Fraction Models: Mixed Numbers and Decimals

GOAL: You will learn how mixed numbers and decimals are equivalent.

GOAL: You will learn how mixed numbers and decimals are equivalent. HOW: You will compare mixed numbers and decimals on a number line.

1 2 You know that fractions can be shown as part of a whole or part of a set and represent a value between zero and one. – Each of these visual models shows the fraction one fourth.

You know that when you see the value 2 You know that when you see the value 2.7, the two represents how many ones there are (write “ones”) – or how many wholes there are if you were talking about a fraction, and the digit to the right of the decimal point stands for PART of a WHOLE.  

You already know about place value. For example, with this number 2  You already know about place value. For example, with this number 2.7, you know that the number to the left of the decimal point represents how many ones we have and the digit to the right of the decimal point stands for tenths (write “tenths”). - You also know that fractions and decimals are just different ways to represent the same value. We’re going to take a closer look at what that means.

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 - Let’s take a look at the value 2.7. - Here is what 2.7 would look like on a number line. You have two wholes (one two – use writing tool) and 7 of the next tens parts shaded in. 2.7 can also be represented as a mixed number.

Two stands for how many wholes we have, so that’s our larger number when we write the mixed number (write 2 in red). Then, the amount to the right of the decimal stands for part of the whole – 7/10. So we can write that as a fraction next to the large number two to come up with our mixed number (write 7/10 in red). Here is what the mixed number would look like on a number line.

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 Now, let’s look at both number lines – the one showing the decimal and the one showing the mixed number.

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 When we compare the decimal plotted on the number line next to the mixed number plotted on the number line, you can see they are equivalent, or equal. Let’s see how this would work in another way.

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 Here we have the improper fraction 13/10. It is an improper fraction because our numerator is greater than our denominator. You know that when we have an improper fraction, we have at least one complete whole. You can either convert this to a mixed number, or plot it on a number line. Let’s plot it.

l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l 1 2 3 Here is what 13/10 looks like on a number line. Our whole numbers are divided into tenths since 10 is our denominator. Remember, the numerator is the counting value, so let’s count to see if we have 13 tenths filled in. We do! We can write the decimal of this also. We have one complete whole and then 3 tenths are shaded. One point three (write in black). Using the number line, you can see that mixed numbers, improper fractions, and fractions can also be shown in decimal form.

In this lesson you learned that mixed numbers and decimals are equivalent when comparing the values on a number line.