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Grade 5 (age 10-11)

Reduction & Common Denominator

Reduction & Common Denominator

Reduction divides the top and bottom of a fraction by the same number to make it simpler, while a common denominator gives two fractions the same denominator. Eating 4 of 8 pizza slices is 4/8, and reducing it gives a simpler 1/2 while the size stays the same. Comparing 1/3 and 1/4 is hard when denominators differ, but a common denominator shows which is larger at a glance. Here you change the numerator and denominator and watch it on fraction bars.

What is reduction?
✂️ Divide both numerator and denominator by the same number
①Eating 4 of 8 pizza slices = 4/8
②Pair them up: 1 of 2 pairs = 2/4 = 1/2
③Same size, simpler form — that's reduction!
6
12
What is finding common denominator?
🔗 Make denominators equal to compare
①Which is bigger: 1/3 or 1/4?
②Different denominators are hard to compare directly
③Convert to a common denominator → easy compare!
3
4
Summary
Reduction
ab = a÷nb÷n
Divide both by the same n → equivalent fraction
Common Denominator
ab → a×mb×m
Use the LCM as the common denominator and multiply numerator by the same m
🎯 Key Points
①Reduction: divide by GCD → simplest form
②Common denom: use the LCM
③Reduction simplifies fractions
④Common denom enables comparing/operating
⑤The size of the fraction does not change!
Examples and Unit Test
Example 1
Reduce 4/8 to lowest terms.
1
The GCD of numerator 4 and denominator 8 is 4.
2
Divide both by 4: 4÷4=1, 8÷4=2. So it is 1/2.
▸ 12
Dividing numerator and denominator by the GCD gives lowest terms at once.
Example 2
What common denominator is used to convert 1/3 and 1/4?
1
Find the LCM of the two denominators, 3 and 4.
2
The LCM of 3 and 4 is 12, so the common denominator is 12. (1/3=4/12, 1/4=3/12)
▸ 12
The common denominator is the LCM of the two denominators.
Unit Test
What is 6/9 in lowest terms?
①39
②23
③69
④13
▸ ② 23
1
The GCD of 6 and 9 is 3.
2
6÷3=2, 9÷3=3, so it is 2/3.
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Fraction Mul/Div