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If the product of any two rational numbers is 2 and one of them is 1/7, find the other?

  • Last Updated : 17 Aug, 2021

In our daily lives, we use numbers. They are frequently referred to as numerals. We can’t count objects, date, time, money, or anything else without numbers. These numerals are sometimes used for measurement and other times for labeling. Numbers have features that allow them to conduct arithmetic operations on them. These figures are expressed both numerically and in words. For example, 3 is written as three, 33 is written as thirty-three, and so on. To learn further, students might practice writing the numbers from 1 to 100 in words.

There are various types of numbers that we learn in Math. Natural and whole numbers, odd and even numbers, rational and irrational numbers, and so on are all examples. In this article, we’ll go through all of the different varieties. Aside from that, the numbers are utilized in a variety of applications, including number series, arithmetic tables, and so on.

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  • A number is an arithmetic value that is used to represent and calculate a quantity. Numbers are represented by numerals, which are written symbols such as “2.”
  • A number system is a meth  od of writing numbers that uses logical digits or symbols to represent them.

Types of Numbers

The number system is a system for categorizing numbers into sets. In math, there are several different types of numbers:

  1. Natural Numbers: Natural numbers are positive integers from 1 to infinity that contain the positive integers 1 to infinity. The set of natural numbers is indicated by the letter “N,” and it consists of N = 1, 2, 3, 4, 5,…………
  2. Whole Numbers: Non-negative integers, often known as whole numbers, are non-negative integers that do not contain any fractional or decimal parts. It is symbolized by the letter “W,” and the set of whole numbers contains W = 0, 1, 2, 3, 4, 5,…………
  3. Integers: Integers are the set of all whole numbers, but they also include a set of negative natural numbers. Integers are represented by the letter “Z,” and the set of integers is Z = -3, -2, -1, 0, 1, 2, 3.
  4. Real Numbers: Real numbers are all positive and negative integers, fractional and decimal numbers that do not contain imaginary values. The letter “R” is used to signify it.
  5. Rational Numbers: Rational numbers are any numbers that may be expressed as a ratio of one number to another number. Any number that may be written in the form of p/q qualifies. The rational number is represented by the symbol “Q.”
  6. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a ratio of one to another and are denoted by the letter P.
  7. Complex Numbers: Complex numbers (C) are numbers that may be expressed in the form a+bi, where “a” and “b” are real numbers and I is an imaginary number.

Even after coining integers, one could not relax! 10 ÷ 5 is no doubt fine, giving the answer 2 but is 8 ÷ 5 comfortable? Numbers between numbers are needed. 8 ÷ 5 seen as 1.6, is a number between 1 and 2. But, where does (-3) ÷ 4 lie? Between 0 and -1. Thus, a ratio made by dividing an integer by another integer is called a rational number. The collection of all rational numbers is denoted by Q.

  A Rational number is a number of the fractional form a/b, where a and b are integers and b ≠ 0.

  Examples: 1/4, 3/7 , (-11)/(-6)

  • All-natural numbers, whole numbers, integers, and fractions are rational numbers.
  • Every rational number can be represented on a number line.
  • 0 is neither a positive nor a negative rational number.

If the product of any two rational numbers is 2 and one of them is 1/7, find the other?

Solution: 

Let the two rational numbers are x and y.

According to the statement given,

One number is 1/7 i.e. y = 1/7



Also, Product of both numbers is 2 i.e.
x * y = 2 
Put the value of y in the equation
x * (1/7) = 2
x/7 = 2
x = 2*7 
x = 14

It can be written as 14/1 or 196/14…. in the form of rational number.

Similar Questions

Question 1: If the product of any two rational numbers is 1/2 and one of them is 1/7, find the other?

Solution:

 Let the two rational numbers are x and y.

According to the statement given,
One number is 1/7 i.e. y = 1/7

Also, Product of both numbers is 2 i.e.
x * y = 1/ 2 
Put the value of y in the equation
x * (1/7) = 1/2
x/7 = 1/2
x = (1*7) / 2
 x = 7/2
So, 7/2 is the other rational number.

Question 2:  If the product of any two rational numbers is 7/2 and one of them is 1/14, find the other?

Solution:

 Let the two rational numbers are x and y.

According to the statement given,
One number is 1/14 i.e. y = 1/14

Also, Product of both numbers is 2 i.e. 
x * y = 7/2 
Put the value of y in the equation
x * (1/14) = 7/2
x/14 = 7/2
x = (14*7) / 2 
x = (98)/2
x = 49
It can be written as 49/1 or 98/2… in the form of rational number.

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