Question

Order the following set of rational numbers from least to greatest: -8, -19, 0, 1/2, 1/4

Answer 1

Answer:

-19, -8, 0, 1/4, 1/2 is the correct order

Answer 2

Answer:

$-19,-8,0,\frac{1}{4}, \frac{1}{2}$

Step-by-step explanation:

Skills required: Ordering a set of numbers

1) $-8,-19,0,\frac{1}{4}, \frac{1}{2}$ are the numbers we are given. There are 2 important things to think about when ordering this set.

1. Negative numbers (the numbers with a "-" sign in front of it) are always less than 0. Negative numbers are: -1, -5, -67, -990
2. Positive numbers (the numbers without a "-" sign in front of them) are always greater than 0. Positive numbers are: 1, 3, 45, 67

2) Based on this, we can split the 5 numbers into 3 groups:

• The negative group: -8,-19
• The special group: 0
• The positive group: $\frac{1}{2}, \frac{1}{4}$

3) Starting with the negative group, we can easily find which number is greater.

-1 is greater than -2.

-23 is greater than -35.

Based on this: -8 is greater than -19. That means when ordering our numbers, -8 is the first number, and -19 is the second number

4) 0 is the 3rd number, since it is less than positive numbers and greater than negative numbers

5) Now onto the positive numbers, which is also easily solvable.

When you have two fractions, there are different ways to find out which fraction is greater than the other. I will show you 2 different ways here.

1. Do division. $\frac{1}{4}$ is 1 ÷ 4 and $\frac{1}{2}$ is 1 ÷ 2. So, generally, given a fraction $\frac{x}{y}$, you would do x ÷ y to find the decimal form. If you know how to compare decimals, this is a good way. 1 ÷ 4 is 0.25 and 1 ÷ 2 is 0.5, and 0.5 is greater than 0.25, making $\frac{1}{2}$ greater than $\frac{1}{4}$
2. Compare denominators. So, these two fractions have the same numerator of 1. To find out which is greater, we can look at the denominators. If 2 fractions have the same numerator, the one with a lower denominator is greater, when looking at positive numbers. 2 is less than 4, so $\frac{1}{2}$ is greater than $\frac{1}{4}$

This means that $\frac{1}{4}$ is the 4th number, and $\frac{1}{2}$ is the 5th term.

Our ordered pair would then be: $-19,-8,0,\frac{1}{4}, \frac{1}{2}$

Hope this helps and have a nice day!! :) :] :D