Positive rational numbers space the numbers for which both the numerator and the denominator space either positive integers or an adverse integers. In other words, a reasonable number is positive if both numerator and also denominator have the very same sign. In this lesson, let's learn about positive rational number in detail.

You are watching: The reciprocal of a positive rational number is

1.What are positive Rational Numbers?
2.Positive Rational numbers Symbols
3.Positive rational Numbers much less Than 1
4.Reciprocal of a hopeful Rational Number
5.FAQs on positive Rational Numbers

What are hopeful Rational Numbers?


Positive rational numbers refer to rational numbers once their numerators and denominators space both confident or both negative. Instances of hopeful rational numbers are 3/8, 9/10, -34/-40, etc. On the other hand, over there are negative rational number that have opposite signs in numerator and denominator, such together -4/15, 5/-6, -17/19, etc.

*

Positive reasonable Number vs an adverse Rational Number

Given listed below are the clues of differences in between a positive and also a negative rational number,

Positive rational NumberNegative rational Number
Both numerator and also denominator have the same signs.Both numerator and denominator have actually opposite signs.
Examples - 3/4, 6/7, 8/11, etcExamples - -3/4, -6/7, -8/11, etc
Numbers greater than 0.Numbers much less than 0.
Represented come the best of 0 ~ above the number line.Represented come the left of 0 on the number line.

Positive Rational numbers Symbol


We recognize that the collection of rational number is denoted by the prize Q. Rational numbers are classified as positive, zero, or an unfavorable rational numbers. Optimistic rational numbers are defined as having the same signs for the numerator and denominator, either both are confident or both are negative.


Positive rational Numbers much less Than 1


The positive rational numbers much less than 1 space as follows: 1/9​=0.11, 1/8​=0.12, 1/7​=0.14, 1/6​=0.16, 1/5​=0.2, 1/4​=0.25, 1/3=0.33, 1/2​=0.5, 2/7​=0.28, 2/5​=0.4, 2/3​=0.66, 3/7=0.42, 3/5​=0.6, 3/4​=0.75, 4/5=0.8, etc.

The over 15 optimistic rational numbers are the numbers that have actually values much less than 1 and also also, the sum of the numerator and also denominator does not exceed 10.


Reciprocal the a optimistic Rational Number


The reciprocal of a optimistic rational number is positive only. Follow to the reciprocal definition, the mutual of a number describes the expression which once multiplied through the number gives the product as 1. In other words, when the product of two numbers is 1, lock are said to be reciprocals of each other. The mutual of a optimistic rational number is for this reason positive only.

Related Articles

Check out a couple of more interesting write-ups related to positive rational numbers.


Positive Rational numbers Examples


Example 1: identify if 7 is a positive rational number.

Solution:

7 have the right to be expressed in the type of a ratio, such that, 7 = 7/1, where both numerator and also denominator, i.e. 7 and 1 are confident integers.

Therefore, 7 is a optimistic rational number.


Example 2: Is -31/-51 a hopeful or an unfavorable rational number?

Solution:

Both numerator and denominator have an adverse signs. Thus, we have the right to multiply and divide both top and also bottom of rational number by -1, to get (-31/-51) x (-1/-1) = 31/51.

Therefore, -3/-5 is a hopeful rational number.


View price >

go come slidego to slide



Breakdown tough ideas through an easy visuals.
Math will certainly no much longer be a hard subject, specifically when you understand the concepts through visualizations.

Book a free Trial Class


Practice inquiries on optimistic Rational Numbers


Check answer >

go to slidego come slide


FAQs on confident Rational Numbers


Which number Are hopeful Rational Numbers?

A reasonable number is positive if that numerator and denominator have actually the very same signs(either both are hopeful or both room negative). 1/4, 2/9, -7/-11, -3/-13, 5/12 are optimistic rationals, vice versa, 2/-5, -3/10, -4/7, 11/-23 are not hopeful rational numbers..

What Is True around Adding 2 Rational numbers That room Positive?

The amount of two rational numbers is a rational number only. Including two rationals complies with the exact same procedure as including two such fractions, bring about another fraction of this same form. Thus, including two rational numbers produces another rational number.

Is 7/8 a hopeful rational number?

7/8 is a ratio of entirety numbers having actually numerator and also denominator both carrying optimistic signs and thus, is considered as a positive rational number.

Is Zero a positive Rational Number?

The number 0 is neither a confident nor a an adverse rational number. A rational number in its standard form has a denominator as a hopeful integer and also the numerator and denominator have no usual factor various other than 1.

What Are confident and negative Rational Numbers?

Rational numbers room classified as positive, zero, or negative rational numbers. A rational number is stated to be positive if the numerator and denominator both are hopeful integers or both are an adverse integers whereas, a reasonable number is considered an adverse if one of two people the numerator or the denominator is a an unfavorable integer.

How come Multiply confident Rational Numbers?

The product of two given fractions is a fraction whose molecule is the product that the molecule of the provided fractions and also whose denominator is the product the the platform of the provided fractions. We follow the same dominance for the product of reasonable numbers. Therefore, the product of two rational numbers equals the product of their numerators/product of their denominators. Thus, if a/b and also c/d are any kind of two reasonable numbers, then a/b × c/d = a × c/b × d.

How to Multiply positive and an adverse Rational Numbers?

Multiplication the a positive and also a an adverse rational number is the very same as multiply fractions. The rules for multiplication space simple.

See more: How To Beat Apple Worm Level 4, Apple Worm Walkthrough All Levels And Solutions

If both numbers room positive, the an outcome is positive.If both numbers space negative, the an outcome is positive.If one of the rational number is negative, the result will it is in negative.