Math Problem Statement

Find two rational numbers between 1 and 3, and 1/2 and 3/4; find four rational numbers between -2 and -1, 2 and 3/4, -4/5 and -3/4, -1/2 and 1/2.

Solution

Let's solve each part of the problem step-by-step.

Problem 13

You need to find two rational numbers between each pair of numbers.

(i) Between 11 and 33:

To find two rational numbers between 1 and 3, we can use numbers like 1.51.5 and 2.52.5 (or in fraction form, 32\frac{3}{2} and 52\frac{5}{2}).

Thus, two rational numbers between 11 and 33 are:

  1. 1.51.5 or 32\frac{3}{2}
  2. 2.52.5 or 52\frac{5}{2}

(ii) Between 12\frac{1}{2} and 34\frac{3}{4}:

To find two rational numbers between 12\frac{1}{2} and 34\frac{3}{4}, we can convert these fractions to have the same denominator (e.g., 8) or find decimal equivalents.

  1. Convert: 12=48\frac{1}{2} = \frac{4}{8} and 34=68\frac{3}{4} = \frac{6}{8}.
  2. Choose numbers between 48\frac{4}{8} and 68\frac{6}{8}, such as 58\frac{5}{8} and 0.6250.625 (which is 58\frac{5}{8} as a decimal).

Thus, two rational numbers between 12\frac{1}{2} and 34\frac{3}{4} are:

  1. 0.550.55 or 58\frac{5}{8}
  2. (

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Math Problem Analysis

Mathematical Concepts

Rational Numbers
Number Line

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8