Susie uses 1/2 to help compare 1/3 to 3/5 and to help in comparing 3/7 with 2/3. Explain how 1/2 help determine which fraction is greater in each combination.
Zusie uses 1/2 to help compare 1/3 to 3/5 and to help in comparing 3/7 with 2/3.explain how 1/2 help determine.wich fraction is greater in each combination
To compare fractions, you can use a common denominator and then compare the numerators. In this scenario, Susie is using the fraction 1/2 as a benchmark to compare other fractions. Let's go through each combination step by step:
1. Comparing 1/3 to 3/5:
To compare 1/3 and 3/5 using 1/2 as a benchmark, you need to find a common denominator for all three fractions. The smallest common denominator for 1/3, 3/5, and 1/2 is 30.
Now, you need to convert each fraction to have the same denominator of 30:
1/3 = (1/3) * (10/10) = 10/30
3/5 = (3/5) * (6/6) = 18/30
1/2 = (1/2) * (15/15) = 15/30
Now that all fractions have the same denominator, you can compare the numerators:
10/30 is smaller than 15/30, so 1/3 is less than 1/2.
2. Comparing 3/7 to 2/3:
Again, you need to find a common denominator for 3/7, 2/3, and 1/2. The smallest common denominator for all three fractions is 42.
Now, convert each fraction to have the same denominator of 42:
3/7 = (3/7) * (6/6) = 18/42
2/3 = (2/3) * (14/14) = 28/42
1/2 = (1/2) * (21/21) = 21/42
Now that all fractions have the same denominator, you can compare the numerators:
18/42 is smaller than 21/42, so 3/7 is less than 1/2.
In both cases, by using 1/2 as a benchmark, Susie found that the numerators of the fractions with the same denominator were smaller than 1/2. Therefore, she concluded that 1/3 is less than 1/2 and 3/7 is also less than 1/2.