Question 50 of 58intermediate🔧 ApplyNumerical2 marks

Find 5 rational numbers between 16\frac{1}{6} and 25\frac{2}{5}.

Correct Answer

15\frac{1}{5}, 730\frac{7}{30}, 415\frac{4}{15}, 310\frac{3}{10}, 13\frac{1}{3}

Exercise: END-OF-CHAPTER EXERCISES | Q: 7 | (Page 25)
For More Understanding

Explanation

To find rational numbers between two fractions, we equate their denominators by finding the LCM. The LCM of 6 and 5 is 30. Converting 1/6 to 5/30 and 2/5 to 12/30 reveals the integers between 5 and 12, which correspond to the rational numbers between the given fractions. Simplifying these fractions gives the final answer.

Solution Steps

  1. Step 1: Find LCM of the denominators 6 and 5, which is 30.

  2. Step 2: Convert fractions to equivalent fractions with denominator 30: 16=530\frac{1}{6} = \frac{5}{30} and 25=1230\frac{2}{5} = \frac{12}{30}.

  3. Step 3: Identify 5 integers between 5 and 12, such as 6, 7, 8, 9, and 10.

  4. Step 4: Write the corresponding fractions: 630,730,830,930,1030\frac{6}{30}, \frac{7}{30}, \frac{8}{30}, \frac{9}{30}, \frac{10}{30}.

  5. Step 5: Simplify the fractions to get the final 5 rational numbers: 15,730,415,310,13\frac{1}{5}, \frac{7}{30}, \frac{4}{15}, \frac{3}{10}, \frac{1}{3}.

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