Comparing and Ordering Fractions
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Comparing and Ordering Fractions
A fraction like 3/4 has two parts: the denominator (the bottom number) tells you how many equal pieces the whole is split into, and the numerator (the top number) tells you how many of those pieces you have.
Same denominator? Just compare the numerators.
If two fractions have the same denominator, the fraction with the bigger numerator is bigger. For example, 5/8 is bigger than 3/8, because 5 eighths is more than 3 eighths of the same-sized pieces.
Related denominators? Find a common one first.
Denominators are "related" when one is a multiple of the other — like 4 and 8, or 3 and 6. To compare 3/4 and 5/8, rewrite 3/4 using eighths: 3/4 = 6/8. Now you can compare 6/8 and 5/8 directly — 6/8 is bigger.
Mixed numerals
A mixed numeral like 2 1/3 means "2 whole ones, plus 1/3 of another one." To compare mixed numerals, compare the whole-number parts first. Only compare the fraction parts if the whole numbers are equal.
Fractions on a number line
Every fraction has a place on the number line between two whole numbers. 3/4 sits three-quarters of the way from 0 to 1. Mixed numerals like 1 1/2 sit between 1 and 2 — exactly halfway, in this case.
Worked Example
Order these from smallest to largest: 2/3, 5/6, 1/2 Step 1: Find a common denominator. 3, 6 and 2 all divide evenly into 6. 2/3 = 4/6 5/6 = 5/6 1/2 = 3/6 Step 2: Compare the numerators over the common denominator: 3/6, 4/6, 5/6. Step 3: Convert back: 1/2, 2/3, 5/6 — smallest to largest.
Practice
Which is bigger, 3/8 or 5/8?
Flashcards
What does the denominator of a fraction tell you?
How many equal pieces the whole is split into (the bottom number).
What does the numerator of a fraction tell you?
How many of those equal pieces you have (the top number).
How do you compare fractions with the same denominator?
Just compare the numerators — the bigger numerator is the bigger fraction.
How do you compare fractions with related (but different) denominators?
Rewrite them with a common denominator first, then compare the numerators.
What is a mixed numeral?
A whole number plus a fraction, like 2 1/3 — 2 whole ones and 1/3 of another.
How do you compare two mixed numerals?
Compare the whole-number parts first; only compare the fraction parts if the whole numbers are equal.
All 12 practice questions
Which is bigger, 3/8 or 5/8?
- They are equal
- 5/8
- Cannot tell
- 3/8
Show the answer to question 1
Answer: 5/8
Same denominator (8), so compare numerators: 5 is more than 3.
Which is bigger, 1/4 or 1/3?
- 1/4
- 1/3
- Cannot tell
- They are equal
Show the answer to question 2
Answer: 1/3
Splitting a whole into 3 pieces (thirds) gives bigger pieces than splitting it into 4 pieces (quarters), so 1/3 > 1/4.
Rewrite 3/4 as eighths.
- 3/8
- 4/8
- 7/8
- 6/8
Show the answer to question 3
Answer: 6/8
Multiply numerator and denominator by 2: 3×2=6, 4×2=8, so 3/4 = 6/8.
Which is bigger: 3/4 or 5/8?
- 5/8
- 3/4
- They are equal
- Cannot tell
Show the answer to question 4
Answer: 3/4
3/4 = 6/8, and 6/8 is bigger than 5/8.
Order from smallest to largest: 1/2, 1/4, 3/4
- 3/4, 1/2, 1/4
- 1/2, 1/4, 3/4
- 1/4, 3/4, 1/2
- 1/4, 1/2, 3/4
Show the answer to question 5
Answer: 1/4, 1/2, 3/4
In quarters: 1/4, 2/4 (=1/2), 3/4 — so smallest to largest is 1/4, 1/2, 3/4.
Which mixed numeral is bigger: 2 1/2 or 2 1/4?
- 2 1/4
- 2 1/2
- Cannot tell
- They are equal
Show the answer to question 6
Answer: 2 1/2
The whole numbers are the same (2), so compare the fraction parts: 1/2 is bigger than 1/4.
Which mixed numeral is bigger: 3 1/4 or 2 3/4?
- They are equal
- Cannot tell
- 3 1/4
- 2 3/4
Show the answer to question 7
Answer: 3 1/4
Compare whole numbers first: 3 is more than 2, so 3 1/4 is bigger — even though 3/4 looks like a "bigger" fraction part, the whole number decides it here.
On a number line from 0 to 1, where does 3/4 sit?
- Halfway along
- Three-quarters of the way along
- At the very end
- One quarter of the way along
Show the answer to question 8
Answer: Three-quarters of the way along
3/4 means 3 out of 4 equal parts, so it sits three-quarters of the way from 0 to 1.
Which fraction sits exactly halfway between 0 and 1 on a number line?
- 1/3
- 1/2
- 3/4
- 1/4
Show the answer to question 9
Answer: 1/2
1/2 is exactly halfway between 0 and 1.
Between which two whole numbers does 1 3/4 sit on a number line?
- 1 and 2
- 0 and 1
- 2 and 3
- 3 and 4
Show the answer to question 10
Answer: 1 and 2
1 3/4 means 1 whole plus 3/4 more, so it sits between 1 and 2 — close to 2.
Which is bigger, 2/6 or 1/3?
- 1/3
- 2/6
- Cannot tell
- They are equal
Show the answer to question 11
Answer: They are equal
2/6 simplifies to 1/3 (divide both by 2), so they are the same size.
Order from largest to smallest: 5/6, 1/6, 1/2
- 1/6, 1/2, 5/6
- 5/6, 1/6, 1/2
- 1/2, 5/6, 1/6
- 5/6, 1/2, 1/6
Show the answer to question 12
Answer: 5/6, 1/2, 1/6
In sixths: 5/6, 3/6 (=1/2), 1/6 — so from largest to smallest: 5/6, 1/2, 1/6.
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