Half of a large pizza is more food than half of a small one. Both are still halves.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Comparing needs the same whole
1/2 is always greater than 1/4 — but only when both are parts of the same whole.
Say what the whole is
A fraction on its own is a number. A fraction of something depends on the something.
Half of what?
Half a small pizza is less food than half a large one, even though both are called one half. A fraction always refers to some whole, and comparing fractions only makes sense when the wholes are the same size.
The rule this creates
You may only compare 1/2 and 1/3 directly when both refer to the same whole. Every comparison exercise in this chapter quietly assumes it. When a real problem involves different-sized wholes, say so — the fractions cannot simply be compared.
Finding the whole from a part
If 1/4 of a bag is 3 sweets, the whole bag is 4 × 3 = 12. Working backwards from a fractional part to the whole is a real and useful skill, and it shows that the whole is a genuine part of what a fraction means.
Step 2: Try It Yourself
Tap and try it out.
1/2
1/4
1/2 is greater than 1/4.
The same number of pieces, but the bigger denominator makes smaller pieces.
Step 3: Watch an Example
One step at a time.
Watch Leo Ask "Of What?"
Leo is told Ana ate 1/2 a pizza and he ate 3/4 of one.
- Step 1
He starts to say he ate more.
Step 4: Your Turn
Practice makes it stick.
Two Different Cakes
Problem 1 of 2
Ana eats 1/2 of a small cake. Leo eats 1/4 of a huge cake. Who ate more cake?
The Same Cake
Problem 2 of 2
Two people share one cake. One takes 1/2 and one takes 1/4. Who took more?
Of What?
1 of 2
Is 1/2 always more than 1/3?
2 of 2
Two same-size bars. Which is more, 2/3 or 2/5?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Two same-size pizzas. Which is more, 3/4 or 1/2?
Question 2 of 2
What must be true before you compare two fractions?
What You Learned
- A fraction of a big thing is bigger than the same fraction of a small thing.
- Comparisons only work when the wholes match.
- Always ask: a fraction of what?