Put rational numbers in order

Key Notes:

🔢 What Are Rational Numbers?

  • A rational number is any number that can be written as a fraction 🧡
    Example: ½, –3, 4, 0.25, –7/8
  • They can be positive (+) or negative (–) ➕➖

📏 Convert All Numbers to the Same Form

Before ordering, convert them to:

  • Decimals OR
  • Fractions with same denominators
    👉 This makes comparison easier! ✨

🔁 Number Line Helps! 📉

  • Numbers on the right are greater 🌞
  • Numbers on the left are smaller 🌙
    Example:
    –5 < –2 < 0 < 3 < 4

➕➖ Compare Positive and Negative Numbers

  • All positive numbers > all negative numbers 💚 > ❤️
  • Among negatives: the number with smaller absolute value is greater
    Example: –2 > –5 ✔️

🔍 Compare Rational Numbers With Fractions

  • Use common denominators
    Example:
    3/8 and 5/12 → Convert to denominator 24
    3/8 = 9/24
    5/12 = 10/24
    So, 3/8 < 5/12 🎉

🧮 Compare Rational Numbers With Decimals

  • Convert fractions to decimals
    Example:
    0.4 = 0.40
    ⅓ ≈ 0.33
    So, ⅓ < 0.4 🌈

🔢 Put the Numbers in Ascending / Descending Order

  • Ascending (small → big): ⬆️
  • Descending (big → small): ⬇️
    Example: Order: –3, 0.5, 2/3, –1
    Convert: –3, –1, 0.5, 0.66
    Final order (ascending): –3, –1, 0.5, 2/3

🎯 Check Using Absolute Values

  • Helps compare negative numbers
    Example: –4 and –7
    |–4| = 4
    |–7| = 7
    Smaller absolute value → greater number
    So, –4 > –7 ✔️

⭐ Ordering Mixed Rational Numbers

If the set has:

  • Fractions
  • Decimals
  • Whole numbers
    👉 Convert all to decimals for easiest comparison 🌟

🌈 Practice Makes You Perfect

Try ordering sets like:

  • 0.2, –3/5, 4, –0.1
  • 7/8, –2, 0, –¾
    The more you practice, the faster you become! ⚡💡

Learn with an example

🗼 Put these numbers in order from least to greatest.

  • – 0.5
  • 0.1
  • – 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.–5 is less than–0.5.
  • Next come the positive numbers. 0.1 is the only positive number. It is the greatest number in the list.
  • The numbers, written as decimals, in order from least to greatest are:
  • – 5
  • – 0.5
  • 0.1

🗼Put these numbers in order from least to greatest.

  • – 8 3/30
  • 8
  • – 8 2/10
  • First, write all the numbers as decimals.
  • -8 3/30=-8.1
  • -8 2/10=-8.2
  • 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. -8.2 is less than -8.1.
  • Next come the positive numbers. 8 is the only positive number. It is the greatest number in the list.
  • The numbers, written as decimals, In order from least to greatest are:
  • – 8.2 < – 8.1 <8
  • So, the correct answer is:
  • – 8 2/10
  • – 8 3/30
  • 8

🗼 Put these numbers in order from greatest to least.

  • – 3
  • 12 / 15
  • – 3 3 / 15
  • First, write all the numbers as decimals.
  • 12 / 15 = 0.8
  • -3 3 / 15 = -3.2
  • You want to order the numbers from greatest to least. Since positive numbers are greater than negative numbers, start with them first.
  • 0.8 is the only positive number. It is the greatest number in the list.
  • Next come the negative numbers, when comparing negative numbers, smaller numbers (If you Ignore the minus sign) are greater than larger numbers. -3 is greater than -3.2.
  • The numbers, written as decimals, in order from greatest to least are:
  • 0.8 > -3 > -3.2
  • So, the correct answer is:
  • 12 / 15
  • – 3
  • – 3 3 / 15

Let’s practice!🖊️