What value could be added to 2/15 to make the sum greater than 1/2. A. 1/15 B. 8/30 C. 5/15 D. 8/15 2. Which set of mixed numbers had a difference less than 1?
well, you want
x + 2/15 > 1/2
x > 1/2 - 2/15
x > 11/30
So, which of the choices fits that condition?
The answer is C
To find the value that could be added to 2/15 to make the sum greater than 1/2, we need to compare the sum of 2/15 with 1/2 and determine the difference between them.
1. First, let's find the common denominator for 2/15 and 1/2, which is 30. To do this, we multiply the denominators, 15 and 2.
2/15 = (2/15) * (2/2) = 4/30
1/2 = (1/2) * (15/15) = 15/30
2. Now we can compare the fractions:
4/30 + ? > 15/30
3. Subtract 4/30 from both sides of the equation:
? > 15/30 - 4/30
= 11/30
4. So the value that could be added to 2/15 to make the sum greater than 1/2 is greater than 11/30.
Looking at the answer choices, we can see that option D, 8/15, is greater than 11/30. Therefore, the answer is D.
Now let's move on to the second question.
To determine which set of mixed numbers has a difference less than 1, we need to find the difference between the given mixed numbers and compare the result with 1.
For example, let's consider two mixed numbers: 5 1/4 and 3 3/8.
1. Convert both mixed numbers to improper fractions:
5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4
3 3/8 = 3 + 3/8 = 24/8 + 3/8 = 27/8
2. Find the absolute difference between the two mixed numbers:
|21/4 - 27/8|
= |(21*2)/(4*2) - 27/8|
= |42/8 - 27/8|
= |15/8|
3. The absolute difference, 15/8, is greater than 1, so this set of mixed numbers does not have a difference less than 1.
By performing similar calculations for each set of mixed numbers and comparing their absolute differences to 1, you can determine which set has a difference less than 1.