Five Rational Numbers Between -3/5 and -1/2

To find five rational numbers between -3/5 and -1/2, we can use the mean method. The mean method involves taking the average of two given rational numbers to find a rational number between them. We will follow a step-by-step process to find these numbers.

Step 1: Find the difference between the two given numbers.
The difference between -3/5 and -1/2 can be calculated as follows:
-1/2 - (-3/5) = -1/2 + 3/5 = -5/10 + 6/10 = 1/10

Step 2: Divide the difference by 6 to find the interval between each rational number.
Dividing 1/10 by 6 gives us:
1/10 ÷ 6 = 1/10 × 1/6 = 1/60

Step 3: Find the mean of the two given numbers.
To find the mean, we add the two given numbers and divide by 2:
(-3/5 + -1/2) ÷ 2 = (-6/10 + -5/10) ÷ 2 = -11/20 ÷ 2 = -11/40

Step 4: Add the interval to the mean to find the first rational number between the two given numbers.
Adding 1/60 to -11/40 gives us:
-11/40 + 1/60 = -33/120 + 2/120 = -31/120

Step 5: Continue adding the interval to the previous result to find the remaining rational numbers.
Adding 1/60 to -31/120 gives us:
-31/120 + 1/60 = -31/120 + 2/120 = -29/120

Adding 1/60 to -29/120 gives us:
-29/120 + 1/60 = -29/120 + 2/120 = -27/120

Adding 1/60 to -27/120 gives us:
-27/120 + 1/60 = -27/120 + 2/120 = -25/120

Adding 1/60 to -25/120 gives us:
-25/120 + 1/60 = -25/120 + 2/120 = -23/120

Therefore, the five rational numbers between -3/5 and -1/2 are:
-31/120, -29/120, -27/120, -25/120, -23/120.

Explanation of the Mean Method:

The mean method is a technique used to find rational numbers between two given rational numbers. It involves finding the mean of the two given numbers and then repeatedly adding the interval (the difference divided by a chosen number) to the mean to obtain the desired number of rational numbers.

By following this method, we ensure that the resulting numbers are rational because we are only performing addition, subtraction, multiplication, and division on rational numbers. This method allows us to find an infinite number of rational numbers between any two given rational numbers.

The mean method is a straightforward and systematic approach to finding rational numbers between two given rational numbers, providing

By mean method
- 3 / 5 and -1/2
take LCM of 5 and 2
- 6 - (-10) /10
-4/10
so 2 rational numbers between -3/5 and -1 /2 a r e
-4/10 - 3 by 10 - 2 by 10 - 1 / 10 - 0 by 10
write any two from these .