Just like, letters are the basic unit of any language similarly numbers are the basic unit of mathematics. The origin of the number system was done in the ancient age by our ancestors. In an early age, they used the barter system. They exchange things. But later they might start using their fingers for calculation purposes and that might lead to the origin of the base-ten number system. And now there are many types of number systems. The followings are some most used number systems.

• Natural Number: The number starts from 1 and ends at infinity. Example: 1,2,3….and so on.
• Whole Number: The whole number started from 0 and finished at infinity. A natural number is a subset of the whole number. Example: 0,1,2,3…
• Integers: Integers are the positive and the negative natural number. Example: …-3,-2,-1,0,+1,+2,+3…
• Rational Number: The number which is represented in p/q form, where q is not equal to zero.
• Complex number: Complex number is the combination of real and imaginary numbers.

Equivalent Fraction

Equivalent fractions are the fraction in which the denominator and numerator increase in the same proportion. If again we simply the equivalent fraction in the lowest term then we will get the same fraction as in the initial or vice versa. 

For example, if we have to find out the equivalent fraction of ‘a/b’ then increase or simplify the fraction into the lowest term in the same proportion, i.e. ‘(a×n)/(b×n)’ or ‘(a÷n)/(b÷n)’.

Here n can be any number.

Steps to find the equivalent fractions:

Step 1: Try to find out whether the numerator and denominator have a common factor or not.

Step 2: If the numerator and denominator are divisible by the same number then we can get the equivalent fraction by converting them into the simplest form.

Step 3: If the fraction is already in the lowest form then to get the equivalent fraction to multiply the numerator and denominator by any same number.

Suppose, a/b is in lowest form, equivalent fraction of a/b = (a×n)/(b×n)

Here n can take any value.

Give some examples of equivalent expressions of 10/13

Answer:

We can see that there is no common factor in numerator and denominator. It means the given fraction is already in the lowest form.

So, to get the equivalent fraction multiply by any number in the numerator and denominator. 

The equivalent fraction of 10/13 = (10×2)/(13×2) = 20/26

The next equivalent fraction of 10/13 = (10×3)/(13×3) = 30/39

The next equivalent fraction of 10/13 = (10×4)/(13×4) = 40/52

And similarly we can any number of equivalent fraction of 10/13.

Similar Questions

Question 1: Give some examples of equivalent expressions of 5/7.

Solution: 

We can see that there is no common factor in numerator and denominator. It means the given fraction is already in the lowest form.

So, to get the equivalent fraction multiply by any number in the numerator and denominator.

The equivalent fraction of 5/7 = (5×2)/(7×2) = 10/14

The next equivalent fraction of 5/7 = (5×3)/(7×3) = 15/21

The next equivalent fraction of 5/7 = (5×4)/(7×4) = 20/28

And similarly we can any number of equivalent fraction of 5/7.

Question 2: Give some examples of equivalent expressions of 12/17.

Solution:

We can see that there is no common factor in numerator and denominator. It means the given fraction is already in the lowest form.

So, to get the equivalent fraction multiply by any number in the numerator and denominator.

The equivalent fraction of 12/17 = (12×2)/(17×2) = 24/34

The next equivalent fraction of 12/17 = (12×3)/(17×3) = 36/51

The next equivalent fraction of 12/17 = (12×4)/(17×4) = 48/68

And similarly we can any number of equivalent fraction of 12/17.