What is the difference between fractions and rational numbers?
Fractional numbers are like… 3/4, 1/3, 0.02, (10)^(-2), 7% all proper fractions. But 7/3 , 11/2…. etc are improper fractions ( as numerator > denominator). …….. any such number excluding 0 & 1 in the denominator, is referred as fractional numbers.Fractional numbers represent :- like 3/4 represents, out of 4 equal parts of a whole piece, we picked 3. If we pick 1 more part. Together it becomes 1 whole.Similarly, 0.02 = 2/100 or 1/50. means out of 50 equal parts of a whole piece, we’re picking just one. OR out of 100 equal parts of that whole piece we pick 2. … Here making 50 equal parts is rather easier. This is the reason , we represent fractional numbers in the least form.Now, 7/3 = read as 2 integer 1/3 , here you already have 2 wholes, & third whole is divided into 3 equal parts & we pick just 1 part & place it with 2 wholes. So it becomes 7/3.All fractional numbers are rational too. But all rational numbers are not fractional.Rational numbers: are like 2/7, 1/2, 0.5, 7/3, 6%, 5² , 32, -16, -8/7 , 32.798, 43.252525, 0(zero), 29.3131313131…31 recurring, 100, etc etc , where numerator & denominator both are integers but denominator not equal to 0.Here all the above rationals from the above mentioned numbers can be represented as fractional numbers except 5², 32, -16, 100… etc. These 5², 32, -16, 100.. are rationals but not fractionals..In short, fractional numbers are written with a slash always…:) But not so with Rational numbers
Is there no difference between a rational number and a fraction?
A “rational” number is the RATIO between two integers; so is a fraction.Some fractions are called “improper” because the numerator exceed the denominator, so that they can be converted to a “mixed” number — which is a whole number plus a “proper” fraction.
What is the difference between rational number and fraction? Explain with example and give suitable reason for the chosen example.
Fraction- In math, a fraction is a part of a whole. It's represented as one number on top of another separated by a line. The top number is the numerator, and the bottom number is the denominator.Examples:½,¾,⅓Rational number - A number is said to be rational if it can be written in the form of a fraction such as p/q where both p (numerator) and q (denominator) are integers and denominator is a natural number (a non-zero number). Integers, fractions including mixed fraction, recurring decimals, finite decimals, etc., are all rational numbers.Examples of Rational Number1/9 – Both numerator and denominator are integers.7 – Can be expressed as 7/1, wherein 7 is the quotient of integers 7 and 1.√16 – As the square root can be simplified to 4, which is the quotient of fraction 4/10.5 – Can be written as 5/10 or 1/2 and all terminating decimals are rational.0.3333333333 – All recurring decimals are rational.
What is the difference between a rational number and a fraction?
a/b is a fraction if and only if a/b is less than 1.a/b is a rational number can be greater than 1 or less than 1 (but b should not be 0).
How would you differentiate between fractions and rational numbers with the help of 5 examples?
Every fraction is a rational number, but positive rational numbers are fractions, not negative rational numbers. So 1, 3/4, and 4/3 are both fractions and rational numbers. -1 and -4/3 are rational numbers, but not fractions.
Is -1/2 a fraction or a rational number?
[math]-\frac{1}{2} = -0.5[/math]It is a fraction or rational number; both mean the same. A rational numbers is defined as a number of the form [math]\frac{p}{q}, q \neq 0[/math].A fraction or a rational number may be terminating decimals, like 6.25, -8.125, -6 etc. or a recurring number like [math]0.\overline{3}[/math] or [math]7.1\overline{8}[/math].
Are all fractions rational numbers? Why?
Rational numbers are those which can be expressed in x/y format where x and y can only be whole numbers or integers. It won't be wrong to say all whole numbers are rational cause they can be expressed as number/1 example:- 3 = 3/1 or 5 = 5/1Where as irrational numbers are those, that can't be expressed as a fraction of whole numbers or integers, example square roots of non perfect squares, like √2 , √3, √5 etcTherefore if a fraction consists an irrational number then the result can't be a rational number. As we can't express square roots of non perfect squares as a fraction of whole numbers or integers.Example √2/7, 5/√7, 9/√5 all are irrational.Therefore we can't say every fraction is a rational number.But every fraction, that contains only whole numbers or integers or square roots of perfect squares will always be a rational numberExample √4/5 is rational as it can be written as 2/5For more information, read this Rational and Irrational Number