simplify-
3+2+7=7+2+3
4(2+1)=4(2)+4(1)
(2+3)+6=2+(3+6)
Huh? Simplify...
3+2+7=12
4(2+1)=12
(2+3)+6=11
To simplify mathematical expressions, you need to follow the order of operations, which states that you should perform operations in the following order: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Let's simplify the first expression:
3 + 2 + 7 = 7 + 2 + 3
This is an addition problem, and according to the commutative property of addition, you can change the order of the numbers being added without changing the result. So, we can rewrite the expression as:
3 + 2 + 7 = 3 + 7 + 2
Now, we can simply add the numbers:
3 + 2 + 7 = 12
Therefore, the simplified expression is 12.
Now, let's simplify the second expression:
4(2 + 1) = 4(2) + 4(1)
Here, we have multiplication and addition within parentheses. According to the distributive property of multiplication over addition, we can multiply each term inside the parentheses separately.
First, we simplify the expression inside the parentheses:
2 + 1 = 3
Now, we can substitute this simplified expression back into the original equation:
4(2 + 1) = 4(2) + 4(1)
Which becomes:
4(3) = 4(2) + 4(1)
Now, we can multiply:
4(3) = 12
4(2) = 8
4(1) = 4
Finally, we can add the results:
4(3) = 12
4(2) = 8
4(1) = 4
12 = 8 + 4
Therefore, the simplified expression is:
12 = 12
Lastly, let's simplify the third expression:
(2 + 3) + 6 = 2 + (3 + 6)
Here, we have addition within parentheses. According to the associative property of addition, we can change the grouping of numbers being added without changing the result. So, we can rewrite the expression as:
5 + 6 = 2 + 9
Now, we can simply add the numbers:
5 + 6 = 11
Therefore, the simplified expression is 11.