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What fraction lies exactly halfway between 2/3 and 3/4?

  • Last Updated : 17 Aug, 2021

In early age, people had a different mindset to compare things. They can’t count like today, because they didn’t know the number system. They used to represent things by symbols. In the later ages, they used small numbers for counting. They might be used to count the things on their fingers and that leads to the developed base 10 number system because they can count up to 10 on their fingers. Arab spread the method of representing numerals and it took hundreds of years to represent the number system. Presently there are different types of number systems.

  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers
  • Real Numbers
  • Complex Numbers

What is Halfway of Two Fractions?

Fraction that lies exactly halfway between 2/3 and 3/4 will not be smaller than 2/3 and not greater than 3/4. Halfway is nothing but the mean of two fractions. The mean of numbers is that number that exactly lies at an equal distance from the lowest and highest number on the number line.

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Formula for finding Halfway of two Fractions

Let us generalize a formula for the calculation of exactly halfway of two fractions.

Step 1: Suppose, there are two fractions ‘a/b’ and ‘c/d’. Here ‘a’ and ‘b’ can not be equal to zero.

Step 2: Add these two fractions by converting them into like a fraction. (Like fraction are those fraction whose denominator is same)

Step 3: For converting two fractions into like fractions, multiply by the denominator of 2nd fraction to the numerator and denominator of the first fraction and by the denominator of the first fraction to the numerator and denominator of the second fraction.

First Fraction: (a×d)/(b×d)  

Second Fraction: (c×b)/(d×b)

Since the denominator of these two fraction is same so we will call it like fraction.

Step 4: Add these two fractions.



= (ad/bd) + (cb/bd)  

=(ad + cb)/(bd)

Step 5: Now divide the summation of these two fractions by 2.

Halfway of two fractions = (ad+cb)/(2bd)

What fraction lies exactly halfway between 2/3 and 3/4?

Solution:  

By comparing the fractions 2/3 and 3/4 with a/b and c/d respectively.

we got, a = 2, b = 3, c = 3 and d = 4

Put these values in the formula,  

Halfway of two fractions = (ad + cb)/(2bd)

                                       = (2 × 4 + 3 × 3)/(2 × 3 × 4)

                                       = (8 + 9)/24

                                       = 17/24

The fraction lies exactly between 2/3 and 3/4 is 17/24.

Similar Questions

Question 1: Find the mean of fractions 6/7 and 8/9.

Solution:

On comparing the fraction 6/7 and 8/9  with a/b and c/d respectively,  

a = 6, b = 7, c = 8 and d = 9

Put these values in the formula,

Mean or halfway of two fraction = (ad + cb)/(2bd)

Mean = (6 × 9 + 7 × 8)/(2 × 7 × 9)



Mean = (54 + 56)/126

Mean = 110/126

Mean = 55/63

The mean of 6/7 and 8/9 is 55/63.

Question 2: Find a fraction that lies in between 5/6 and 8/9.

Solution:

By using the formula of halfway of two fractions we can find out at least one fraction which will always lie in between 5/6 and 8/9.

On comparing 5/6 and 8/9 with a/b and c/d respectively.

a = 5, b = 6, c = 8 and d = 9

Halfway of two fraction = (ad + cb)/(2bd)

                 = (5 × 9 + 6 × 8)/(2 × 6 × 9)

                 = (45 + 48)/108

                 = 93/108

                 = 31/36

So, 31/36 will always lie in between 5/6 and 8/9.

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