Question

А) (6-7 1\8) * (2\9 + 2\3) б) 8 1\7 - 4 1\7 : 3 5\8

Answer 1

а) 1. 6-7 1/8= -1 1/8

2. 2/9+2/3= 8/9

3. -1 1/8*8/9= -9/8*8/9= -1

б) 1. 4 1/7:3 5/8=29/7*8/29=8/7

2. 8 1/7-8/7=7 8/7-8/7=7

Answer 2

To solve the given expressions, let's simplify the calculations step by step.

a) (6 - 7 1/8) * (2/9 + 2/3):

First, let's convert the mixed numbers into improper fractions: 6 - 7 1/8 = 6 - (7 + 1/8) = 6 - 57/8 = 6 * 8/8 - 57/8 = 48/8 - 57/8 = -9/8

Similarly, 2/9 + 2/3 = (2 * 3)/(9 * 3) + (2 * 9)/(3 * 9) = 6/27 + 18/27 = (6 + 18)/27 = 24/27

Now we can multiply the two fractions: (-9/8) * (24/27) = (-9 * 24)/(8 * 27) = -216/216 = -1

Therefore, the value of (6 - 7 1/8) * (2/9 + 2/3) is -1.

b) 8 1/7 - 4 1/7 : 3 5/8:

Again, let's convert the mixed numbers into improper fractions: 8 1/7 = 8 + 1/7 = 8 * 7/7 + 1/7 = 56/7 + 1/7 = 57/7

4 1/7 = 4 + 1/7 = 4 * 7/7 + 1/7 = 28/7 + 1/7 = 29/7

3 5/8 = 3 + 5/8 = 3 * 8/8 + 5/8 = 24/8 + 5/8 = 29/8

Now we can perform the division operation: 29/7 : 29/8 = (29/7) * (8/29) = (29 * 8)/(7 * 29) = 232/203

Finally, we subtract: 57/7 - 232/203 = (57 * 203 - 232 * 7)/(7 * 203) = (11571 - 1624)/(1421) = 995/1421

Therefore, the value of 8 1/7 - 4 1/7 : 3 5/8 is 995/1421.