Fractions and Decimals Solved Problems (With Step-by-Step Solutions)
Fractions and decimals are two different ways of representing parts of a whole. These concepts are introduced early in school mathematics and are used extensively in daily life, such as money calculations, measurements, percentages, and data interpretation.
In this article, you will learn how to solve fractions and decimals problems step by step. Each solved example is explained clearly so students can understand the method and apply it confidently in exams.
Important Concepts
Fraction: A number written in the form a/b, where a is the numerator and b is the denominator.
Decimal: A number written using a decimal point to represent parts of a whole.
Key Rules:
- To simplify a fraction, divide numerator and denominator by their HCF.
- To convert a fraction to a decimal, divide numerator by denominator.
- To compare fractions, convert them to a common denominator or decimals.
Solved Problems
Problem 1: Simplify the fraction 18/24
Solution:
Step 1: Find the HCF of 18 and 24.
HCF = 6
Step 2: Divide numerator and denominator by 6.
18 ÷ 6 = 3
24 ÷ 6 = 4
Simplified fraction = 3/4
Problem 2: Convert the fraction 5/8 into a decimal
Solution:
To convert a fraction to a decimal, divide the numerator by the denominator.
5 ÷ 8 = 0.625
Decimal form = 0.625
Problem 3: Convert the decimal 0.75 into a fraction
Solution:
Step 1: Write the decimal as a fraction.
0.75 = 75/100
Step 2: Simplify the fraction.
HCF of 75 and 100 = 25
75 ÷ 25 = 3
100 ÷ 25 = 4
Fraction form = 3/4
Problem 4: Which is greater: 3/5 or 0.6?
Solution:
Convert the fraction to a decimal.
3 ÷ 5 = 0.6
Since both values are equal,
3/5 = 0.6
Problem 5: A ribbon is 2.5 meters long. How many such ribbons are needed to make 10 meters?
Solution:
Number of ribbons = Total length ÷ Length of one ribbon
= 10 ÷ 2.5
= 4
Required ribbons = 4
Common Mistakes to Avoid
- Not simplifying fractions to lowest terms
- Incorrect decimal placement during division
- Comparing fractions without common denominators
- Forgetting to convert units in word problems
Practice Tips
✔ Always simplify fractions completely
✔ Convert fractions to decimals for easier comparison
✔ Double-check decimal division carefully
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