How to add matrices that involve improper fractions?
I have this assignment and one of the questions were:
C= [ 7 11] D= [ 1 0 ]
[ -15 3] [ 4 -11/12]
This is what I have so far
C+D= [ 8 11 ]
-11 25/12 So the 25/12, do I keep it that way or do I convert it to a decimal?
No reason to try to use decimals. Fractions are exact.
Your addition is correct.
Thank you :)
To add matrices that involve improper fractions, you need to follow the same rules as adding regular fractions. Here's how to do it:
Step 1: Add the corresponding elements in the matrices. So for C + D, add the elements in the top-left corners, top-right corners, bottom-left corners, and bottom-right corners separately.
C + D = [ 7 + 1 11 + 0 ]
[ -15 + 4 3 + (-11/12) ]
Step 2: Simplify each addition.
Note: To add fractions, you need to make sure they have the same denominator.
For the first element, 7 + 1, it equals 8.
For the second element, 11 + 0, it equals 11.
For the third element, -15 + 4, it equals -11.
For the fourth element, 3 + (-11/12), since the fractions have different denominators, we need to find a common denominator. In this case, the least common denominator is 12. To add fractions with different denominators, we need to convert them to have the same denominator.
To convert 3 to have a denominator of 12, we multiply the numerator and denominator by 12: (3/1)(12/12) = 36/12.
Now we can add the fractions: 36/12 + (-11/12) = (36 - 11)/12 = 25/12.
Step 3: Write the result in improper fraction form.
C + D = [ 8 11 ]
[ -11 25/12 ]
So, in the matrix C + D, you keep the fraction 25/12 as it is since it is in simplest form. However, if needed, you can convert the fraction to a decimal by dividing the numerator by the denominator. In this case, 25 divided by 12 equals 2.0833 (rounded to four decimal places).