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Grade 5 (age 10-11)

grade 5 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. Change the numerator and the denominator to reduce, then use two denominators to compare the unit fractions 1/x and 1/y.

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 is reduction. When numerator and denominator share no common divisor except 1, the fraction is in lowest terms
6
12

What is finding common denominator?

🔗 Make denominators equal to compare
①The bars here compare unit fractions 1/x and 1/y. The same common-denominator step works for 2/3 and 3/4
②1/3 and 1/4 are hard to compare until both use 12: 4/12 and 3/12
③2/3=8/12 and 3/4=9/12, so 3/4 is larger
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 Multiplication & Division