When comparing numbers, it is best to first ensure that they are as similar as possible. In this exercise, we are given two mixed numbers with different denominators in the fraction.
- 2 1316 ? - 2 1114
Let's then rewrite each of the numbers as a decimal. Before we do so, we should make sure to write each number as a fraction. Let's also ignore the negative sign for just a moment.
We found that 2 1316 is equal to 45 16 when it is written as a fraction. This means that we actually want to find the quotient 45÷ 16. We find the quotient by dividing the numerator of the fraction by its denominator. Let's do it!
We found that 4516 written as a decimal is 2.8125. Since we previously found that 2 1316 is equal to 4516, we can say that 2 1316 written as a decimal is 2.8125.
2 1316=45/16
⇓
2 1316=2.8125
Therefore, - 2 1316 is equal to - 2.8125. We can do the same for - 2 1114. Let's ignore the negative sign for just a moment and rewrite the mixed fraction!
Let's rewrite the fraction as a decimal by dividing the numerator of the fraction by its denominator!
Here are the results.
Mixed Number to Fraction
Fraction to Decimal
- 2 1316 = - 45/16
- 45/16 = - 2.8125
- 2 1114= - 39/14
- 39/14= - 2.785714...
Now that we have each mixed number written as decimal, we can graph them on a number line. We will use the fact that the position of the number is the position of its corresponding decimal. Then we will compare which one is greater than the other.
On the number line, we can see that - 2 1316 is to the left of - 2 1114. As a result, - 2 1316 is less than - 2 1114.
- 2.8125 < - 2.785714... ⇔ - 2 1316 < - 2 1114
