B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Fractions: What the Numerator and Denominator Mean

B1.4About 35 minutes

Learning goals

I can show fractions from halves to tenths with drawings and paper strips.
I can write a fraction with a numerator and a denominator.
I can explain what the denominator tells me and what the numerator tells me.
I can explain why a whole must be cut into equal parts.

Words to know

fraction
A number that names part of a whole or part of a group, like 3/4.

denominator
The bottom number. It tells how many equal parts make one whole.

numerator
The top number. It tells how many of those equal parts we are talking about.

unit fraction
A fraction with 1 on top, like 1/5. It names one equal part.

equal parts
Parts that are exactly the same size.

Remember from Grade 3

In Grade 3 you shared things fairly and found shares like 1/4 and 3/8. You also added unit fractions: 1/4 + 1/4 + 1/4 = 3/4. This year you will explain exactly what each part of a fraction means, for every fraction from halves to tenths.

Let's start with a story

Maya's family made a pan of maple squares. They cut the pan into 8 equal pieces. Maya and her brother ate 3 pieces.

What fraction of the pan did they eat? 3/8, which we read as three eighths.

A pan cut into 8 equal pieces. 3 pieces are shaded: 3/8 of the pan.

The two parts of a fraction

In 3/8:

The denominator is 8, the bottom number. It tells us the whole is cut into 8 equal parts. It names the size of each part: eighths.
The numerator is 3, the top number. It counts how many of those parts we mean: 3 of them.

A trick to remember: Denominator is Down at the bottom. Numerator tells the Number of parts.

Denominator	Name of the parts	Example	Read as
2	halves	1/2	one half
3	thirds	2/3	two thirds
4	fourths (or quarters)	3/4	three fourths
5	fifths	4/5	four fifths
6	sixths	5/6	five sixths
8	eighths	3/8	three eighths
10	tenths	7/10	seven tenths

Fractions from halves to tenths.

The same whole cut into 2, 3, 4, 5, 6, 8 and 10 equal parts, with the fractions from the table shaded.

Bigger denominator, smaller pieces

Look at the strips above. They are all the same length. The more parts a whole is cut into, the smaller each part is.

So 1/10 is smaller than 1/2, even though 10 is bigger than 2. A tenth is a tiny slice; a half is a big piece!

Worked example

Example 1: Name the fraction

A garden is split into 6 equal beds. Carrots are planted in 5 of them. What fraction of the garden has carrots?

How many equal parts make the whole? 6. That is the denominator.
How many parts have carrots? 5. That is the numerator.

5/6 (five sixths) of the garden has carrots.

Worked example

Example 2: Equal parts matter

A pizza is cut into 4 pieces, but two pieces are big and two are small. Is each piece 1/4 of the pizza?

A denominator of 4 means 4 equal parts.
These pieces are not equal.

No. The pieces are not fourths because they are not the same size.

Worked example

Example 3: The whole

What fraction is 5/5? What fraction of the bar is not shaded if 2/5 is shaded?

5/5 means all 5 of the 5 equal parts. That is one whole.
If 2 of 5 parts are shaded, then 5 − 2 = 3 parts are not.

5/5 = 1 whole. 3/5 is not shaded.

Draw it

If you're not sure what a fraction means, draw it! Draw a bar, split it into the number of parts the denominator says, then shade the number of parts the numerator says.

Just for fun

A customer at a pizza shop says, "Please cut my pizza into 4 slices, not 8. I'm not hungry enough to eat 8!" Silly! 4/4 and 8/8 are both one whole pizza. Only the size of the slices changes.

Hands-on activity

Fold fraction strips

You need: 5 strips of paper all the same length (cut from the long side of a sheet, with a grown-up's help if you use scissors), a pencil and crayons.

Leave strip 1 whole. Label it 1.
Fold strip 2 in half. Open it, draw a line on the fold, and label each part 1/2.
Fold strip 3 in half and in half again. Label each part 1/4.
Fold strip 4 in half three times. Label each part 1/8.
For strip 5, fold it into 3 equal parts: roll it into an S shape and squish it flat so the three layers are even. Label each part 1/3.
Lay the strips under each other. Colour 3/4, 5/8 and 2/3.

Math talk: "Which strip has the biggest pieces? Why?" Keep your strips for the next lessons!

Your turn

In 4/10, what is the numerator? What is the denominator?

What does the denominator in 2/5 tell you?

What does the numerator in 2/5 tell you?

Write five eighths as a fraction.

A pie is cut into 6 equal pieces. 1 piece is eaten. What fraction is eaten? What fraction is left?

Which is bigger: 1/3 or 1/8? Why?

What fraction of the bar is shaded? (A bar has 10 equal parts and 7 are shaded.)

More practice: warm-up

Read this fraction in words: 3/4

Write one sixth as a fraction.

A whole is cut into 10 equal parts. What is each part called?

What fraction is the same as one whole: 3/3 or 1/3?

In 7/8, which number is the denominator?

More practice: on your own

A flag is made of 5 equal stripes. 2 are green. What fraction is green? What fraction is not green?

Describe how you would draw 3/10 on a bar.

Order these unit fractions from smallest to biggest: 1/4, 1/10, 1/2

Leo cut a sandwich into 3 pieces of different sizes and says he has thirds. Is he right?

What fraction is missing to make a whole: 5/8 + □ = 1 whole?

Challenge

Ben says 1/6 is bigger than 1/5 because 6 is bigger than 5. Explain why he is wrong.

Two strips are the same size. One is cut into fourths and one into eighths. How many eighths fit in one fourth?

Write a fraction with a denominator of 10 that is more than half of the whole. Explain how you know.

Check your understanding

Quiz

In the fraction 3/5, what does the 5 tell you?

In the fraction 3/5, what does the 3 tell you?

Which fraction is seven tenths?

Which unit fraction is the biggest?

A whole is cut into 4 equal parts and 4 are shaded. What fraction is shaded?

Why are these not fourths: a cake cut into 4 pieces of different sizes?

For parents and teachers

Big idea: B1.4 asks Grade 4 students to represent fractions from halves to tenths using drawings, tools and standard fractional notation, and to explain the meaning of the denominator and the numerator. The denominator names the size of the parts (how many equal parts make the whole); the numerator counts the parts.

Common difficulties:

Thinking a bigger denominator means a bigger fraction (1/8 > 1/3). Use fraction strips of the same length side by side.
Ignoring equal size. Any cut into 4 pieces is not automatically fourths.
Reading fractions as two separate whole numbers ("three five"). Model "three fifths".

How to help: Fold paper strips, cut sandwiches or toast into equal parts, and talk about fractions while cooking (measuring cups often show 1/2, 1/3, 1/4). Keep the folded strips from the activity; they will be useful all unit.