Why 1/2 + 1/3 Is Not 2/5

You cannot count two different things together.

10 problems · about 15 minutes · 4.NF.B.3

NameDate

Figure — use these to answer the problems

Try adding halves and thirds. The widget will say why it cannot be done yet.

1/2

1/3

These are halves and thirds. They are different things, so they cannot be counted together yet.

First top number1

First bottom number2

Second top number1

Second bottom number3

Figure 1

From earlier lessons. Loosen up before the new work.

3 problems

From “Adding Fractions with the Same Unit”
3/10 + 4/10. What is the top number of the answer?
Answer
From “Comparing Unlike Fractions”
2/3 written in twelfths has what top number?
Answer
From “Equivalent Fractions”
2/3 = ?/9. What is the top number?
Answer

Straightforward practice. Get the method working first.

3 problems

1/4 + 1/2, in quarters. What is the top number?
Answer
5
How can you tell 2/5 is a wrong answer to 1/2 + 1/3?
- It is smaller than the half you started with.
- The numbers look odd.
1/2 + 1/3, in sixths. What is the top number?
Answer

The same ideas with more to keep track of.

1 problem

Mixed problems. Work out what kind of question it is before you start.

3 problems

8
Can you add halves and thirds by counting them together?
- No. They are different units.
- Yes.
9
The Size Test
Is 1/2 + 1/4 bigger or smaller than 1/2?
- Bigger.
- Smaller.
In Quarters
1/2 + 1/4, written in quarters. What is the top number?
Answer