The denominator of a rational number is 4 more than the numerator. if the numerator and the denominator are increased by 1 each, the rational number becomes 1/2. find the number.
Answers
Step-by-step explanation:
Let the numerator of the rational number be x.
Then, the denominator of the rational number =x+4
It is given that the numerator is increased by 2 and the denominator is increased by 3 to get the new rational number
4
3
.
According to the given condition,
(x+4)+3
x+2
=
4
3
By cross multiplying, we get
4(x+2)=3(x+7)
⟹4x+8=3x+21
⟹4x−3x=21−8 ....[Transposing 3x to LHS and 8 to RHS]
or x=13
Therefore, numerator of the rational number =13 and denominator =13+4=17.
Hence the original rational number is
17
13
.
A number that can be expressed in the form p/q, where p and q are integers and q ≠≠ 0, is called a rational number. All integers and fractions are rational numbers.
Examples: -2/7, 3/8, etc.
Numerator and denominator
In p/q, the integer p is the numerator, and the integer q (≠ 0) is the denominator.
Equivalent rational numbers: By multiplying the numerator and denominator of a rational number by the same non zero integer, we obtain another rational number equivalent to the given rational number.
Positive rational numbers: When the numerator and denominator both are positive
negative rational numbers: When the numerator is positive and denominator is negative.
The number 0 is neither a positive nor a negative rational number.
Subsequently, the concept of rational numbers on a number line is also explained.