Fractions and the Identity Property
Grade 4 Mathematics Understanding why multiplying by 1 doesn't change a fraction's value
Essential Questions
How can two fractions be equivalent even if they look different? Why does multiplying by 1 not change the value of a fraction? How do models help us prove fractions are equivalent?
Learning Target
I am learning how to explain why multiplying a fraction by 1 does not change its value
Success Criteria
I can identify fractions equal to 1 I can explain the identity property using fractions I can support my explanation with a model or equation
Review: Multiplying Whole Numbers by 1
5 × 1 = 5 12 × 1 = 12 100 × 1 = 100 The number stays the same!
What Fractions Equal 1?
2/2 = 1 3/3 = 1 4/4 = 1 5/5 = 1 When numerator = denominator, the fraction equals 1
Quick Check: Find the Fraction Equal to 1
Circle the fractions that equal 1: 6/6 3/4 8/8 2/5 10/10
The Identity Property with Fractions
4/5 × 1 = 4/5 The fraction stays the same! This is called the Identity Property Multiplying by 1 doesn't change the value
Model: 4/5 × 2/2 = 8/10
4/5 × 2/2 Since 2/2 = 1, we're really multiplying by 1 4/5 × 1 = 4/5 8/10 = 4/5 (equivalent fractions!)
Why This Works
{"left":"We multiply the numerator by 2: 4 × 2 = 8\nWe multiply the denominator by 2: 5 × 2 = 10","right":"Since we multiply both parts by the same number\nThe fraction's value stays the same"}
Guided Practice: Find Equivalent Fractions for 1/6
Start with 1/6 Multiply by 2/2: 1/6 × 2/2 = ? Multiply by 3/3: 1/6 × 3/3 = ? What patterns do you notice?
Let's Solve Together!
1/6 × 2/2 = 2/12 1/6 × 3/3 = 3/18 1/6 × 4/4 = 4/24 All of these fractions are equivalent to 1/6!
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