I am trying to help my son with his homework but I have no Idea on how to solve the problem. If you can please explain step by step how to solve it. (Simplify (4 1/8 + 6 1/4) - 2 1/2 I am lost when it tells me to rename if possible.
(4 1/8 + 6 1/4) - 2 1/2
First find the common denominator of the fractions. In this problem the common denominator is 8.
1/4 = 2/8
1/2 = 4/8
(4 1/8 + 6 2/8) - 2 4/8
10 3/8 - 2 4/8
9 11/8 - 2 4/8 = 7 7/8
Thank you Ms Sue. But how did you get 9 11/8 I'm stuck on that last step
Since we can't take a larger number from a smaller one, we have to borrow from the whole number.
1 = 8/8
10 3/8 = 9 11/8
I would do it this way:
(4 1/8 + 6 1/4) - 2 1/2
first of all, there is no need for the brackets in this case
secondly, I change all my mixed fractions to workable fractions
= 33/8 + 25/4 - 5/2
LCD is 8
= 33/8 + 50/8 - 20/8
= 63/8 or 7 7/8
mixed numbers are "nice" to look at, but totally useless when it comes to doing any real arithmetic with them, especially when it comes to multiplication or division.
To simplify the expression (4 1/8 + 6 1/4) - 2 1/2, you need to add the mixed numbers and whole numbers separately, and then perform the subtraction. Here are the step-by-step instructions:
Step 1: Rewrite the mixed numbers as improper fractions.
To rewrite a mixed number as an improper fraction, multiply the whole number by the denominator, then add the numerator. Place the sum over the denominator.
4 1/8 = (4 * 8 + 1) / 8 = 33/8
6 1/4 = (6 * 4 + 1) / 4 = 25/4
Step 2: Add the improper fractions and whole numbers separately.
To add fractions, the denominators need to be the same, so find a common denominator.
The denominators in this case are 8 and 4. The least common multiple of 8 and 4 is 8, so we can use 8 as the common denominator.
33/8 + 25/4 = (33/8) * (2/2) + 25/4
= (66/16) + 25/4
= 66/16 + (25 * 4) / (4 * 4)
= 66/16 + 100/16
= (66 + 100)/16
= 166/16
Step 3: Simplify the fraction.
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.
The GCD of 166 and 16 is 2.
166/16 = (166/2) / (16/2)
= 83/8
Step 4: Rename the answer if possible.
Now, we need to rename the answer as a mixed number if possible.
83/8 = 10 3/8
So, the simplified expression is 10 3/8.
In summary:
(4 1/8 + 6 1/4) - 2 1/2 = 10 3/8