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Rational Numbers Challenge

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Rational Numbers Challenge

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Practice problems on rationals

Created by

sowmiya Sowmi68
sowmiya Sowmi68
India

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Rational Numbers Challenge
 

Rational Numbers ChallengeOnline version

Practice problems on rationals

by sowmiya Sowmi68
1

Represent the rational numbers 2/3, -5/4, and 1 1/2 on a single number line.

2

Find three distinct rational numbers strictly between -1/2 and 1/4.

3

Simplify the expression (-1/4) + (5/12).

4

A tailor has 15 3/4 metres of silk. If one kurta needs 2 1/4 metres, how many kurtas can be made?

5

Find three rational numbers between 3.1415 and 3.1416.

6

Can you think of any method(s) to find a rational number between any two rationals?

7

Find a rational between 7/8 and 3/4.

8

Between 4 2/3 and 5, give a rational between them.

9

Convert 4 2/3 and 2 5/6 to improper fractions and find a reasonable between number.

10

True or False: Every rational number has a finite decimal expansion.

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Each value position is relative to 0; 2/3 ≈ 0.667, -5/4 = -1.25, 3/2 = 1.5.

Between -1/2 and 1/4 you can choose negative and nonnegative fractions like -1/4, -1/8, and 0.

(-1/4)+(5/12) = (-3/12)+(5/12) = 2/12 = 1/6.

15 3/4 ÷ 2 1/4 = 15.75 ÷ 2.25 = 7 kurtas.

Any three numbers between 3.1415 and 3.1416 work; here are valid examples.

Common methods: average of the two rationals or the mediant between them.

Between 7/8 (0.875) and 3/4 (0.75) a mediant gives (7+3)/(8+4)=10/12=5/6.

4 2/3 = 14/3 and 5 = 15/3; 14/3 < 29/6 < 15/3, so 4 5/6 works.

14/3 = 4 2/3, 17/6 = 2 5/6; a between like 29/6 (4 5/6) lies between.

Rationals can be repeating, e.g., 1/3 = 0.333...; finite only when denominators have factors 2 and 5.

 
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