LESSON: Equivalent Fractions
| Site: | MN Partnership for Collaborative Curriculum |
| Course: | Mathematics Essentials Q1 |
| Book: | LESSON: Equivalent Fractions |
| Printed by: | Guest user |
| Date: | Thursday, November 21, 2024, 8:34 PM |
Description
Equivalent Fractions
INTRODUCTION
READ: Write Equivalent Fractions
Write Fractions Equivalent to a Given Fraction
What is a fraction?
A fraction is a part of a whole. When we work with fractions we think about the relationship between a part of something and the whole thing. Fractions show up all the time in real life. Sometimes, we don’t even realize that we are working with fractions because they are everywhere!
A fraction has two parts. It has a top number and a bottom number. The top number is called the numerator and tells us how many parts we have out of the whole. The bottom number is the denominator. It tells us how many parts the whole has been divided into.
Example
= means we have four out of five parts.
The four is our numerator it tells us how many parts we have.
The five is our denominator it tells us how many parts the whole has been divided into.
We can also show fractions in a visual way by using a picture.
Here our whole has been divided into ten parts. This is our denominator.
Five out of ten are shaded. This is our numerator.
We could also write the fraction that is not shaded. In this example it would be the same thing since five out of ten are shaded and five out of ten are not shaded.
Notice that are shaded and this is the same as
of the whole being shaded. Because this whole has been divided into five parts,
is the same as
. These two fractions are equal or equivalent fractions.
What is an equivalent fraction? Equivalent Fractions are fractions that have the same value.
For example, is equivalent to the fractions below. The bars below visually represent why this is true.
If we add up each part then we have a fraction that is equivalent to one half
The fractions below are equivalent to .
The bars below visually represent why this is true. The little numbers above each box show the number of sections that each whole has been divided into. Notice that this number is also the denominator.
We can write an equivalent set of fractions for one-third too.
Anytime that we want to create an equivalent fraction we multiply the numerator and denominator by the same number.
Example
Create a fraction equivalent to .
To do this, we need to multiply the numerator and denominator by the same number. Let’s choose 2. Two is always a good place to start.
We could create another equivalent fraction by choosing a different number. Let’s try four.
These fractions are also equivalent.
READ: Write Given Fractions in Simplest Form
Write Given Fractions in Simplest Form
One of the trickiest things to think about with equivalent fractions is being able to determine whether or not they are equivalent. Look at this example.
Example
Are and
equivalent?
This is tricky because we can’t tell if the numerator and denominator were multiplied by the same number. These fractions look like they might be equal, but how can we tell for sure? This is where simplifying fractions is important.
How do we simplify fractions?
You can think of simplifying fractions as the opposite of creating equal fractions. When we created equal fractions we multiplied. When we simplify fractions, we divide.
What do we divide?
To simplify a fraction, we divide the top and the bottom number by the Greatest Common Factor.
Let’s simplify . To do this, we need to divide the numerator and denominator by the GCF.
The GCF of 3 and 6 is 3.
Let’s simplify . To do this, we need to divide the numerator and the denominator by the GCF.
The GCF of 4 and 8 is 4.
We can see that and
. They are equivalent fractions.
We can use simplifying to determine if two fractions are equivalent, or we can just simplify a fraction to be sure that it is the simplest it can be. Sometimes you will also hear simplifying called reducing a fraction.