = 8/12 and 3/4 = 9/12. So 2/3 < 3/4. Count the same-sized pieces.
Match different fraction names
Compare these marked lengths
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Quarters | marked; marked; empty; empty |
| Sixths | marked; marked; marked; empty; empty; empty |
Check the amount, then the sign
Check your understanding 4
Fix one comparison
Check your understanding 4
Fix one comparison
Compare both cards
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| A · 3/8 | marked; marked; marked; empty; empty; empty; empty; empty |
| A · 2/3 | marked; marked; empty |
| B · 2/5 | marked; marked; empty; empty; empty |
| B · 5/6 | marked; marked; marked; marked; marked; empty |
A · 3/8 > 2/3
B · 2/5 < 5/6
See the amounts in equal partsHide answer
A needs less than. Rename both amounts using twenty-fourths.
Now both amounts use twenty-fourths
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| First amount | marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty; empty |
| Second amount | marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty |
3/8 = 9/24 and 2/3 = 16/24. Nine twenty-fourths is less than sixteen twenty-fourths.
B already works: two fifths is less than five sixths. The pieces differ in size. A bigger top number alone cannot tell you which is greater.
Compare the empty parts
Read the part named in the question. Here, compare the blank space.
Check your understanding 5
Compare the blank parts
Check your understanding 5
Compare the blank parts
Look at the unmarked parts
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| A | marked; empty; empty; empty |
| B | marked; marked; empty; empty; empty; empty |
See the blank amounts in equal partsHide answer
The blank amounts are 3/4 of A and 4/6 of B.
Now stripe only the original blank amounts
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 |
|---|---|
| Blank amount of A | marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty |
| Blank amount of B | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
3/4 = 9/12 > 8/12 = 4/6. Three bigger blank pieces can cover more than four smaller ones.
What is left after removal?
Crossed-out parts have gone. Compare only the marks that remain.
Check your understanding 6
Compare what is left
Check your understanding 6
Compare what is left
Compare the marks left in A and B
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| A | marked; marked; removed; removed; removed; empty |
| B | marked; marked; removed; empty |
See the amounts left in equal partsHide answer
There are two marks left in each whole. Their pieces have different sizes.
Keep only the marks that remain
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Marks left in A | marked; marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty |
| Marks left in B | marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty |
2/6 = 4/12 < 6/12 = 2/4. The whole of A still has six equal parts. Removing marks does not change its denominator.
Can top numbers settle it?
Sam says, “A larger top number always means a larger fraction.” Look at these same-sized wholes.
Fewer pieces can cover more
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Two thirds | marked; marked; empty |
| Three fifths | marked; marked; marked; empty; empty |
2/3 > 3/5, although 2 < 3. The top number counts pieces. The bottom number tells us their size. We need both to compare the amounts.
Find a pair that breaks the rule
Choose a fraction with a smaller top number but greater value.
Check your understanding 7
Make a pair that breaks the shortcut
Check your understanding 7
Make a pair that breaks the shortcut
Make the first fraction greater than the second, even though its top number is smaller.
Use fractions in simplest form between 0 and 1. Use bottom numbers from 2 to 6. Keep the same whole.
Write each fraction with a slash.
Show another counterexampleHide answer
Compare the amounts in tenths
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| One half | marked; marked; marked; marked; marked; empty; empty; empty; empty; empty |
| Two fifths | marked; marked; marked; marked; empty; empty; empty; empty; empty; empty |
1/2 > 2/5, although 1 < 2. Five tenths is greater than four tenths. Here the larger top number names a smaller amount. Its pieces are smaller.
Other pairs work too. One pair can show why an “always” rule fails. This does not make the opposite rule true. A larger top number does not always mean a smaller fraction.
Choose an amount between two others
Task reminder
Where does your fraction fit?
Leave room on both sides
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| One quarter | marked; empty; empty; empty |
| One half | marked; empty |
Between means greater than the first amount and less than the second. The two ends do not count.
See one way using eighthsHide answer
The middle amount fits both comparisons
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| One quarter | marked; marked; empty; empty; empty; empty; empty; empty |
| One possible amount | marked; marked; marked; empty; empty; empty; empty; empty |
| One half | marked; marked; marked; marked; empty; empty; empty; empty |
1/4 = 2/8 < 3/8 < 4/8 = 1/2. The marked part has room on both sides. Four eighths would reach the upper end.
Find a fraction between two fifths and three quarters
Check your understanding 8
Make both comparisons true
Check your understanding 8
Make both comparisons true
Choose your own marked amount
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 |
|---|---|
| Two fifths | marked; marked; empty; empty; empty |
| Three quarters | marked; marked; marked; empty |
Write a fraction that fits: 2/5 < square < 3/4. More than one answer works.
Show some possible fractionsHide answer
1/2, 3/5 and 2/3 all work. Each is greater than 2/5 and less than 3/4. Equivalent names, such as 5/10 for 1/2, work too.
Neither end works as your answer. Both signs are less than. Neither sign allows equal amounts.
Check your understanding 9
Order unlike fractions
Check your understanding 9
Order unlike fractions
Put 1/2, 5/6 and 2/3 in both orders. Separate fractions with commas. Or use < signs for smallest first. Use > signs for largest first.
Show answerHide answer
Use sixths: 1/2 = 3/6 and 2/3 = 4/6. Five sixths already uses that unit.
Increasing: 1/2 < 2/3 < 5/6.
Decreasing: 5/6 > 2/3 > 1/2.
Each order uses all three values. Equivalent fraction names work too.
Make room for one more fraction
A, B and C already increase. Where does D belong? Compare D with the cards on either side of its new place.
Check your understanding 10
Place the new card
Check your understanding 10
Place the new card
One card to place
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 |
|---|---|
| A · 1/4 | marked; empty; empty; empty |
| B · 1/2 | marked; empty |
| C · 5/6 | marked; marked; marked; marked; marked; empty |
| D · 2/3 | marked; marked; empty |
Show D's placeHide answer
The complete order in twelfths
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| A · one quarter | marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty; empty |
| B · one half | marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty |
| D · two thirds | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
| C · five sixths | marked; marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty |
Three, six, eight, ten twelfths: A, B, D, C. D goes third. The other cards keep their order.
Build your own order
Choose the fractions yourself. Compare each pair of neighbours. Check that your fractions meet every rule.
Check your understanding 11
Three fractions, your choice
Check your understanding 11
Three fractions, your choice
Make three different fractions between 0 and 1 in simplest form, smallest first. Use bottom numbers from 2 to 6, with at least two different top numbers and two different bottom numbers. Write each fraction using a slash.
Show one possible orderHide answer
One choice, compared in equal parts
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| One quarter | marked; marked; marked; empty; empty; empty; empty; empty; empty; empty; empty; empty |
| One half | marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty |
| Two thirds | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
1/4 < 1/2 < 2/3 works. All three are in simplest form, between zero and one. Their bottom numbers are in range. Both top and bottom numbers vary.
The twelfths in the picture help us compare. Write the simplest forms in the boxes. Twelfths are outside this task’s chosen bottom-number range.
A different answer, 1/3 < 3/5 < 5/6, also works. One third is below one half. Three fifths is 18/30. That is less than five sixths, 25/30.
Find and repair a wrong order
Smallest first. Check each row from left to right.
Which row stops increasing?
A: 3/4; 1/2; 2/3. B: 1/3; 3/5; 5/6.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Values |
|---|---|
| A | 3/4; 1/2; 2/3 |
| B | 1/3; 3/5; 5/6 |
Show answerHide answer
A needs fixing. Three quarters is greater than one half. It cannot go first.
Use the same-sized pieces to rebuild the order
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 |
|---|---|
| One half | marked; marked; marked; marked; marked; marked; empty; empty; empty; empty; empty; empty |
| Two thirds | marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty; empty |
| Three quarters | marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty |
1/2 = 6/12 < 8/12 = 2/3 < 9/12 = 3/4.
Row B already increases: 1/3 < 3/5 < 5/6.
Repair a new order
Check your understanding 12
Repair one row
Check your understanding 12
Repair one row
Check both rows
A: 1/6; 3/8; 2/3. B: 5/6; 1/4; 2/5.
Scroll across to read every label.
Figure data
This table is included in print while it is open.
| Set | Values |
|---|---|
| A | 1/6; 3/8; 2/3 |
| B | 5/6; 1/4; 2/5 |
Use commas between fractions.
Show the repaired rowHide answer
B: 1/4 < 2/5 < 5/6.
One quarter is 5/20 and two fifths is 8/20. Then 2/5 < 1/2 < 5/6, so five sixths goes last. Equivalent names, such as 2/8,4/10,10/12, work too.
A already works: 1/6 = 4/24 < 9/24 = 3/8 < 16/24 = 2/3.
Task reminder
Does the shortcut always work?
Test Mia’s shortcut
Mia says 6/10 = 3/5. She subtracted three from the top and five from the bottom. Does her method always make equivalent fractions?
Show answerHide answer
The equality is true. To explain it, divide both counts by two. Subtracting different amounts does not always work. It would change 4/5 to 1/0. That is not a valid fraction.
Rename nine twelfths in simplest form
Check your understanding 13
Hold the marked amount fixed
Check your understanding 13
Hold the marked amount fixed
Rename the marked amount
Each full strip is one equal-sized whole.
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Figure data
This table is included in print while it is open.
| Whole | Parts in order |
|---|---|
| Twelfths | marked; marked; marked; marked; marked; marked; marked; marked; marked; empty; empty; empty |
Name the marked fraction in simplest form. Split this same whole into four equal parts. How many would be marked?
Show answerHide answer
9/12 = 3/4: divide both counts by three. You would mark three of the four larger quarters. The pieces changed. The marked amount stayed the same.
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.
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Syllabus and review details
- Primary 3 Mathematics 2023 · 2021-updated-2025-10
- Primary 5 Foundation Mathematics 2025 · 2021-updated-2025-10
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