find two fractions with a sum that is greater than 3/4 and less than 15/16. Write your fractions in simplest form and find the actual sum.
3/4 = 12/16
so between 12/16 and 15/16
say for example 6/16 and 7/16 which is 3/8 and 7/16
6/16 + 7/16 = 13/16
To find two fractions with a sum between 3/4 and 15/16, we can start by finding fractions that are close to the midpoint of these two values.
First, let's find the midpoint between 3/4 and 15/16. To do this, we add the two fractions and divide by 2:
(3/4 + 15/16) / 2 = 27/32
So, we need to find two fractions that add up to 27/32.
To start, we can choose a fraction that is close to but smaller than 27/32. A good choice is 1/2, which simplifies to 16/32.
Now, we need to find the second fraction that, when added to 16/32, gives us 27/32.
Let's call this second fraction x. Therefore:
16/32 + x = 27/32
To solve for x, we can subtract 16/32 from both sides of the equation:
x = 27/32 - 16/32
x = 11/32
So, the two fractions that add up to a sum between 3/4 and 15/16 are 16/32 and 11/32.
To find their actual sum, we add them together:
16/32 + 11/32 = 27/32
The actual sum of these fractions is 27/32.