Answer:
a) 35/40, 36/40
b) 4/8, 6/8, 6/8
Step-by-step explanation:
In order to convert into like fractions, we must find a common denominator for both.
This just means finding the LCM of the existing denominators.
To find the LCM, list the prime factorization of each number, and multiply each factor together the maximum amount of times it appears in one factor.
Then figure out what you need to multiply the existing denominator by to get the common denominator, and multiply that number to the numerator as well.
Note that multiplying a fraction by x/x won't change the value because x/x is equal to 1.
If this sounds confusing- don't worry- it'll become more clear in the work below.
<u>a) 7/8 and 9/10</u>
Start by finding the LCM of 8 and 10
<u>Prime factorization:</u>
8- 2*2*2
10- 2*5
Multiple: 2*2*2*2*5
However, 2 appears in 10 once and 8 three times.
So we can cross out one "2" since the maximum amount of times it appears is three times, not four.
Hence the LCM is 2*2*2*5=40
40 will be the common denominator.
To get to 40 from 8, you need to multiply it by 5.
So we can do:
7/8*5/5=35/40
Repeat with the second fraction.
To get to 40 from 10, you need to multiply it by 4.
So we can do:
9/10*4/4=36/40
36/40>35/40
Therefore, the ascending order would be
35/40, 36/40 or 7/8, 9/10
<u>b) 1/2, 3/4, 6,8</u>
Start by finding the LCM of 2, 4 and 8.
<u>Prime Factorization:</u>
2: 2
4: 2*2
8: 2*2*2
Since 2 appears a maximum of 3 times in one number the LCM is:
2*2*2=8
So our common denominator will be 8.
To get to 8 from 2, you need to multiply it by 4.
1/2*4/4=4/8
To get to 8 from 4, you need to multiply it by 2.
3/4*2/2=6/8
The last fraction is already good.
6/8
Hence, the ascending order would be:
4/8, 6/8, 6/8 or 1/2, 3/4, 6/8
Hope that helps! Let me know if you have any questions :)
