Put rational numbers in order

Key Notes :

What are Rational Numbers? 🤔

Rational numbers are numbers that can be written as fractions p/q, where p and q are integers and q ≠ 0.

They include:

  • Positive numbers ➕
  • Negative numbers ➖
  • Zero 0️⃣

Examples: 3/4, -2/5, 0, 7

Steps to Arrange Rational Numbers in Order 🔢

Step 1: Convert to Same Form (Fractions or Decimals) 🔄

Convert all numbers to decimals or fractions with the same denominator.

Example: Arrange 1/2, -3/4, 2/3

  • Convert to decimals: 1/2 = 0.5, -3/4 = -0.75, 2/3 ≈ 0.667

Step 2: Compare the Numbers 👀

  • For positive numbers ➡ bigger decimal/fraction = bigger number
  • For negative numbers ➡ bigger decimal (less negative) = bigger number
  • Example: -0.75 < 0.5 < 0.667

Step 3: Arrange in Order ⬆️ or ⬇️

  • Ascending Order (Smallest to Largest): -0.75, 0.5, 0.667
  • Descending Order (Largest to Smallest): 0.667, 0.5, -0.75

Tips & Tricks 💡

Always watch the signs!

  • Negative numbers are smaller than zero. ❌0️⃣

Use a number line 📏

  • Helps visualize which number is bigger or smaller.

Convert fractions first if denominators are different:

  • Example: 1/3, 2/5 → common denominator 15 → 5/15, 6/15
  • Compare numerators: 5 < 6 → 1/3 < 2/5

Decimals make comparison easier:

  • -3/4 ≈ -0.75
  • 2/3 ≈ 0.667

Example Problem 📝

Arrange in ascending order:
-1/2, 3/4, -2/3, 1/3

Step 1: Convert to decimals

  • -1/2 = -0.5
  • 3/4 = 0.75
  • -2/3 ≈ -0.667
  • 1/3 ≈ 0.333

Step 2: Compare

  • Smallest → -0.667
  • Then → -0.5
  • Then → 0.333
  • Largest → 0.75

✅ Answer (Ascending Order): -2/3, -1/2, 1/3, 3/4

Quick Reminder Chart 🗂️

SignOrder Rule
Positive ➕Bigger value → bigger number
Negative ➖More negative → smaller number
Zero 0️⃣In between negative and positive

Learn with an example

Put these numbers in order from least to greatest.

9 ,-28/40, 6/15, -3/6

First, write all the numbers as decimals.

–28/40= –0.7

6/15= 0.4

–3/6= –0.5

You want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them first.

When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers.

–0.7 is less than–0.5.

Next come the positive numbers. The positive numbers, from least to greatest, are 0.4 and 9.

The numbers, written as decimals, in order from least to greatest, are:
–0.7<–0.5<0.4<9

So, the correct answer is:

–28/40 < –3/6 < 6/15 <9

Put these numbers in order from greatest to least.

First, write all the numbers as decimals.

18/25 = 0.72

-1/20 = -0.05

You want to order the numbers from greatest to least. Since positive numbers are greater than negative numbers, start with them first.

0.72 is the only positive number. It is the greatest number on the list.

Next, come the negative numbers. When comparing negative numbers, smaller numbers (if you ignore the minus sign) are greater than larger numbers. 

The numbers, written as decimals, in order from greatest to least, are:

0.72 > –0.05 > –8

So, the correct answer is:

Put these numbers in order from least to greatest.

First, write all the numbers as decimals.

-24/40 = -0.6

-18/20 = -0.9

6/15 = 0.4

You want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them first.

When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers. –0.9 is less than –0.6.

Next come the positive numbers. The positive numbers, from least to greatest, are 0.4 and 7.

The numbers, written as decimals, in order from least to greatest, are:

–0.9 < –0.6 < 0.4 < 7

So, the correct answer is:

Let’s practice!🖊️