Question

Find rational numbers exactly halfway between 1/6 and 1/9

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given,

The two rational numbers = 1/6 and 1/9.

To find,

The rational number exactly halfway between 1/6 and 1/9.

Solution,

The rational number exactly halfway between 1/6 and 1/9 will be 5/36.

We can easily solve this problem by following the given steps.

To find the rational numbers between two rational numbers, we will have to make their denominators the same.

So, we need to find the LCM of 6 and 9.

The prime factors of 6 are 2×3.

The prime factors of 9 are 3×3.

So, the LCM of 6 and 9 is 18.

To make the denominator of 1/6 18, we will multiply the numerator and denominator by 3.

1×3/6×3 = 3/18

To make the denominator of 1/9 18, we will multiply the numerator and denominator by 2.

1×2/9×2 = 2/18

Now, we still can not find the rational numbers between 2/18 and 3/18. So, we need to increase these rational numbers. We can multiply both the fractions by 10.

2×10/18×10 = 20/180

3×10/18×10 = 30/180

The exactly half of 20 and 30 is 25 (20+30/2).

So, the rational number exactly halfway between 20/180 and 30/180 is 25/180.

We can convert it into the simplest form by dividing the numerator and denominator by 5.

25÷5/180÷5 = 5/36

Hence, the rational number exactly halfway between 1/6 and 1/9 is 5/36.