how do i solve this 1/6 +4(2/5-7/10)=
I need all the answers
To solve the expression 1/6 + 4(2/5 - 7/10), we can follow the order of operations (also known as PEMDAS or BODMAS). This acronym stands for parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Step 1: Simplify within parentheses
Inside the parentheses, we have 2/5 - 7/10. To subtract these fractions, we need to have a common denominator. In this case, the least common multiple of 5 and 10 is 10. So, let's convert the fractions to have the denominator of 10.
2/5 = (2/5) * (2/2) = 4/10
7/10 = 7/10
Now, the expression becomes: 1/6 + 4(4/10 - 7/10).
Step 2: Simplify multiplication
Next, we have to multiply 4 by (4/10 - 7/10).
4 * (4/10 - 7/10) = 4 * (-3/10) = -12/10 = -6/5
Now, the expression becomes: 1/6 + (-6/5).
Step 3: Find the common denominator
To add or subtract fractions, they need to have the same denominator. The least common multiple of 6 and 5 is 30. So, let's convert the fractions to have the denominator of 30.
1/6 = (1/6) * (5/5) = 5/30
-6/5 = -6/5 * (6/6) = -36/30
Now, the expression becomes: 5/30 - 36/30.
Step 4: Simplify addition/subtraction
Since the fractions have the same denominator, we can directly add/subtract their numerators.
5/30 - 36/30 = (5 - 36)/30 = -31/30
So, the solution to the expression 1/6 + 4(2/5 - 7/10) is -31/30.
distribute the 4.
1/6 + 8/5 - 28/10
then find Least Common Denominator.
which would be 30.
(5/5)(1/6) + (6/6)(8/5) - (3/3)(28/10)
5/30 + 48/30 - 84/30
solve