Finding the Whole from a Percentage
Year 8 Mathematics WALT: Calculate the whole when given a percentage amount Building on our knowledge of percentages
WALT & Success Criteria
WALT: Calculate the whole when given a percentage amount Success Criteria: • I can identify when I need to find the whole • I can set up the correct equation • I can solve problems using inverse operations • I can check my answers make sense
Quick Revision: Finding Percentages
Let's recall what we already know: To find 20% of 150: 20% = 20/100 = 0.2 0.2 × 150 = 30 So 20% of 150 = 30
Think About This...
If 20% of a number equals 30... What is the original number? How could we work backwards to find it?
The Method: Using Inverse Operations
If 20% of a number = 30 Then: 0.2 × ? = 30 To find the whole, we divide: ? = 30 ÷ 0.2 ? = 150 Check: 20% of 150 = 0.2 × 150 = 30 ✓
Worked Example 1
Problem: 15% of a number is 45. Find the number. Step 1: Write as equation: 0.15 × ? = 45 Step 2: Divide both sides by 0.15 Step 3: ? = 45 ÷ 0.15 = 300 Step 4: Check: 15% of 300 = 0.15 × 300 = 45 ✓
Different Methods - Same Answer
{"left":"Method 1: Using Decimals\n25% of ? = 60\n0.25 × ? = 60\n? = 60 ÷ 0.25 = 240","right":"Method 2: Using Fractions\n25% = 1/4\n1/4 of ? = 60\n? = 60 × 4 = 240"}
Your Turn - Guided Practice
Solve these problems: 1. 30% of a number is 90. Find the number. 2. 8% of a number is 24. Find the number. 3. 125% of a number is 50. Find the number. Work with a partner and check each other's answers!
Real-World Applications
Where might we use this skill? • Sales: If a $45 item is 25% off, what was the original price? • Statistics: If 60 students represent 15% of the school, how many students total? • Finance: If $200 is 8% interest, what was the principal amount?
Summary & Extension
Key Steps to Remember: 1. Convert percentage to decimal 2. Set up equation: decimal × ? = given amount 3. Divide the given amount by the decimal 4. Always check your answer! Extension: Try problems with percentages over 100%