Fractions And Decimals Lesson: Concepts And Comparisons

Lesson Overview

• Comparing and Ordering Decimals
• Equivalent Fractions
• Simplifying Fractions
• Converting Fractions to Decimals
• Converting Fractions to Percentages
• Converting Decimals to Percentages
• Practice Tips

Decimals and fractions are ways to show parts of a whole. You will see them in everyday life when dealing with money, measurements, and data. Each section of this guide will explain these ideas with easy examples and steps you can follow.

Fractions

A fraction shows a part of a whole. It has two numbers:

• The top number is called the numerator. It shows how many parts we have.
• The bottom number is called the denominator. It shows how many total parts make the whole.

Example:
3 over 4 (written as 3/4) means 3 parts out of 4 total parts.

Decimals

Decimals also show parts of a whole. They are written with a dot called a decimal point.

Example:
0.5 means five tenths, or 5 parts out of 10.
0.25 means twenty-five hundredths, or 25 parts out of 100.

Comparing and Ordering Decimals

To compare or arrange decimals:

• Look at the numbers from left to right.
• Start with the digit just after the decimal point (tenths place).
• Add zeros to make them the same length if needed.

Example Question:
Arrange these decimals from smallest to largest:
0.25, 0.75, 1.5, 0.20, 0.5, 0.6

Steps:

• Make them all the same length:
  0.20, 0.25, 0.50, 0.60, 0.75, 1.50
• Order them:
  0.20 < 0.25 < 0.50 < 0.60 < 0.75 < 1.50

Answer: 0.20, 0.25, 0.5, 0.6, 0.75, 1.5

Equivalent Fractions

Equivalent fractions are different-looking fractions that show the same value.

How to find them:
Multiply or divide both the top and bottom numbers by the same number.

Examples:

• 1/2 is equal to 2/4 (because 1x2 = 2 and 2x2 = 4)
• 3/5 is equal to 6/10 (multiply both numbers by 2)

These fractions have the same value even though they look different.

Simplifying Fractions

Simplifying means making the fraction as small as possible.

How to simplify:

• Find the biggest number that divides both the top and bottom.
• Divide both by that number.

Examples:

• 3/9: The biggest number that goes into both 3 and 9 is 3.
  Divide both: 3 ÷ 3 = 1, 9 ÷ 3 = 3.
  So 3/9 becomes 1/3.
• 12/24: The biggest number that goes into both 12 and 24 is 12.
  12 ÷ 12 = 1, 24 ÷ 12 = 2
  So 12/24 becomes 1/2

Converting Fractions to Decimals

To change a fraction to a decimal, divide the top number by the bottom number.

Examples:

• 1/2 = 1 ÷ 2 = 0.5
• 3/4 = 3 ÷ 4 = 0.75
• 1/4 = 1 ÷ 4 = 0.25
• 7/10 = 7 ÷ 10 = 0.7
• 1/5 = 1 ÷ 5 = 0.2
• 45/100 = 45 ÷ 100 = 0.45
• 1/25 = 1 ÷ 25 = 0.04

Use division to change any fraction into a decimal.

Converting Fractions to Percentages

To change a fraction to a percentage:

• First divide the top number by the bottom number.
• Then multiply the answer by 100.

Examples:

• 1/2 = 0.5 → 0.5 x 100 = 50 percent
• 3/4 = 0.75 → 0.75 x 100 = 75 percent
• 1/4 = 0.25 → 0.25 x 100 = 25 percent
• 1/5 = 0.2 → 0.2 x 100 = 20 percent
• 9/10 = 0.9 → 0.9 x 100 = 90 percent

So:

• 1/2 = 50 percent
• 3/4 = 75 percent
• 1/4 = 25 percent
• 1/5 = 20 percent
• 9/10 = 90 percent

Converting Decimals to Percentages

To change a decimal to a percentage:

• Multiply the decimal by 100.

Examples:

• 0.30 → 0.30 x 100 = 30 percent
• 0.90 → 0.90 x 100 = 90 percent
• 0.75 → 0.75 x 100 = 75 percent

Shortcut:
Move the decimal point two spaces to the right and add a percent sign.

• 0.3 → 30 percent
• 0.75 → 75 percent
• 0.9 → 90 percent

Practice Tips

• Always check your answers by reversing the steps.
  For example, if you change a fraction to a decimal, try changing it back.
• Use simple division to find decimals from fractions.
• Remember common values:
  • 1/2 = 0.5 = 50 percent
  • 1/4 = 0.25 = 25 percent
  • 3/4 = 0.75 = 75 percent
  • 1/5 = 0.2 = 20 percent
  • 9/10 = 0.9 = 90 percent

Fractions and decimals are two ways to show the same idea - a part of a whole. By learning how to compare, convert, and simplify these numbers, students can become confident in solving any problem related to this topic.