Question

(3\4 - 5\6) * 3 + (3\4 + 5\6) * 4

Answer 1

I can answer your question in detail. The expression you have given is:

(3/4 - 5/6) * 3 + (3/4 + 5/6) * 4

To simplify this expression, we need to follow the order of operations, which is:

- Parentheses - Exponents - Multiplication and Division - Addition and Subtraction

First, we need to simplify the expressions inside the parentheses. To do this, we need to find the common denominator of the fractions and then subtract or add the numerators.

The common denominator of 3/4 and 5/6 is 12, since 12 is the least common multiple of 4 and 6. To find the equivalent fractions with denominator 12, we need to multiply 3/4 by 3/3 and 5/6 by 2/2. This gives us:

3/4 = 9/12 5/6 = 10/12

Now, we can subtract 9/12 from 10/12 and add 9/12 to 10/12. This gives us:

(3/4 - 5/6) = (9/12 - 10/12) = -1/12 (3/4 + 5/6) = (9/12 + 10/12) = 19/12

Next, we need to multiply the expressions in the parentheses by 3 and 4, respectively. To do this, we need to multiply the numerators by 3 and 4 and keep the denominators the same. This gives us:

(3/4 - 5/6) * 3 = (-1/12) * 3 = -3/12 (3/4 + 5/6) * 4 = (19/12) * 4 = 76/12

Then, we need to add the two expressions. To do this, we need to find the common denominator of the fractions and then add the numerators. The common denominator of -3/12 and 76/12 is 12, since 12 is already the least common multiple of 12 and 12. To find the equivalent fractions with denominator 12, we do not need to do anything, since they already have the same denominator. This gives us:

(-3/12) + (76/12) = (-3 + 76) / 12 = 73/12

Finally, we need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor. The greatest common divisor of 73 and 12 is 1, since 1 is the only positive integer that divides both 73 and 12 evenly. Therefore, we do not need to simplify the fraction any further, since it is already in its lowest terms. This gives us:

73/12

Therefore, the answer is:

(3/4 - 5/6) * 3 + (3/4 + 5/6) * 4 = 73/12

I hope this helps you understand how to simplify fractions. If you want to learn more about fractions, you can check out these websites:

- [Fraction calculator - calculation: 3/4 x 5/6](https://www.hackmath.net/en/calculator/fraction?input=3%2F4+x+5%2F6) - [Subtract 3/4 from 5/6](https://answers.everydaycalculation.com/subtract-fractions/5-6-minus-3-4) - [Solve 1+2+3+4+5+6+7+8+9](https://mathsolver.microsoft.com/en/solve-problem/1%2B2%2B3%2B4%2B5%2B6%2B7%2B8%2B9)