Which fraction is bigger? Learn powerful strategies to compare and order fractions! Use visuals, common parts, and smart shortcuts. Let's become fraction comparison experts! 🔍📊
Master fraction comparison with these engaging activities!
Compare fractions when the bottom numbers match!
Compare when the top numbers are the same!
🖱️ Drag options below to the correct boxes (computer) or click to move (mobile)
Use fraction bars to compare fractions!
Put several fractions in order from least to greatest!
Drag to sort or use ↑↓ buttons to adjust · Smallest to Biggest
Explore 7 powerful techniques for comparing fractions!
When fractions have the same denominator, comparing is super simple! The denominator tells us the SIZE of the pieces, and if they're the same size, we just need to compare HOW MANY pieces we have (the numerator). More pieces of the same size = more total. It's like comparing 3 cookies vs 5 cookies - obviously 5 is more!
When denominators match, compare numerators!
3/7 vs 5/7: Since 5 > 3, then 5/7 > 3/7
2/9 vs 8/9: Since 8 > 2, then 8/9 > 2/9
Think: Same-size pieces, so more pieces = more total!
This is the EASIEST comparison method!
Always check denominators first! If they match, you're golden - just compare the top numbers and you're done! This saves time and reduces mistakes!
Comparing denominators instead of numerators! For 3/8 vs 5/8, don't think about the 8s - just compare 3 vs 5. The 8s are already equal!
If two pizzas are cut into 8 slices each, and you eat 3 slices from one and 5 from another, you obviously ate more from the 5-slice pizza! Same idea!
Make flashcards with same-denominator comparisons! Practice until you can instantly say '7/10 > 4/10' without thinking hard!
This rule seems backwards but makes perfect sense! When you cut something into MORE pieces, each piece gets SMALLER! 1/10 of a pizza is tiny because the pizza is split 10 ways. 1/2 of the same pizza is huge - only split 2 ways! Same numerator (1 piece) but very different sizes! BIGGER denominator = SMALLER pieces!
When numerators match, LARGER denominator = SMALLER fraction!
1/3 vs 1/5: Since 5 > 3, then 1/5 < 1/3 (seems backwards!)
2/7 vs 2/9: Since 9 > 7, then 2/9 < 2/7
Think: More pieces = smaller pieces!
This rule trips up many students - practice it!
Use the pizza analogy! Would you rather have 1/4 of a pizza or 1/8? Quarter is bigger! Cutting into 8 pieces makes each piece smaller!
Thinking bigger denominator = bigger fraction! WRONG when numerators are the same! 1/100 is tiny, 1/2 is big, even though 100 > 2!
Sharing scenarios! If you split a candy bar with 2 friends (1/3 each) vs 9 friends (1/10 each), you get way more with fewer people sharing!
Draw circles divided into different numbers of parts! Physically SEE that 1/8 of a circle is smaller than 1/4!
Sometimes the best way to compare fractions is to DRAW them! Visual models make abstract numbers concrete. Draw two equal-sized rectangles, divide one into thirds and shade 2, divide the other into fifths and shade 3. Now you can SEE which is bigger! Visual comparison never lies and builds deep understanding!
Draw fraction bars or circles to SEE sizes!
Shade 2/3 and 3/5 side-by-side - compare visually
Number lines show fractions in order from 0 to 1
Fraction circles (pizza models) make sizes obvious
When numbers confuse you, draw it out!
When stuck, always sketch it! Even a quick rough diagram helps you see the answer. Visualizing is a powerful problem-solving tool!
Relying only on number manipulation! Sometimes drawing is faster and less error-prone. Don't skip visual strategies - they're valid and valuable!
Real-world fractions are visual! When cooking, you SEE 1/2 cup vs 1/3 cup measuring cups and know 1/2 is bigger. Use that visual instinct!
Draw fraction comparison problems! Make cards with two fractions - draw both, then write < or >. Build visual-numerical connection!
When denominators AND numerators are different, convert to common denominators! Find a number both denominators divide into (often their product), convert both fractions, then compare. Now they have same-size pieces, so comparison is easy! This is the 'universal' method that always works!
Convert fractions to same denominator, then compare!
2/3 vs 3/4: Convert to 8/12 vs 9/12, so 3/4 > 2/3
1/2 vs 2/5: Convert to 5/10 vs 4/10, so 1/2 > 2/5
Find a common denominator both original ones divide into
After converting, use same-denominator rule!
For 3rd grade, use simple common denominators! For 1/2 vs 1/3, use 6 (2×3). Convert: 3/6 vs 2/6. Now easy to see 1/2 > 1/3!
Forgetting to multiply numerator when changing denominator! If you multiply denominator by 2, you MUST multiply numerator by 2 to keep the fraction equivalent!
Comparing prices! Is 2/3 of a dollar more than 3/5? Convert to sixtieths: 40/60 vs 36/60. Yes, 2/3 costs more!
Practice with small denominators first! Compare 1/2, 1/3, 1/4 by converting to twelfths. Build confidence before harder problems!
Benchmark fractions are reference points that help you estimate! Every fraction is somewhere between 0 (nothing) and 1 (whole). 1/2 is a key middle benchmark. If one fraction is less than 1/2 and another is more than 1/2, you instantly know which is bigger - no calculation needed! This strategy builds number sense!
Compare fractions to landmarks: 0, 1/2, and 1
1/8 is close to 0 (small), 4/5 is close to 1 (big)
If one fraction < 1/2 and other > 1/2, you know the answer!
3/10 < 1/2 but 4/7 > 1/2, so 4/7 > 3/10
Benchmarks give you quick estimates!
Learn to quickly judge 'close to 0', 'close to 1/2', or 'close to 1'! For example, 1/10 ≈ 0, 5/9 ≈ 1/2, 9/10 ≈ 1. This makes rough comparisons fast!
Overusing exact calculation! If comparing 1/8 to 7/8, you don't need complex math - obviously 7/8 is way bigger (close to 1 vs close to 0)!
Quick estimates in life! 'Is the gas tank more or less than half full?' You glance and estimate - same skill as benchmark thinking!
Sort fractions into three categories: 'Close to 0', 'Close to 1/2', 'Close to 1'. Build estimation skills!
Ordering multiple fractions combines all your comparison skills! Convert to common denominators OR use benchmarks to get rough order, then fine-tune. Always double-check: does 1/8 < 1/4 < 1/2 make sense? (Yes!) Ordering builds deep understanding of fraction magnitude and relationships!
Order from least to greatest: arrange fractions in ascending order
Example: Order 1/4, 3/8, 1/2 → Answer: 1/4, 3/8, 1/2
Strategy: Convert to common denominator, then sort numerators
Or use benchmarks: group by size, then refine within groups
Check your work: Does it 'feel' right?
Start with obvious ones! In any list, quickly identify the smallest and largest (like 1/8 and 7/8), place those, then work on the middle ones!
Not having a strategy! Don't randomly guess. Use common denominators OR benchmarks OR visual models. Pick a method and apply it systematically!
Ranking scores, measurements, or portions! 'Who ate the most pizza: Alice (3/8), Bob (1/2), or Charlie (1/4)?' Answer: Bob > Alice > Charlie!
Order fractions with same denominator first (easy), then same numerator, then mixed. Build skills progressively!
Comparison symbols show the relationship between fractions! The symbol '<' (less than) opens toward the bigger number like a mouth eating the bigger value. '>' (greater than) does the opposite. '=' means they're equivalent (same value, even if written differently). Using these symbols correctly shows you understand fraction magnitude!
< means 'less than' (smaller on left): 1/4 < 1/2
> means 'greater than' (larger on left): 3/4 > 1/2
= means 'equal to' (same value): 2/4 = 1/2
Arrow points to smaller number: 1/8 < 3/8
Read left to right: '1/4 is less than 1/2'
Remember: the symbol 'eats' the bigger number! The open side (big side) faces the larger value. So 2 < 5 (mouth opens toward 5) and 5 > 2 (same relationship)!
Confusing < and >! Remember the mnemonic: 'Less than: L makes the angle <.' Or remember the 'eating' rule!
Math notation is universal! Whether comparing fractions, decimals, or whole numbers, these symbols work the same way everywhere in math!
Write comparison statements! For every fraction pair, write with <, >, or =. Say it aloud: '2/3 is greater than 1/2' helps memory!