please help me to figure out in algebra 2/3-4/5-(-11/15) +7/10-5/2 the answer is 6/5 and I do not know how to work this out
2 / 3 - 4 / 5 - ( - 11 / 15 ) + 7 / 10 - 5 / 2 =
2 / 3 - 4 / 5 + 11 / 15 + 7 / 10 - 5 / 2
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Least Common factor = 30
2 / 3 = 20 / 30
4 / 5 = 4 * 6 / ( 5 * 6 ) = 24 / 30
11 / 15 = 2 * 11 / ( 2 * 15 ) = 22 / 30
7 / 10 = 3 * 7 / ( 3 * 10 ) = 21 / 30
5 / 2 = 15 * 5 / ( 15 * 2 ) = 75 / 30
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2 / 3 - 4 / 5 + 11 / 15 + 7 / 10 - 5 / 2 =
20 / 30 - 24 / 30 + 22 / 30 + 21 / 30 - 75 / 30 =
- 36 / 30 = - 6 * 6 / ( 6 * 5 ) = - 6 / 5
To simplify the expression 2/3 - 4/5 - (-11/15) + 7/10 - 5/2, you'll need to find a common denominator and combine the fractions.
Here are the steps to solve it:
Step 1: Find a common denominator
The denominators of the given fractions are 3, 5, 15, 10, and 2. To find the least common denominator (LCD), you can find the least common multiple (LCM) of these denominators, which is 30.
Step 2: Rewrite the fractions with the common denominator
For our example, we'll rewrite all the fractions with a denominator of 30:
2/3 = (2/3) * (10/10) = 20/30
4/5 = (4/5) * (6/6) = 24/30
-(-11/15) = 11/15 (double negatives become a positive)
7/10 = (7/10) * (3/3) = 21/30
5/2 = (5/2) * (15/15) = 75/30
So, our simplified expression becomes: 20/30 - 24/30 + 11/15 + 21/30 - 75/30.
Step 3: Add or subtract the fractions
To add or subtract the fractions, simply keep the denominator the same and perform the operation on the numerators:
20/30 - 24/30 + 11/15 + 21/30 - 75/30 = (20 - 24 + 11 + 21 - 75)/30
= (20 - 24 + 11 + 21 - 75)/30
= (-47)/30
Step 4: Simplify the fraction
The fraction -47/30 is already in its simplest form, but if we express it as a mixed number, it becomes -1 17/30.
Therefore, the answer to the expression 2/3 - 4/5 - (-11/15) + 7/10 - 5/2 is -1 17/30 or -47/30.
Note: The given answer of 6/5 does not seem to be correct based on the working of the expression you provided. Please double-check the question or verify the given answer again.