# Mathematics Questions and Answers – Representation of Numbers on Number Line

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Representation of Numbers on Number Line”.

1. On a number line, the arrangement of numbers is as follows _________
a) Negative -> 0 -> positive
b) Positive -> 0 -> negative
c) Positive -> 0 -> positive
d) Negative -> 0 -> negative

Explanation: When we refer to any number line, we observe that considering 0 as the center, the numbers to the left are negative and to the right are positive. The correct option would be “negative -> 0 -> positive”.

2. The number $$\frac{-16}{7}$$ lies on which side on a number line?
a) Right side
b) Left side
c) On the center
d) Can be on either of the sides

Explanation: As we know that on a number line the negative numbers are placed on the left side of the 0 and positive numbers on the right side. Here $$\frac{-16}{7}$$ is a negative number and hence has to be placed on the left side. Other options are wrong as negative numbers cannot be place on right side or at the center.

3. The number line for natural numbers is ____________
a) the line that extends indefinitely on both sides
b) the line that extends indefinitely to the right, but from 0
c) the line that extends indefinitely only to the right side of 1
d) the line that extends indefinitely on both sides, but you can see numbers only between –1, 0 and 0, 1 etc

Explanation: The set of natural numbers is [1, 2, 3, 4, 5…..] i.e. natural numbers start from 1 and extends to infinity on the positive side. The option which states that ‘The line that extends indefinitely to the right, but from 0′ shows the number line for whole numbers.
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4. When the numbers $$\frac{5}{2}, \frac{12}{11}, \frac{5}{4}, \frac{7}{6}$$ are placed on the number line, which of the following will be nearest to 0?
a) $$\frac{5}{4}$$
b) $$\frac{12}{11}$$
c) $$\frac{7}{6}$$
d) $$\frac{5}{2}$$

Explanation: All the numbers given to us are positive and according to the sign convention they would be placed on the right side of the 0. Here we have 4 numbers which are
$$\frac{5}{2}$$ = 2.5
$$\frac{7}{6}$$ = 1.67
$$\frac{5}{4}$$ = 1.25
$$\frac{12}{11}$$ = 1.09
Among these four decimal numbers the smallest is 1.09 which is decimal representation of $$\frac{12}{11}$$, this will be nearest to the center i.e. 0.

5. Which of the following form an equivalent pair of rational numbers?
a) $$\frac{120}{45} \,and \,\frac{160}{6}$$
b) $$\frac{55}{6} \,and \,\frac{220}{12}$$
c) $$\frac{-8}{13} \,and \,\frac{16}{26}$$
d) $$\frac{-230}{300} \,and \,\frac{-46}{60}$$

Explanation: When the rational numbers in their reduced form give equal fractions those numbers are called equivalent pair of rational numbers.
Here, we have 4 pairs of rational numbers in fractional form.
$$\frac{120}{45} \,and \,\frac{160}{6}$$ when reduced we get 8/3 and 80/3
$$\frac{55}{6} \,and \,\frac{220}{12}$$ when reduced we get 55/6 and 55/3
$$\frac{-8}{13} \,and \,\frac{16}{26}$$ when reduced we get (-8)/13 and 8/13
$$\frac{-230}{300} \,and \,\frac{-46}{60}$$ when reduced we get $$\frac{-23}{30} \,and \,\frac{-23}{30}$$. Here we see that both the numbers are equal and hence this pair is equivalent pair.

6. A number line which consists only integers will consider all the numbers like 1, -1, 2.5, etc.
a) True
b) False

Explanation: The number line which consists of only integers, the set of integers is [……,-3, -2, -1, 0, 1, 2, 3, ……] Hence the number line won’t consist of decimal like 2.5. Hence the given statement is false.

7. -8 is ____ than 8 and -12 is ____ than -9.
a) greater and smaller
b) smaller and greater
c) greater and greater
d) smaller and smaller

Explanation: When the numbers -8 and 8 placed on the number line -8 would be on the left side of 0 and 8 would be on the right side of 0. Hence -8 is smaller than 8. Similarly, for -12 and -9, -12 is smaller than -9. This is because as we go towards left on a number line the magnitude of the number increases but due to its negative sign it is smaller than the rest of the number to the right of that number.

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