Practice · Grade 6 Fractions
Compare Fractions — Practice Problems
Training problems on comparing fractions in rising difficulty plus a boss problem. Cross-multiplication, a hint and full working per question. Grade 6, free.
Q1 of 6
0 correct
Which fraction is bigger?
2/3 ? 3/5
Quick answer
How do I practice comparing fractions effectively?
Cross-multiply several pairs: for a/b and c/d, compare a · d with c · b — the larger product belongs to the larger fraction. Mix the task types: sometimes pick the bigger fraction, sometimes judge a statement like "3/8 > 1/2" as true or false. Do a quick decimal check per problem (0.667 > 0.6) and watch pairs with equal numerators — there the one with the smaller denominator is larger.
HowTo
Solving strategy in 4 steps
This order works for any pair a/b and c/d with positive denominators.
- 1Step 1 of 4
Check the special cases first
Same denominator? Then only the numerator decides (3/7 < 5/7). Same numerator? Then the fraction with the smaller denominator is larger (1/3 > 1/4). Only when both differ do you need cross multiplication.
- 2Step 2 of 4
Cross-multiply
Numerator of the first times denominator of the second (a · d), and numerator of the second times denominator of the first (c · b). Keep the order clean: a · d belongs to the left side, c · b to the right.
- 3Step 3 of 4
Compare the two products
The larger cross-product sits above the larger fraction. If the two products are equal, the fractions are equal (e.g. 1/2 = 2/4).
- 4Step 4 of 4
Write the sign and verify
Record the result with <, > or =. To check, convert both fractions to decimals: 2/3 ≈ 0.667 and 3/5 = 0.6 → 2/3 > 3/5 — checks out.
Examples
Worked practice examples with full working
Four typical fraction comparisons from Grade 6. Try each yourself first, then check against the working.
Easy
Which is bigger: 2/3 or 3/5?
2/3 ? 3/5 | cross-multiply
2 · 5 = 10
3 · 3 = 9
10 > 9
Decimal check: 0.667 > 0.6 ✓
The larger cross-product (10) belongs to the left side, so 2/3 > 3/5.
Easy
Which is bigger: 3/8 or 1/2?
3/8 ? 1/2 | cross-multiply
3 · 2 = 6
1 · 8 = 8
6 < 8
Decimal check: 0.375 < 0.5 ✓
A bigger numerator does not mean a bigger fraction: 3/8 < 1/2 even though 3 > 1.
Medium
Are 1/2 and 2/4 equal?
1/2 ? 2/4 | cross-multiply
1 · 4 = 4
2 · 2 = 4
4 = 4
Decimal check: 0.5 = 0.5 ✓
Equal cross-products mean equivalent fractions: 1/2 = 2/4.
Hard
Boss: which is bigger, 4/9 or 5/11?
4/9 ? 5/11 | cross-multiply
4 · 11 = 44
5 · 9 = 45
44 < 45
Decimal check: 0.444 < 0.4545 ✓
A tight case — careful arithmetic pays off here: 5/11 is the larger fraction.
Pitfalls
Common mistakes — and how to avoid them
These five traps show up again and again when comparing fractions.
Comparing only the numerators
1/2 is larger than 3/8 even though 1 is smaller than 3 — the denominator counts too. Put them over a common denominator or cross-multiply first.
Swapping the cross-products
a · d belongs to the left side (a/b), c · b to the right. Swapping them accidentally flips the comparison sign.
Assuming bigger denominator = bigger fraction
With equal numerators it is the opposite: 1/4 is smaller than 1/3, because the whole is split into more pieces.
Guessing tight cases too quickly
For 4/9 and 5/11 the values are very close (0.444 vs. 0.4545). Only clean cross multiplication decides this — no gut feeling.
Ignoring negative fractions
With negative numerators the logic reverses: −1/2 is smaller than 1/3, even though the numbers look small.
Study
Practice with a plan — three quick tips
Special cases before cross multiplication
Look for equal denominators or equal numerators first. Often you spot the larger fraction in two seconds without computing — that saves precious time in a test.
Always confirm with a decimal check
Divide both fractions briefly in your head or on paper (2/3 ≈ 0.67). If the decimal result agrees with your cross-product, you made no sign or order error.
On every wrong answer: why?
Was it a slip in the cross-product? Order swapped? Compared only numerators? Note the cause — next time you will spot the mistake instantly.
FAQ
Frequently asked questions about practicing
Glossary
Terms in one sentence
- Numerator
- The top number of a fraction — how many parts are taken.
- Denominator
- The bottom number — how many parts the whole is split into.
- Cross multiplication
- Numerator times the opposite denominator (a · d versus c · b), to compare fractions without a common denominator.
- Cross-product
- One of the two products from the cross-multiplication method — the larger belongs to the larger fraction.
- Common denominator
- A denominator both fractions are rewritten over, often the LCM.
- Equivalent
- Fractions with the same value, e.g. 1/2 = 2/4 — their cross-products are equal.
- Boss problem
- The last and hardest problem of a practice set, here the tightest fraction comparison.