Question

8/9*3/4-(5/6-1/4), 3/5+4/5*3/7+6/7, (2/5-2/7):2/7*2/5, (5/6-3/10):(3/10+2/15)

Answer 1

А) 8/9*3/4-(5/6-1/4)=1/12
1) 5/6-1/4=10/12-3/12=7/12
2) 8/9*3/4=2/3
3) 2/3-7/12=8/12-7/12=1/12
б) 3/5+4/5*3/7+6/7=1 4/5
1) 4/5*3/7=12/35
2) 3/5+12/35=21/35+12/35=33/35
3) 33/35+6/7=33/35+30/35=1 4/5
в) (2/5-2/7):2/7*2/5=4/25
1) 2/5-2/7=14/35-10/35=4/35
2) 4/35:2/7=2/5
3) 2/5*2/5=4/25
г) (5/6-3/10):(3/10+2/15)=1 3/13
1) 5/6-3/10=25/30-9/30=16/30=8/15
2) 3/10+2/15=9/30+4/30=13/30
3) 8/15:13/30=16/13=1 3/13

Answer 2

To solve the given expression in detail:

Step 1: Evaluate the expression within parentheses first.

8/9 * 3/4 - (5/6 - 1/4) + 3/5 + 4/5 * 3/7 + 6/7 + (2/5 - 2/7):2/7 * 2/5 + (5/6 - 3/10) : (3/10 + 2/15)

The expression within the first set of parentheses is (5/6 - 1/4).

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 6 and 4 is 12.

So, (5/6 - 1/4) = (10/12 - 3/12) = 7/12

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + (2/5 - 2/7):2/7 * 2/5 + (5/6 - 3/10) : (3/10 + 2/15)

Step 2: Evaluate the expression within the second set of parentheses next.

The expression within the second set of parentheses is (2/5 - 2/7).

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 5 and 7 is 35.

So, (2/5 - 2/7) = (14/35 - 10/35) = 4/35

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + 4/35 : 2/7 * 2/5 + (5/6 - 3/10) : (3/10 + 2/15)

Step 3: Evaluate the expression within the third set of parentheses next.

The expression within the third set of parentheses is (5/6 - 3/10).

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 6 and 10 is 30.

So, (5/6 - 3/10) = (25/30 - 9/30) = 16/30 = 8/15

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + 4/35 : 2/7 * 2/5 + 8/15 : (3/10 + 2/15)

Step 4: Evaluate the expression within the fourth set of parentheses next.

The expression within the fourth set of parentheses is (3/10 + 2/15).

To add fractions, we need a common denominator. The least common multiple (LCM) of 10 and 15 is 30.

So, (3/10 + 2/15) = (9/30 + 4/30) = 13/30

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + 4/35 : 2/7 * 2/5 + 8/15 : 13/30

Step 5: Evaluate the division (:) operations from left to right.

First, let's evaluate 4/35 : 2/7 * 2/5.

To divide fractions, we invert the second fraction and multiply.

So, 4/35 : 2/7 * 2/5 = 4/35 * 7/2 * 2/5 = 4/35 * 7/5 = (4 * 7)/(35 * 5) = 28/175 = 4/25

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + 4/25 + 8/15 : 13/30

Next, let's evaluate 8/15 : 13/30.

To divide fractions, we invert the second fraction and multiply.

So, 8/15 : 13/30 = 8/15 * 30/13 = (8 * 30)/(15 * 13) = 240/195 = 48/39 = 16/13

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 4/5 * 3/7 + 6/7 + 4/25 + 16/13

Step 6: Continue evaluating the expression from left to right.

Next, let's evaluate 4/5 * 3/7.

To multiply fractions, we multiply the numerators and denominators.

So, 4/5 * 3/7 = (4 * 3)/(5 * 7) = 12/35

The expression now becomes:

8/9 * 3/4 - 7/12 + 3/5 + 12/35 + 6/7 + 4/25 + 16/13

Step 7: Continue evaluating the expression from left to right.

Next, let's evaluate the addition and subtraction operations from left to right.

8/9 * 3/4 = 2/3

7/12

3/5

12/35

6/7

4/25

16/13

Step 8: Finally, add all the fractions together.

2/3 - 7/12 + 3/5 + 12/35 + 6/7 + 4/25 + 16/13

To add fractions, we need a common denominator. The least common multiple (LCM) of 3, 12, 5, 35, 7, 25, and 13 is 27300.

So, the expression becomes:

(2 * 27300)/(3 * 27300) - (7 * 2275)/(12 * 2275) + (3 * 5460)/(5 * 5460) + (12 * 780)/(35 * 780) + (6 * 3900)/(7 * 3900) + (4 * 1092)/(25 * 1092) + (16 * 2100)/(13 * 2100)

= 54600/81900 - 15925/27300 + 16380/27300 + 9360/27300 + 23400/27300 + 4368/27300 + 33600/27300

Now, simplify each fraction:

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/2730 + 520/1519 + 780/910 + 182/1139 + 336/273

= 1820/2730 - 15925/27300 + 1638/