Find two mixed numbers so that the sum is 8 4/8 and the difference is 2 2/8

Asked By nmcolem On 11/29/2017 02:22


Let's convert these mixed numbers to improper fractions first, then simplify them. It makes our calculation easier. 2 2/8 will become 9/4, and 8 4/8 will become 34/4. Let's say one of the mixed numbers is A, another one is B. We will have two equations like this: A+B=34/4 and A-B=9/4. We know how to solve an equation with one letter term only, so we will try to eliminate either A or B from these two equations. In this case, adding the equations helps us to eliminate the B terms. We will have 2A=43/4 Solving this equation gives us A=43/8. Substituting 43/8 A in A-B=9/4 gives B=25/8. The question asks you to find two mixed numbers, so we need to convert them to mixed numbers. A=43/8 became 5 3/8, B=25/8 became 3 1/8. The answer is 5 3/8 and 3 1/8. Best. Hande
Answered On 11/29/2017 08:09

First we need to change the mixed numbers into an improper fraction So for the first mixed number we have to multiply the eight on the left times the denominator 8 x 8=64 Then we add the numerator 64 + 4=68 So now the improper fraction is 68/8 Now we do the other mixed number the same way we did this mixed number 2 x 8=16 16 + 2=18 So now the improper fraction is 18/8 Now we have to do system of equations now x + y=68/8 x - y=18/8 The y's cancel out And you add the two x's then you add the two fractions on the right So now we're left with 2x=86/8 Divide 2 by both sides 2x/2=x (86/8)/2=86/16 x=86/16 Put the 86/16=43/8 in lowest terms So x=43/8 Now we have to put x into one of the original system of equations to find y I'ma choose x - y=18\8 43/8 - y=18/8 Now we had to subtract 43/8 by both sides 18/8 - 43/8= -25/8 Now we're here -y= -25/8 We divide -1 by both sides and we get this y=25/8 So x=43/8 And y=25/8 So 43/8 back to a mixed number is 5 3/8 And 25/8 back to a mixed number is 3 1/8 So the two mixed numbers are 5 3/8 and 3 1/8
Answered On 11/29/2017 13:02