Question 23 of 58intermediate🔧 ApplyDiagram3 marks

Represent the rational numbers 23\frac{2}{3}, −54-\frac{5}{4} and 1121\frac{1}{2} on a single number line.

Correct Answer

To represent the given rational numbers on a single number line, we first draw a line and mark the origin as 0. We then mark the integers -2, -1, 0, 1, and 2 at equal distances.

For the number 2/3, we divide the unit interval between 0 and 1 into 3 equal parts. Moving 2 parts to the right of 0 gives the point for 2/3. For 1 1/2, we divide the interval between 1 and 2 into 2 equal parts. Moving 1 part to the right of 1 locates 1 1/2.

For -5/4 (which is -1 1/4), it lies between -2 and -1. We divide the interval between -2 and -1 into 4 equal parts. Moving 1 part to the left of -1 locates -5/4.

Exercise: Exercise Set 3.4 | Q: 1 | (Page 12)
For More Understanding

Explanation

The textbook states that to represent a rational number p/q on the number line, we divide the unit interval into q equal parts and move p parts from 0 (right if positive, left if negative). For fractions greater than 1 or less than -1, we first convert them to mixed fractions to identify the consecutive integers they lie between, and then divide that specific interval into the denominator's number of parts.

Solution Steps

  1. Step 1: Draw a number line and mark integers -2, -1, 0, 1, 2 at equal distances.

  2. Step 2: For 2/3, divide the interval between 0 and 1 into 3 equal parts. Mark the 2nd part to the right of 0 as 2/3.

  3. Step 3: For 1 1/2, divide the interval between 1 and 2 into 2 equal parts. Mark the 1st part to the right of 1 as 1 1/2.

  4. Step 4: For -5/4 (-1 1/4), divide the interval between -2 and -1 into 4 equal parts. Mark the 1st part to the left of -1 as -5/4.

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