One piece out of five equal pieces is one fifth, written 1/5.
Unit fraction is one single equal piece, such as 1/5.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
A fraction is a count
3/5 is three fifths. It counts three pieces, each one a fifth.
The bottom number is the name
In 3/5, the 5 says the pieces are fifths. It names them, it does not count them.
Fifths behave like objects
Two fifths and one fifth make three fifths, exactly as two apples and one apple make three apples.
The bottom number names the unit
3/8 means three eighths — a count of 3, with the unit being one eighth. Read every fraction this way and it behaves like every other measurement you know: 3 metres is 3 of the unit "metre"; 3/8 is 3 of the unit "one eighth".
Why this reading explains everything
Once a fraction is a count of a named unit, same-unit addition is obvious, same-unit comparison is obvious, and the failure of 1/2 + 1/3 is obvious too. One reading resolves nearly every fraction difficulty in this chapter.
Counting units along the line
On a number line cut into eighths, counting 1/8, 2/8, 3/8 is exactly like counting 1, 2, 3 with a smaller step. Nothing stops at 8/8 — you carry on to 9/8 and beyond, which is why fractions greater than one need no special explanation.
The unit depends on the whole
One eighth of a small pizza is not the same amount as one eighth of a large one. The unit is defined by the whole, so every fraction statement quietly refers to some whole. When two fractions refer to different wholes, they cannot be compared.
Step 2: Try It Yourself
Every piece drawn is one unit fraction.
The whole is cut into 5 equal shares.
0/5 shaded
Step 3: Watch an Example
One step at a time.
Watch Ana Read 5/8
Ana reads the fraction 5/8 out loud.
- Step 1
She looks at the bottom number first: 8 means eighths.
Step 4: Your Turn
Practice makes it stick.
The Pizza
Problem 1 of 2
A pizza is cut into 6 equal slices. Ana eats 4. How many sixths did she eat?
sixths
The Ribbon
Problem 2 of 2
How many tenths make up 7/10?
tenths
Name the Unit
1 of 4
How many quarters are in 3/4?
2 of 4
In 5/12, what does the 12 tell you?
3 of 4
How many eighths make one whole?
4 of 4
How many fifths are in 6/5?
Step 5: Quick Check
Show what you know.
Question 1 of 2
How many sixths are in 5/6?
Question 2 of 2
What does the bottom number of a fraction do?
What You Learned
- A unit fraction is one equal piece.
- The bottom number names the pieces.
- The top number counts how many you have.