Unit 1: Common Fractions
Topic A: Introducing Common Fractions
This unit gives you the background details that you need for working with common fractions.
Parts of Common Fractions
Common fractions are written with two numbers, one above the other, with either a straight or slanted line in between. The straight-line style is the one used most.
The denominator is the bottom number. It tells how many equal parts are in the whole thing. The numerator is the top number. It tells how many of the equal parts we are dealing with.
Example A
The whole thing is the bunch of bananas. The whole thing has 5 equal parts (the bananas). The denominator is 5.
How many bananas have been eaten? 1
What fraction of the bananas have been eaten? [latex]\tfrac{1}{5}[/latex] of bananas.
Example B
The whole thing is a carton of one dozen eggs. One dozen has 12 equal parts, so if we are talking about the carton, the denominator is 12.
How many eggs are still in the carton? 7
What fraction of the eggs are left? [latex]\tfrac{7}{12}[/latex] of the eggs.
A fraction is always looking at things as parts of a whole. In the previous example of the eggs, the whole is 12 eggs. The part is the 7 eggs that are left. 7 is part of the whole of 12.
Example C
This pizza is one whole pizza. The pizza is cut into 8 pieces. This means the whole is 8. How many parts are left? (The pieces that are shaded are the ones left.) Write a fraction of how many pieces of pizza are left.
The amount left over can be shown as a fraction: [latex]\tfrac{4}{8}[/latex]
Example D
It is Peter’s 82nd birthday. There were 7 people, including Peter, at the party. Everyone wants a small piece of cake, so Kathleen cut the cake into 12 equal parts. This means the whole is 12. There will be some left over.
The amount left over can be shown as a fraction: [latex]\tfrac{5}{12}[/latex]
Example E
Sue made a strawberry pie to share with her family of 5. The pie was cut into 8 equal parts. This means the whole is 8. The kids are excited because there will be parts left over.
The fraction showing what amount of pie is left is: [latex]\tfrac{3}{8}[/latex]
Exercise 1
Look at the fraction below. Fill in the blank labels with the four terms you are given:
- Numerator
- Denominator
- Whole
- Fraction
Answers to Exercise 1
Writing Common Fractions
Exercise 2
Each shape drawn here is a whole. The shapes have been divided into parts.
- Ask yourself, “How many equal parts in the whole?” That number is the denominator.
- Count the number of parts that are shaded; that is the numerator.
- Write the common fraction to describe the shaded portion of each shape.
-
- How many parts make the whole? 4
- How many parts are shaded? 3
- Fraction: [latex]\tfrac{3}{4}[/latex]
-
- How many parts make the whole?
- How many parts are shaded?
- Fraction:
-
- How many parts make the whole?
- How many parts are shaded?
- Fraction:
-
- How many parts make the whole?
- How many parts are shaded?
- Fraction:
Answers to Exercise 2
- Square.
- 4
- 3
- [lat