If P = 2/3 and Q = 5/6 on the number line, what is the distance from P to Q?
Answer and explanation
Correct answer: 1/6 unit
The governing concept is that the distance between two points on a number line is the absolute difference of their coordinates. Here Q is to the right of P because 5/6 > 2/3. Use a common denominator: 2/3 = 4/6. Therefore the distance is |5/6 − 4/6| = |1/6| = 1/6 unit. Option A is correct. Option B would result from an incorrect denominator operation, option C treats the numerators or denominators separately without equivalence, and option D adds the two coordinates instead of finding their separation. Because the points are ordered, ordinary subtraction gives a positive distance; absolute value would also give the same result.
Frequently asked questions
What is the correct answer to this question?
1/6 unit
Why is this the correct answer?
The governing concept is that the distance between two points on a number line is the absolute difference of their coordinates. Here Q is to the right of P because 5/6 > 2/3. Use a common denominator: 2/3 = 4/6. Therefore the distance is |5/6 − 4/6| = |1/6| = 1/6 unit. Option A is correct. Option B would result from an incorrect denominator operation, option C treats the numerators or denominators separately without equivalence, and option D adds the two coordinates instead of finding their separation. Because the points are ordered, ordinary subtraction gives a positive distance; absolute value would also give the same result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Representing real numbers on the number line.
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