Question

4/5*(6/7-5/4)+6/5*(5/6-4/7)

Answer 1

4/5*(6/7-5/4)+6/5*(5/6-4/7)= 0
1)6\7-5\4=-11\28
2)4\5*(-11\28)=-11\35
3)5\6-4\7=11\42
4)6\5*11\42=11\35
5)-11\35+11\35=0

Answer 2

To evaluate the expression, let's simplify it step by step:

Step 1: Evaluate the expressions within parentheses. Inside the first parentheses: 6/7 - 5/4 = (24/28) - (35/28) = (24 - 35)/28 = -11/28

Inside the second parentheses: 5/6 - 4/7 = (35/42) - (24/28) = (35/42) - (30/42) = 5/42

Now the expression becomes: 4/5 * (-11/28) + 6/5 * (5/42)

Step 2: Simplify the fractions: (-11/28) can be simplified no further. (5/42) can be simplified no further.

The expression becomes: 4/5 * (-11/28) + 6/5 * (5/42)

Step 3: Multiply the fractions: 4/5 * (-11/28) = (-44/140) 6/5 * (5/42) = (30/42)

The expression becomes: (-44/140) + (30/42)

Step 4: Find a common denominator and add the fractions: To add fractions, we need a common denominator. The least common multiple (LCM) of 140 and 42 is 420. So we'll convert the fractions to have a denominator of 420.

(-44/140) = (-44/140) * (3/3) = (-132/420) (30/42) = (30/42) * (10/10) = (300/420)

Now the expression becomes: (-132/420) + (300/420)

Step 5: Add the fractions: (-132/420) + (300/420) = (-132 + 300)/420 = 168/420

Step 6: Simplify the fraction: 168/420 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 84. 168/420 = (168/84) / (420/84) = 2/5

Therefore, the simplified value of the expression 4/5 * (6/7 - 5/4) + 6/5 * (5/6 - 4/7) is 2/5.