4th Grade Math
Analyzing Fractions
Unit 3
All About Fractions!
Remember, denominators represent the total amount of equal sized pieces of a whole! The numerator represents how many of those pieces are in the fraction!
Think about it like this: one fraction has divided a cake into 3 equal sized pieces, and one fraction has divided a cake into 5 equal sized pieces. These cakes are the same size. When a cake is divided into less pieces, those pieces are bigger. ⅓ of a cake will be bigger than ⅕ of a cake.
A higher denominator divides the whole into more pieces. A numerator tells you how many of those pieces are in question.
Modeling and Learning Equivalent Fractions
Equivalent fractions are fractions that have the same value even though their numerators and denominators are different.
For example, think of the fraction 1/2. This is equal to 2/4, 3/6, 4/8, and many more fractions. They are all equal because they represent the same part of a whole.
Look at the diagram on the top left! Each row represents a whole! Look through the diagram. You'll see how the amount that is taken by 1/2 is the same amount as how much is taken by 2/4. When two fractions like these have the same value and are equal parts of a whole, they are equivalent fractions.
Try these games to practice equalizing fractions!
Simplest Form
When fractions are in their simplest form, it means the fraction can not be simplified to any smaller whole number.
Let's stick with the fraction 4/8. This fraction can be simplified to smaller numbers than 4 and 8. Fractions are simplified by dividing the numerator and denominator by the same number.
If you divide the numerator, 4, and the denominator, 8, by their highest common factor (the highest multiple), you will get the numbers in their simplest form. The highest common factor of 4 and 8 is 4. So you would divide both by 4. The numerator would become 1 and the denominator would be 2. The simplified fraction would be 1/2. Since there is no smaller whole number than one, this fraction is the simplest form of 4/8.
Practice Question: What is 6/8 in its simplest form?
3/4. If you divide the numerator and denominator of 6/8 by its highest common factor, 2, you get the fraction 3/4.
Practice Question: What is 1/3 of 30?
10 or 10/30. Since you have to multiply the denominator, 3, by 10 to get to 30, you also have to multiply the numerator by 10.
Comparing and Ordering Fractions Using a Benchmark
Fractions can be ordered and compared by their size and how much of a whole they take up. Some fractions make up more of a whole than others.
Just like you compared whole numbers with the symbols >,<, and =, you compare fractions the same way. Look at the tip on the right! Once you figure out the value of two fractions (how much out of a whole they each take) you can compare and find which one takes more!
Benchmarks
On a number line with fractions, there are "benchmarks". These are common fractions that you can use to compare other fractions. Some common benchmarks on a number line are 1/2 and 1. By figuring out a fractions relation to these benchmarks, you can see where it is on a number line. If a fraction is bigger than 1/2, its farther on the number line than 1/2. If it is smaller than 1/2, then it is placed earlier.
Benchmarks can also be used to compare two fractions. If one fraction is greater than 1/2, but another is smaller, you can determine which one is bigger.
For example, lets take the fractions 5/8 and 1/4. 5/8 is greater than 1/2 (1/2 is equivalent to 4/8), and 1/4 is smaller than 1/2 (equivalent of 2/4). This clearly shows you that 5/8 > 1/4.
Here's a little tip!
A smaller denominator means less, equal sized groups and a bigger denominator means more equal sized groups. Look at the picture above. The two fractions have the same numerator, 2. However, one fraction has a denominator of 3 and the other has a denominator of 5. Because 2/3 has a smaller denominator, it is a larger fraction than 2/5.
Try this game to practice equalizing fractions!
Practice Question: What sign makes this true? 4/5 _ 4/9.
4/5 > 4/9. 4/5 has a smaller denominator and less groups while 4/9 has a higher denominator and more groups. 4 out of 5 groups is greater than 4 out of 9 groups.
Practice Question: What sign makes this true? 2/8 _ 3/4.
2/8 < 3/4. 3/4 is higher than the bencmark 1/2 while 2/8 is lower.