Understanding fractions
See a fraction as parts of a whole — before the exam turns it into a trap.
← All countdown tipsA fraction is simply parts of a whole. The bottom number (denominator) says how many equal parts the whole is cut into. The top number (numerator) says how many of those parts we are talking about.
Picture it: three-quarters
Say it out loud with your child: “three out of four equal parts.” That sentence stops a lot of mix-ups later.
Remember
- Denominator = how many equal pieces the whole is cut into
- Numerator = how many pieces we have / use / shade
- Pieces must be equal — unequal slices are not a proper fraction picture
Same fraction, different shapes
Shape changes; the idea does not. Half always means one of two equal parts.
Exam trap
Children sometimes treat the bigger digit as “more” even when the whole is cut differently. Example: they may think 13 is bigger than 12 because 3 > 2. The pictures say otherwise — halves are larger pieces than thirds.
Question patterns you might see
Same idea, different outfits — from straightforward to exam-style traps.
1 · Simple — Read a clear picture
“What fraction is shaded?” Equal parts, no extras. Answer is literally shaded ÷ total.
2 · Simple — Word story → fraction
“A pizza has 8 equal slices; Sam eats 3. What fraction did he eat?” Still parts of one whole.
3 · Medium — Fraction of a set (many items)
“3 out of 12 beads are blue. What fraction are blue?” The “whole” is the group, not one shape.
4 · Medium — What’s left / unshaded
“38 of a bar is eaten. What fraction is left?” Flip to the unused part (58), don’t repeat the given fraction.
5 · Trickier — Compare unit fractions
“Which is larger: 15 or 14?” Bigger denominator → smaller piece. Picture beats digit size.
6 · Trickier — Unequal “looks like a fraction”
A shape split into unequal regions with some shaded. Trap: counting regions as equal. Only equal parts make a true fraction picture.
7 · Trickiest — Same shading, different wholes
Both diagrams shade “3 parts,” but one whole is cut into 4 and the other into 6. Same numerator look ≠ same fraction. Always check the denominator of that whole.
Coach tip: before answering, ask “What is the whole?” and “Are the parts equal?” Those two questions unlock most of the list above.
Four operations — quick tactics
Memorise the move, then check with a tiny example. Same pieces only when adding or subtracting.
Addition (+)
Different bottoms? Multiply top and bottom by the same number so denominators match, then add the tops.
12 + 14
12 = 1×22×2 = 24
(×2 top & bottom — common denominator 4)
24 + 14 = 34
Subtraction (−)
Same move: multiply top and bottom to get a common denominator, then subtract the tops. Bottoms stay the same.
56 − 13
13 = 1×23×2 = 26
(×2 top & bottom — common denominator 6)
56 − 26 = 36 = 12
Multiplication (×)
Tops × tops, bottoms × bottoms. No need to match denominators. “Of” usually means multiply.
23 × 12
→ 2×13×2 = 26 = 13
Division (÷)
Keep · Change · Flip: keep the first fraction, change ÷ to ×, flip the second (use its reciprocal).
34 ÷ 12
→ 34 × 21 = 64 = 1 12
Flip the divider, then multiply
Tomorrow (D-29): verbal ordering — who comes before, behind, or between.
Next step
Practice locks the idea in. WhatsApp delivers tomorrow’s tip to your phone — same group as mock updates.