What is the simplified form of the following expression?
7m^2 + 6.5n - 4n + 2.5m^2 - n
a. 9.5m^2 + 1.5n (?)
b. 4.5m^2 + 1.5n
c. 1.5m^2 - 4.2n
d. 9.5m^2 - 1.5n
Simplify the following expression.
1/3(21m + 27)
a. 7m + 27
b. 7m + 9 (?)
c. 63m + 9
d. 7m + 81
What is the sum?
7/4 + (-1/5)
a. 31/20 (?)
b. 39/20
c. 6/9
d. -7/20
Yup, they are all correct. :)
Why did the math book go to the therapy session? Because it had too many unresolved issues!
For the first question, let's simplify the expression 7m^2 + 6.5n - 4n + 2.5m^2 - n.
Combining like terms, we get 9.5m^2 + 1.5n. So the simplified form is option a. 9.5m^2 + 1.5n.
Now, let's tackle the second question. We have to simplify 1/3(21m + 27).
Multiplying 1/3 with each term inside the parentheses, we get (21/3)m + (27/3).
Simplifying further, we get 7m + 9. So the simplified form is option b. 7m + 9.
Lastly, let's add the fractions 7/4 + (-1/5).
To add these fractions, we need a common denominator. The lowest common denominator of 4 and 5 is 20.
Converting both fractions to have a denominator of 20, we get 35/20 + (-4/20).
Adding the numerators, we get 31/20. So the sum is option a. 31/20.
I hope my clownish explanations and answers brought a smile to your face!
To simplify the expression 7m^2 + 6.5n - 4n + 2.5m^2 - n:
1. Combine like terms.
7m^2 + 2.5m^2 + 6.5n - 4n - n
= (7m^2 + 2.5m^2) + (6.5n - 4n - n)
= 9.5m^2 + 1.5n
Therefore, the simplified form of the expression is a. 9.5m^2 + 1.5n.
To simplify the expression 1/3(21m + 27):
1. Distribute the 1/3 to each term inside the parentheses.
1/3 * 21m + 1/3 * 27
= 7m + 9
Therefore, the simplified form of the expression is b. 7m + 9.
To find the sum of 7/4 + (-1/5):
1. Convert the fractions to have a common denominator.
7/4 = 35/20
-1/5 = -4/20
2. Add the fractions together.
35/20 + (-4/20)
= 31/20
Therefore, the sum is a. 31/20.
To simplify the expression
7m^2 + 6.5n - 4n + 2.5m^2 - n,
we can combine like terms. Like terms have the same variable raised to the same power, so we group them together.
Grouping the m^2 terms, we have 7m^2 + 2.5m^2 = 9.5m^2.
Grouping the n terms, we have 6.5n - 4n - n = 1.5n.
Putting it all together, we have 9.5m^2 + 1.5n.
So the answer is (a) 9.5m^2 + 1.5n.
To simplify the expression
1/3(21m + 27),
we distribute the 1/3 to both terms inside the parentheses.
1/3 * 21m = 7m
1/3 * 27 = 9
Putting it all together, we have 7m + 9.
So the answer is (b) 7m + 9.
To find the sum of
7/4 + (-1/5),
we need to have a common denominator. The least common multiple of 4 and 5 is 20.
Multiplying the numerator and denominator of 7/4 by 5, we get 35/20.
Multiplying the numerator and denominator of -1/5 by 4, we get -4/20.
Now we can add the fractions:
35/20 + (-4/20) = 31/20.
So the answer is (a) 31/20.