Chapter 3 of 8

All 8 chapters
  1. 1Fair shares: equal parts, readunderstood
  2. 2One part: halves, quarters, thirds, fifths, readunderstood
  3. 3More than one part, readunderstood
  4. 4Fractions of a group, readunderstood
  5. 5The number line, past 1, readunderstood
  6. 6Same amount, different names, readunderstood
  7. 7Which is bigger, readunderstood
  8. 8Adding and taking away parts, readunderstood

M2.4.3 Chapter 3

More than one part

If 1/4 is one part, what do I call three parts?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Read and write a fraction such as 3/4
  • Say what the top and bottom numbers tell you
  • Write a whole as 4/4 or 5/5

A fraction names some equal parts of a whole. Last time you named one part. Now you can take more.

Cut a strip into 4 equal parts. Each part is 1/4. Count the parts as you take them.

Draw it first

Count quarters to make three quarters

  1. A strip cut into 4 equal parts. One part is shaded and labelled 1/4. Two parts are shaded and the second is labelled 2/4. Three parts are shaded and the third is labelled 3/4.

    1 Draw a strip. Cut it into 4 equal parts.

  2. A strip cut into 4 equal parts. One part is shaded and labelled 1/4. Two parts are shaded and the second is labelled 2/4. Three parts are shaded and the third is labelled 3/4.14

    2 Shade one part. That is 1/4.

  3. A strip cut into 4 equal parts. One part is shaded and labelled 1/4. Two parts are shaded and the second is labelled 2/4. Three parts are shaded and the third is labelled 3/4.1424

    3 Shade a second part. Now 2 parts are shaded. That is 2/4.

  4. A strip cut into 4 equal parts. One part is shaded and labelled 1/4. Two parts are shaded and the second is labelled 2/4. Three parts are shaded and the third is labelled 3/4.142434

    4 Shade a third part. Now 3 parts are shaded. That is 3/4.

You counted 1, 2, 3 quarters. So the fraction is 3/4. We say three quarters.

The bottom number is 4. It tells how many equal parts make the whole. It is also called the denominator.

The top number is 3. It tells how many parts you take. It is called the numerator.

Fifths work the same way. Cut a bar into 5 equal parts. Count the fifths you take.

Three bars of the same length, each cut into 5 equal parts. The first has 1 part shaded, labelled 1/5. The second has 2 parts shaded, labelled 2/5. The third has 3 parts shaded, labelled 3/5.152535
Each bar has 5 equal parts. The top number counts the shaded parts.

What if you take every part? You have the whole. All 4 quarters make 4/4. All 5 fifths make 5/5.

Two bars of the same length. The top bar is cut into 4 equal parts, all shaded, labelled four quarters, one whole. The bottom bar is cut into 5 equal parts, all shaded, labelled five fifths, one whole.four quarters, one wholefive fifths, one whole
When the top number equals the bottom number, you have one whole.

See it three ways

With things

Fold a paper into 4 equal parts. Open it. Colour 3 of the parts.

As a picture

A circle cut into 4 equal parts. Three parts are shaded and one part is not. Caption: three quarters.three quarters

In symbols

3 parts of 4 equal parts is 3/4.

Worked example

A bar has 5 equal parts. Mei shades 2 parts. What fraction is shaded?

  1. Count all the equal parts. There are 5. That is the bottom number.
  2. Count the shaded parts. There are 2. That is the top number.
  3. Write the top number over the bottom number.

Answer: 2/5

Try it

Fold and colour three quarters

You need: a sheet of paper, or an old page, a pencil.

  1. Fold the paper in half. Fold it in half again.
  2. Open it. Count the equal parts. There are 4.
  3. Colour 3 of the parts.
  4. Count the coloured parts, then count all the parts.

What you will see: 3 coloured parts out of 4 equal parts is 3/4. The part left over is 1/4. Together they make 4/4, the whole.

If you cannot try it, this is what happens.
A bar cut into 4 equal parts. Three parts are shaded. Caption: three quarters.three quarters

A wrong idea many people have

The bottom number says how many parts you take.

Why it feels right: In 3/4, the 4 is the bigger number. It looks like the count.

The test that breaks it: Fold a paper into 4 equal parts. Colour 3. Count the parts you coloured. Then count all the parts.

What is true: You coloured 3, and the paper has 4 parts. The top number counts the parts you take. The bottom number counts all the equal parts.

Key words

fraction
a number that names equal parts of a whole, like 3/4.
numerator
the top number. It tells how many parts you take.
denominator
the bottom number. It tells how many equal parts make the whole.

Back to your guess

The answer is B: It is 3/4, three of the quarter parts.

Count the quarter parts you take. Three quarters is 3/4. The top number counts the parts you take.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. What fraction of the bar is shaded?

    A bar cut into 5 equal parts. The first 3 parts are shaded.
    Tap your answer.

    1. Yes, that is right. There are 5 equal parts, so the bottom number is 5. 3 are shaded, so the top number is 3.

    2. Not this one. You counted the parts that are not shaded. The top number counts the shaded parts. Try another.

    3. Not this one. You may have put shaded parts over parts not shaded. The bottom number counts all the equal parts. That is 5, not 2. Go to M2.4.2. Try another.

    See the answer

    3/5

    There are 5 equal parts, so the bottom number is 5. 3 are shaded, so the top number is 3.

    • If you chose B: You counted the parts that are not shaded. The top number counts the shaded parts.
    • If you chose C: You may have put shaded parts over parts not shaded. The bottom number counts all the equal parts. That is 5, not 2. Go to M2.4.2.

  2. Which bar shows 2/3?

    Bar A is cut into 3 equal parts with 2 shaded. Bar B is cut into 5 equal parts with 2 shaded.AB
    Tap your answer.

    1. Yes, that is right. Bar A has 3 equal parts and 2 are shaded. That is 2/3.

    2. Not this one. Bar B has 5 equal parts, so it shows 2/5. The bottom number must be 3. Go to M2.4.2. Try another.

    See the answer

    Bar A

    Bar A has 3 equal parts and 2 are shaded. That is 2/3.

    • If you chose B: Bar B has 5 equal parts, so it shows 2/5. The bottom number must be 3. Go to M2.4.2.

  3. A bread is cut into 4 equal parts. Kofi eats all 4 parts. What fraction did he eat?

    Tap your answer.

    1. Yes, that is right. The bread has 4 equal parts. He took 4 of them. So the top and bottom numbers are both 4.

    2. Not this one. That is one part. Kofi ate 4 parts. Try another.

    3. Not this one. The bottom number is the number of equal parts in the whole. That is 4. Go to M2.4.2. Try another.

    See the answer

    4/4, the whole bread

    The bread has 4 equal parts. He took 4 of them. So the top and bottom numbers are both 4.

    • If you chose B: That is one part. Kofi ate 4 parts.
    • If you chose C: The bottom number is the number of equal parts in the whole. That is 4. Go to M2.4.2.

  4. From an earlier chapter

    Which is the biggest part: one third, one quarter or one fifth?

    Tap your answer.

    1. Yes, that is right. Cutting into 3 parts gives bigger parts than 4 or 5.

    2. Not this one. Cutting into 3 parts gives bigger parts than 4. Go to M2.4.2. Try another.

    3. Not this one. More parts means smaller parts. Cutting into 5 gives the smallest part here. Go to M2.4.2. Try another.

    See the answer

    one third

    Cutting into 3 parts gives bigger parts than 4 or 5.

    • If you chose B: Cutting into 3 parts gives bigger parts than 4. Go to M2.4.2.
    • If you chose C: More parts means smaller parts. Cutting into 5 gives the smallest part here. Go to M2.4.2.

  5. Draw a bar in 5 equal parts. Shade 3 parts. Write the fraction, and name the top and bottom numbers.

    See the answer

    3/5. The top number is 3. The bottom number is 5.

    The bar has 5 equal parts. You shaded 3 of them. The top number counts shaded parts.

  6. Sipho cuts a bread into 8 equal parts and eats 3. What does the 8 in 3/8 tell you?

    Tap your answer.

    1. Not this one. Sipho ate 3 parts, the top number. The bottom number counts all the equal parts. Try another.

    2. Yes, that is right. The bread is cut into 8 equal parts. The bottom number counts all of them.

    3. Not this one. The bottom number counts the equal parts. It does not say which part he ate. Try another.

    See the answer

    How many equal parts the whole bread has.

    The bread is cut into 8 equal parts. The bottom number counts all of them.

    • If you chose A: Sipho ate 3 parts, the top number. The bottom number counts all the equal parts.
    • If you chose C: The bottom number counts the equal parts. It does not say which part he ate.

  7. Hana shades the whole bar. Which fraction names what she shaded?

    A bar cut into 8 equal parts. All the parts are shaded. The label is a whole bar.a whole bar
    Tap your answer.

    1. Not this one. That is one part. Hana shaded every part. Try another.

    2. Not this one. The bottom number counts the equal parts in the whole. That is 8, not 1. Try another.

    3. Yes, that is right. The bar has 8 equal parts and Hana shaded all 8. The top and bottom numbers are both 8.

    See the answer

    8/8

    The bar has 8 equal parts and Hana shaded all 8. The top and bottom numbers are both 8.

    • If you chose A: That is one part. Hana shaded every part.
    • If you chose B: The bottom number counts the equal parts in the whole. That is 8, not 1.

  8. What fraction of the flat bread is shaded?

    A round flat bread cut into 8 equal slices. 5 slices are shaded. The label is a flat bread.a flat bread
    Tap your answer.

    1. Not this one. You put shaded parts over parts not shaded. The bottom number counts all the equal parts, 8. Try another.

    2. Yes, that is right. There are 8 equal slices, so the bottom number is 8. 5 are shaded, so the top number is 5.

    3. Not this one. You counted the parts that are not shaded. The top number counts the shaded parts. Try another.

    See the answer

    5/8

    There are 8 equal slices, so the bottom number is 8. 5 are shaded, so the top number is 5.

    • If you chose A: You put shaded parts over parts not shaded. The bottom number counts all the equal parts, 8.
    • If you chose C: You counted the parts that are not shaded. The top number counts the shaded parts.

  9. Which bar shows 3/4?

    Three bars, each 240 long and cut into 4 parts. Bar A has parts 60, 60, 60 and 60 long, with the first part shaded. Bar B has parts 24, 72, 72 and 72 long, with the first three parts shaded. Bar C has parts 60, 60, 60 and 60 long, with the first three parts shaded.ABC
    Tap your answer.

    1. Not this one. You counted the parts that are not shaded. The top number counts the shaded parts. Try another.

    2. Not this one. Bar B has 3 parts shaded. But its 4 parts are not equal. A fraction needs equal parts. Go to M2.4.1. Try another.

    3. Yes, that is right. Bar C has 4 equal parts and 3 are shaded. That is 3/4.

    See the answer

    Bar C

    Bar C has 4 equal parts and 3 are shaded. That is 3/4.

    • If you chose A: You counted the parts that are not shaded. The top number counts the shaded parts.
    • If you chose B: Bar B has 3 parts shaded. But its 4 parts are not equal. A fraction needs equal parts. Go to M2.4.1.

Keep it

Copy this into your exercise book.

The bottom number counts all the equal parts. The top number counts the parts you take. 3/4 is three quarters. 4/4 is one whole.

Draw: A strip in 4 equal parts. Shade 3 parts and write 3/4 under it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (790 KB). It opens on any phone.