Mathematics · Grade 6 · First Term Exam
Every fraction problem is a locked mechanism. There is a combination for each one, and once the tumblers fall in the right order the answer just opens. Six vaults, then the full 32-item exam.
EXAM · THURSDAY, SEPTEMBER 3, 2026
Vault 00 · Prep work
Not listed on the pointers — but items 1–3 of the teacher’s reviewer are exactly this. Learn it anyway.
The first three questions never ask you to add or subtract anything. They just ask you to rewrite a fraction. Three free points, if you know the two moves.
M A D — Multiply, Add, Denominator stays.
Multiply the whole number by the bottom. Add the top. The bottom never changes.
Worked
3 2/5 → 3 × 5 = 15
15 + 2 = 17
answer = 17/5 (bottom stayed 5)
How many times, and what’s left over.
Divide the top by the bottom. The quotient is the whole number, the remainder is the new top, the bottom stays.
Worked
28/8 → 8 fits into 28 3 times (that’s 24)
28 − 24 = 4 left over
answer = 3 4/8 (= 3 1/2 in lowest terms)
Divide top and bottom by the SAME number until nothing fits any more.
Not “until it looks smaller.” Until nothing else divides both. 18/24 becomes 9/12, then 3/4 — and only 3/4 is the answer.
Vault 01 · Pointers topic 1
Teacher’s reviewer items 4, 5, 6, 13, 14, 15
Eight-twelfths plus nine-twelfths. The bottoms never move. That is the whole secret — and it is also the trap that catches half the class.
Same bottom? Add the tops. Different bottom? Make them match first.
The denominator is the size of the pieces. You cannot add fifths to thirds for the same reason you cannot add 3 pesos to 3 kilos. Never, ever add the bottoms.
Similar fractions — the easy case
8/12 + 9/12
tops: 8 + 9 = 17, bottom stays 12
17/12 is top-heavy → 1 5/12
Different bottoms: find the LCD.
The teacher’s reviewer only shows this once (item 15), but the pointers just say “Addition of Fractions” with no limit. So learn it. The LCD is the smallest number both bottoms divide into — count the multiples of the bigger bottom until the smaller one fits.
Worked — dissimilar
2/5 + 1/3 → multiples of 5: 5, 10, 15 ← 3 fits
2/5 = 6/15 (5 × 3, so 2 × 3)
1/3 = 5/15 (3 × 5, so 1 × 5)
6/15 + 5/15 = 11/15
Mixed numbers — wholes with wholes, parts with parts
2 12/20 + 3 4/20
wholes: 2 + 3 = 5 parts: 12/20 + 4/20 = 16/20
5 16/20 → simplify by 4 → 5 4/5
Vault 02 · Pointers topic 2
Teacher’s reviewer items 7, 8, 13, 14, 15
Same lock, turned the other way. The only new thing is what to do when the top of the first fraction is too small to take from.
Same bottom? Subtract the tops. The bottom does not move.
Then simplify. 10/18 − 7/18 = 3/18, and 3 divides into both → 1/6. Stopping at 3/18 is the most common lost point on this topic.
Mixed number minus a fraction
2 8/15 − 5/15
whole stays 2, tops: 8 − 5 = 3
2 3/15 → divide by 3 → 2 1/5
Not enough on top? Borrow ONE whole and hand it over as a full set.
Your reviewer never shows this, but “Subtraction of Fractions” on the pointers does not rule it out. One whole is always the bottom over itself: one whole = 8/8 when you are working in eighths.
Worked — borrowing
5 1/8 − 2 5/8 → 1 is too small to take 5 from
borrow: 5 1/8 = 4 + 8/8 + 1/8 = 4 9/8
4 9/8 − 2 5/8 = 2 4/8 = 2 1/2
Vault 03 · Pointers topic 3
Teacher’s reviewer items 9, 11, 16–19, 28, 29
This is the one operation where the bottoms do not have to match. No LCD, no renaming, nothing. Most people make it harder than it is.
STRAIGHT ACROSS. Top × top, bottom × bottom, then simplify.
That is the whole rule, and it is the exact wording of item 11: multiply numerators and denominators, then simplify.
Worked
4/6 × 1/6
tops 4 × 1 = 4, bottoms 6 × 6 = 36
4/36 → divide by 4 → 1/9
Cancel BEFORE you multiply.
Look at every top against every bottom and cross out common factors first. Your teacher’s solutions do this on every slide — those crossed-out numbers are not decoration, they are the shortcut that keeps you out of four-digit multiplication.
Worked — cancel first
8/15 × 5/12
5 and 15 both ÷ 5 → 1 and 3
8 and 12 both ÷ 4 → 2 and 3
2/3 × 1/3 = 2/9
Vault 04 · Pointers topic 4
Teacher’s reviewer items 10, 12, 20–24, 30–32
Here is the secret nobody tells you: you never actually divide fractions. You flip one of them and multiply. The entire topic is built on that swap.
K C F — Keep, Change, Flip.
Keep the first fraction exactly as it is. Change the ÷ into a ×. Flip the second fraction upside down. Then it is just Vault 03 again.
Worked
24/30 ÷ 3/5
keep 24/30, change to ×, flip 3/5 → 5/3
24/30 × 5/3 = 120/90 = 4/3 = 1 1/3
Flip the SECOND one only.
The second fraction is the divisor — that is the one that flips. Not the first one, not both. Three of item 12’s four choices are that exact mistake, which tells you your teacher expects it.
| What you see | What to do first | Example |
|---|---|---|
| Fraction ÷ fraction | Straight to KCF | 6/8 ÷ 1/4 → 6/8 × 4/1 = 3 |
| Fraction ÷ whole number | Put a 1 under the whole number, then KCF | 8/10 ÷ 4/1 → 8/10 × 1/4 = 1/5 |
| Whole number ÷ fraction | Put a 1 under the whole number, then KCF | 8/1 ÷ 4/12 → 8/1 × 12/4 = 24 |
| Mixed number anywhere | MAD it into an improper fraction FIRST | 1 1/4 ÷ 2/6 → 5/4 × 6/2 = 3 3/4 |
Vault 05 · Pointers topic 5
Teacher’s reviewer items 25–32 · addition, subtraction, multiplication and division of fractions
Nobody fails these because the arithmetic is hard. They fail because they picked the wrong operation. The words tell you which one — if you know the four signals.
OF is times. INTO is divide. ALTOGETHER adds. HOW MUCH LONGER takes away.
Say it once out loud. Then read the question twice before you write anything — underline the signal word, and the operation picks itself.
| Signal in the question | Operation | From your reviewer |
|---|---|---|
| “of this sack”, “of the water” | Multiply | Items 28, 29 |
| “how many can she make”, “each bottle contains” | Divide | Items 30, 31 |
| “packs it equally into 3 bags” | Divide | Item 32 |
| “Monday and Tuesday”, “altogether”, “in total” | Add | Items 25, 26 |
| “how much longer”, “how much is left” | Subtract | Item 27 |
Bernard’s week — three exam items come from it.
Monday 3/12 · Tuesday 5/12 · Wednesday 1 2/12 · Thursday 2 1/12 hours. Everything is already in twelfths, so no LCD is ever needed — which is exactly why this vault is called Twelve.
The real thing
Three parts, exactly the types listed on your pointers: Multiple Choice, Computational Skills, and Problem Solving. These are your teacher’s own 32 items. 32 points.
Choose the letter of the best answer. 15 points.
Perform the indicated operation. Type your answer in lowest terms. 9 points.
Read carefully, find the signal word, then compute. 8 points.
Vault status
0/44
Apprentice
Nothing cracked yet. Start at Vault 00 and tap every card before you answer — the cards are where the combinations are.
Vaults 0/12 · Multiple Choice 0/15 · Computational 0/9 · Problem Solving 0/8
Night before · one screen
Screenshot this. It is everything, in the exam’s own order.
Mixed → improper
M A D — Multiply, Add, Denominator stays.
3 2/5 → 3×5=15, +2=17 → 17/5
Improper → mixed
How many times, and what’s left over.
28/8 → 3 times, 4 left over → 3 4/8
Lowest terms
Divide top and bottom by the SAME number until nothing fits any more.
20/36 → both ÷4 → 5/9
Adding & subtracting
Same bottom? Add the tops. Different bottom? Make them match first.
Never add the bottoms. LCD = smallest number both bottoms divide into.
Subtracting mixed numbers
Not enough on top? Borrow ONE whole and hand it over as a full set.
5 1/8 = 4 9/8, because one whole is 8/8.
Multiplying
STRAIGHT ACROSS. Top × top, bottom × bottom, then simplify.
Cancel before you multiply. Whole number gets a 1 underneath. Mixed number gets MAD first.
Dividing
K C F — Keep, Change, Flip.
Flip the SECOND one only — the divisor. Then it is just multiplication.
Word problems
OF is times. INTO is divide. ALTOGETHER adds. HOW MUCH LONGER takes away.
Then label the answer: hours, litres, kg, bottles, bags.
Every single answer
THE LAST CLICK — lowest terms, and top-heavy becomes a mixed number.
16/20 is not the answer. 4/5 is.
Come back and run this again in two days. Repeating it beats staring at it — and the second run is always faster.