Question

А)1/2+1/3+1/5. Б)1/2+1/5+3/7. В)1/2+2/3+3/5. Г)2/3+1/4+1/5.

Answer 1

А) $\frac{1}{3}+ \frac{1}{2}+ \frac{1}{5} = \frac{10}{30} + \frac{15}{30}+ \frac{6}{30}= \frac{31}{30}= \frac{1}{30}$

Answer 2

Let's calculate the values for each expression:

A) 1/2 + 1/3 + 1/5

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 2, 3, and 5 is 30.

1/2 can be rewritten as 15/30 (multiplying numerator and denominator by 15). 1/3 can be rewritten as 10/30 (multiplying numerator and denominator by 10). 1/5 remains as 1/5.

Adding these fractions together, we get: 15/30 + 10/30 + 1/5 = (15 + 10)/30 + 1/5 = 25/30 + 1/5

Now, we need to find a common denominator for 25/30 and 1/5. The LCM of 30 and 5 is 30.

25/30 can be simplified to 5/6 (dividing numerator and denominator by 5). 1/5 remains as 1/5.

Adding these simplified fractions together, we get: 5/6 + 1/5 = (5 + 6)/6*5 = 11/30

So, the value of expression A is 11/30.

B) 1/2 + 1/5 + 3/7

Again, we need to find a common denominator. The LCM of 2, 5, and 7 is 70.

1/2 can be rewritten as 35/70 (multiplying numerator and denominator by 35). 1/5 can be rewritten as 14/70 (multiplying numerator and denominator by 14). 3/7 remains as 3/7.

Adding these fractions together, we get: 35/70 + 14/70 + 3/7 = (35 + 14)/70 + 3/7 = 49/70 + 3/7

Now, we have a common denominator of 70.

49/70 remains as 49/70. 3/7 can be simplified to 30/70 (multiplying numerator and denominator by 10).

Adding these fractions together, we get: 49/70 + 30/70 = (49 + 30)/70 = 79/70

However, we can simplify this fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.

79/70 is already in its simplest form.

So, the value of expression B is 79/70.

C) 1/2 + 2/3 + 3/5

Once again, we need to find a common denominator. The LCM of 2, 3, and 5 is 30.

1/2 can be rewritten as 15/30 (multiplying numerator and denominator by 15). 2/3 can be rewritten as 20/30 (multiplying numerator and denominator by 10). 3/5 can be rewritten as 18/30 (multiplying numerator and denominator by 6).

Adding these fractions together, we get: 15/30 + 20/30 + 18/30 = (15 + 20 + 18)/30 = 53/30

So, the value of expression C is 53/30.

D) 2/3 + 1/4 + 1/5

Again, we need to find a common denominator. The LCM of 3, 4, and 5 is 60.

2/3 can be rewritten as 40/60 (multiplying numerator and denominator by 20). 1/4 can be