4th Grade Math
Fractions and Decimals
Unit 5
Lesson One: Fractions with Denominators of 10, 100, 1000
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!
Denominators of 10, 100, 1000
Fractions with the denominators, 10, 100, or 1000 can be converted to have the same, common denominator. This makes it easier to add and subtract them with each other!
For example, lets look at the fraction 7/10. Lets convert this too the denominator /100, so we can see how much 7/10 is out of a 100.
To make the fraction 7/10 have the denominator of 100, you have to multiply both the numerator and denominator by 10. This way, they have the same denominator.
After converting, you see that the fraction, 7/10, with a denominator of 100 becomes 70/100. They are still equivalent!
Adding and Subtracting Denominators of 10, 100, 1000
Watch this Video to Learn More!
Once you get two fractions into common denominators, you can add and subtract them much easier!
Adding: Lets do a problem together! Lets add 4/10 + 3/100.
Our first step is to identify that the denominator 10 can be multiplied by 10 to be 100. This means we also have to multiply our numerator by 10! When me multiply both the numerator (4) and the denominator (10) by 10, we get 40/100.
Now, all we have to do is add it to 3/100. Since both fractions have a common denominator, you can add them like you would normally add two numbers.
40/100 + 3/100= 43/100
Subtracting: You can do the same process with subtraction! Lets use the 1000 denominator and do the problem 70/100 - 26/1000.
Again, the first step is to identify that the denominator 100 can be multipied by 10 to be 1000. This is so we can have a common denominator. Because we are multiplying our denominator by 10, we also have to multiply our numerator. When we multiply the numerator (70) and the denominator (100) by 10, we get 700/1000.
Now, we just have to subtract 700/1000- 26/1000. We subtract normally because they have a common denominator!
700/1000 - 26/1000= 674/1000
Lesson Two: Fractions and Decimals
Converting Decimals to Fractions
Decimals may seem a little new to you, but they are very similar to fractions! They are different ways of showing parts of a whole. The "whole" of a decimal is 1.
Decimals also have place value! They have an infinite amount of place values, but the two that you use are the tenths and hundredths places! These are the first two places to the two places to the right of the decimal point.
In the number 0.75, the number in the tenths place is 7, and the number in the hundredths place is 5.
Let's Try an Example of Converting Decimals to Fractions!
Lets convert 0.75 to fraction form. Remember, the whole of a decimal is 1. So lets say this is 0.75/1.0.
To convert a decimal to a fraction, you multiply the numerator and the denominator by 100. This allows you to see the fraction out of 100. When you multiply the numerator 0.75 by 100, it becomes 75. This is 75/100.
The next step is to simplify this to its simplest form. We covered this in unit 3! To simplify it, we have to divide it until it can not be simplified anymore.
Divide 75 and 100 both by 5. This gives you 15/25. This can be simplified even more if you continue divide it. If you divide 15 and 25 by 5 again, you get 3/4. These can not be divided anymore, so 3/4 is the simplest form.
This whole process shows you how 3/4 = 0.75
When converting decimals to fractions, follow this process.
Multiply the decimal by 100. It shows you the fraction out of 100.
Put it in simplest form and it shows you the simplest fraction it can be!
This is an example of a mixed number. They contain both whole numbers and fractions!
Mixed Numbers
A mixed number uses both whole numbers and a fraction.
You can convert decimals over 1 to mixed numbers by doing the same process.
For example, lets use 1.5/1. If we multiply both the numerator and the denominator by 100, you get 150/100.
This is pretty easy to simplify. Divide both 150 and 100 by 10. This gives you 15/10. You can keep simplifying! Divide both by 5. This gives you 3/2. 3/2 is a mixed number.
1.5 = 3/2
Converting Fractions to Decimals
To convert the fraction to a decimal, you must first convert it so it has a denominator of 10, 100, 1000. This allows you to find its decimal much easier.
Lets take the fraction, 3/5. The easiest way to find the decimal of this is to convert the denominator to 10. Multiply the denominator by 2 so it can be 10. You also have to multiply the numerator! This gives you the fraction 6/10. Read the tip!
Because you are dividing by 10, you move the decimal point one place to the left. 6 becomes 0.6.
Tip!
When multiplying or dividing a number by 10, 100, or 1000, there is a trick that can make it much easier. Move the decimal point over! Remember, that at the end of every number is an invisible decimal point. When you multiply, you move the decimal point to the right. When you divide you move the decimal point to the left. If there is nothing in the place you are moving to, you put in a zero.
Multiply or divide by 10: move the point one spot: 6x10 = 60
Multiply or divide by 100: move the point two spots: 6x100 = 600
Multiply or divide by 1000: move the point three spots: 6 / 1000 = 0.006
Comparing Decimals!
Just like digits and fractions, you can put decimals in order!
When ordering decimals and fractions on a number line, use what we learned in Unit 3! Use the benchmark to your advantage.
The greater the decimal or fraction, the farther it goes on a number line!