Comparing the Costs of Mathematics and Science Books: A Detailed Guide

Introduction

When comparing the cost of textbooks, it is crucial to understand the various formats of numbers that might be presented. In this guide, we will delve into the process of comparing the costs of a mathematics book priced at Rs 25 3/4 and a science book priced at Rs 20 1/2. We will use both mixed numbers and improper fractions to ensure accurate comparison.

Conversion of Mixed Numbers to Improper Fractions

To compare the costs of the mathematics book and the science book, we first need to convert the mixed numbers into improper fractions. This step is essential for a precise comparison.

Mathematics Book:

Rs 25 3/4 can be converted as follows:

Rs 25 3/4 Rs (25 3/4) Rs 25 Rs 3/4

Converting 3/4 to a decimal:

Rs 3/4 Rs 3 ÷ 4 Rs 0.75

Therefore, Rs 25 3/4 Rs 25.75 (or Rs 25 0.75)

Science Book:

Rs 20 1/2 can be converted as follows:

Rs 20 1/2 Rs (20 1/2) Rs 20 Rs 1/2

Converting 1/2 to a decimal:

Rs 1/2 Rs 1 ÷ 2 Rs 0.50

Therefore, Rs 20 1/2 Rs 20.50 (or Rs 20 0.50)

Comparison Through Common Denominators

To compare the two costs, we need to find a common denominator for the fractions. The least common multiple (LCM) of 4 and 2 is 4.

Converting the science book cost to have a denominator of 4:

Rs 20 1/2 Rs 20 1/2 Rs (20 × 2)/2 Rs 1/2 Rs 40/2 Rs 1/2 Rs 41/2

Convert the science book cost to have a denominator of 4:

Rs 41/2 Rs 41 × 2/2 × 2 Rs 82/4

Now we can compare the two costs:

Mathematics Book: Rs 103/4 Science Book: Rs 82/4

Subtract the two costs to determine the difference:

Rs 103/4 - Rs 82/4 (103 - 82)/4 21/4

Convert 21/4 back to a mixed number:

21/4 5 1/4

Conclusion

The mathematics book costs more than the science book by Rs 5.25. This can also be expressed as 5 rupees and 25 paise, which is the same as Rs 5 Rs 0.25.

Comparison Using Money Format

Another way to see the comparison is by expressing the costs in their money form:

First Book (Mathematics Book):

Rs 25 3/4 Rs 25 Rs 3/4 Rs 25 75 paise (since 1/4 rupee 1/4 × 100 paise 25 paise)

Second Book (Science Book):

Rs 20 1/2 Rs 20 Rs 1/2 Rs 20 50 paise (since 1/2 rupee 1/2 × 100 paise 50 paise)

Subtracting the two costs:

First Book Cost - Second Book Cost Rs 5.25 (5 rupees and 25 paise)

Hence, the first book (mathematics book) costs more than the second book (science book) by Rs 5.25 (5 rupees and 25 paise).