3rd Grade Math
Fractions
Unit 3
What are Fractions?
A fraction is a part of a whole. A fraction is formed when something is broken up into smaller parts.
There are two types of fractions: proper fractions and improper fractions!
Proper Fractions: Worth less than 1 (< whole)
Improper Fractions: Worth more than 1 (> 1)
How are fractions written?
Fractions are written as two numbers on top of each other, separated by a dividing line! The bottom number is called the denominator and tells us how many parts an object has been broken into. The top number is called the numerator and tells us how many of those smaller parts we will be using.
Fractions As Pictures!
For example, the picture to the right shows that the circle has been broken down into 6 parts! This means that the denominator of the fraction is 6. Because only 5 of the parts are highlighted and are being used, the numerator is 5. This means that the picture shows the fraction 5/6!
Can the same fraction be written in different ways?
Yes! Even though the picture on the left shows the fraction 5/6, by multiplying both the numerator and denominator by the same number, you can discover different versions of the same fraction! These different versions are called fraction equivalents because they are equal to the original fraction! For example, 10/12 and 15/18 both equal 5/6!
Let's Watch!
Watch the videos below to learn more about fractions and how to find equal versions of them!
Fractions on a Number Line
Fractions can also be placed on a number line. Since proper fractions are less than 1, they can be placed on the number line at points between 0 and 1!
Can you tell that, in one line, each of the parts is equal? This is because larger fractions are multiples of smaller fractions! For example, 5/6 is really 5 segments of 1/6 added together (1/6 + 1/6 + 1/6 + 1/6 + 1/6)!
BONUS: Can you see all the different versions of 1/2 on each number line? 1/2 can also be 2/4, 3/6/ and 4/8!
Comparing Fractions
Last unit, we learned how to compare numbers and decide which numbers are larger than others! Now, we can do the same with fractions! Look at the number line above! Can you tell that the fractions closer to 1 are greater than those farther away? This is because, when comparing fractions have the same denominator, the fraction with the bigger numerator is greater.
In the pictures above, which fraction is larger? The green circle shows the fraction 6/8 and the yellow circle shows 7/8. Because 7 > 6, we know the 7/8 > 6/8!
Let's Watch!
Check out this video to learn more about finding fractions on the number line!
Tips for Adding and Subtracting Fractions!
When fractions have the same denominator (bottom number), you can easily combine them by adding or subtracting the numerators (top numberss)! Let's try one together!
2/6 + 3/6 = ?
Because their denominators are the same we can go ahead and add our numerators!
2 + 3 = 5 ..... Our answer is 5/6!
How to Simplify Fractions
Sometimes, when you have a version of a fraction that is harder to deal with, you have to make it more manageable. You can do this by finding a Greatest Common Factor (the largest number that two number can be divided by) for the numerator and denominator, then dividing both by that number. Let's walk through an example below!
25/100
This seems like a difficult fraction to handle, but it's not! What is the Greatest Common Factor between 25 and 100?
If you said 25, that's right! ... 25/25 = 1 and 100/25 = 4. This means that our simplified version of 25/100 is ...
1/4!
Need More Help? Let's Watch!
Check out these videos to learn more about fractions!