Compare the fractions [tex]3 \frac{3}{22}[/tex] and [tex]3 \frac{2}{33}[/tex]. Which is greater?
I know:
1. Multiply the denominator by the whole number and then add the numerator to that.
- [tex]3 \frac{3}{22}[/tex] becomes [tex]\frac{69}{22}[/tex]
- [tex]3 \frac{2}{33}[/tex] becomes [tex]\frac{101}{33}[/tex]
2. The least common multiple (LCM) of the denominators 22 and 33 is 66.
What is the next step to determine which fraction is greater? Thank you.
Answer (2)
3 3/22 isn't 69/66. 3 3/22 is like 3+3/22. To sum them,you have to have the same denominator. So 3=66/22. Know you can add them, so 3 3/22=3+ 3/22= 66/22+3/22=69/22. Same way, 3 2/33= 3+2/33=99/33+2/33=101/33. Know you have to compare 69/22 with 101/33. For this, you need to get them to the same denominator. So you multiply 69/22 with 3, and 101/33 with 2. Know you have to compare 207/66 with 202/66. Obviously, the first one is bigger, because 207>202. So in the end, 3 3/22> 3 2/33
To determine which fraction is greater, I converted both mixed numbers to improper fractions and then found a common denominator. After converting 3 22 3 to 22 69 and 3 33 2 to 33 101 , I found that after converting both fractions to a common denominator of 66, 66 207 is greater than 66 202 . Therefore, 3 \frac{2}{33}"> 3 22 3 > 3 33 2 .
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