Fractions and Decimals Notes for SSC Exams

Fractions and Decimals form the base of simplification, percentage and ratio in SSC Quantitative Aptitude. Many questions need quick comparison, conversion and operations on fractions and decimals. These fractions and decimals notes for SSC explain the types, the rules of operations, the recurring decimal formulas and the comparison tricks with solved examples.

Types of Fractions

• Proper fraction: numerator is less than the denominator (3/5).
• Improper fraction: numerator is greater than or equal to the denominator (7/4).
• Mixed fraction: a whole number with a proper fraction (1 3/4).
• Like fractions: fractions with the same denominator. Unlike fractions: fractions with different denominators.
• Equivalent fractions: fractions with the same value (1/2 = 2/4 = 3/6).

Operations on Fractions

Comparing Fractions

• Cross-multiplication: to compare a/b and c/d, compare ad and bc. If ad is more than bc, then a/b is greater.
• Decimal method: convert each fraction into a decimal and compare.
• Same numerator: the fraction with the smaller denominator is greater.
• Same denominator: the fraction with the larger numerator is greater.

Decimals and Recurring Decimals

To multiply decimals, multiply as whole numbers and count the total number of decimal places. To divide by a decimal, multiply both the dividend and the divisor by 10, 100 and so on, until the divisor becomes a whole number.

Fraction and Decimal Values to Memorise

Notice that 1/7 gives the recurring block 142857, and 2/7 = 0.285714..., 3/7 = 0.428571... use the same digits in a different order. This helps to compare and convert sevenths quickly. Also remember that a fraction in its lowest terms is a terminating decimal only if the denominator has no prime factor other than 2 and 5.

Quick Approach to Mixed Operations

When an expression contains both fractions and decimals, convert them all into the same form. Use fractions when the decimals are simple (0.25, 0.5, 0.75, 0.125) and use decimals when the fractions have awkward denominators. For example, 0.75 + 1/4 is easier as 3/4 + 1/4 = 1. Always apply BODMAS to decide the order of operations.

Solved Examples

Example 1: Add: 3/4 + 5/6.
Solution: LCM of 4 and 6 = 12. 9/12 + 10/12 = 19/12 or 1 7/12.

Example 2: Arrange 5/7, 3/5 and 7/9 in the descending order.
Solution: Decimals: 5/7 = 0.714, 3/5 = 0.6, 7/9 = 0.778. Order: 7/9 > 5/7 > 3/5.

Example 3: Convert 0.444... into a fraction.
Solution: Recurring digit 4, so 4/9. The answer is 4/9.

Example 4: Convert 0.3636... into a fraction.
Solution: 36 / 99 = 4/11.

Example 5: Find the value of 2.5 x 0.04.
Solution: 25 x 4 = 100 with three decimal places in total, so the answer is 0.100 = 0.1.

Example 6: Convert 0.125 into a fraction.
Solution: 0.125 = 125 / 1000 = 1/8.

Quick Tips to Solve Faster

• Use cross-multiplication to compare two fractions in a few seconds.
• Learn the decimal values of 1/2 to 1/12 and 1/16, 1/20.
• Convert a mixed fraction to an improper fraction before multiplying or dividing.
• Reduce every fraction to its lowest terms before multiplying.
• For recurring decimals, remember "number of 9s = number of recurring digits".

Common Mistakes to Avoid

• Adding numerators and denominators separately.
• Not taking the reciprocal in division.
• Putting the decimal point in the wrong place after multiplication.
• Comparing fractions by looking at denominators only.
• Forgetting the non-recurring digit in mixed recurring decimals.

Quick Revision Points

• a/b + c/d = (ad + bc)/bd.
• Divide by a fraction = multiply by its reciprocal.
• 0.aaa... = a/9 and 0.abab... = ab/99.
• Compare a/b and c/d by comparing ad and bc.
• "Of" means multiplication.

Practice Questions With Answers

1. Find the value of 2/3 + 1/4.
   Answer: 11/12 (8/12 + 3/12).
2. Find the value of 5/6 - 1/3.
   Answer: 1/2 (5/6 - 2/6).
3. Find the value of 3/5 divided by 9/10.
   Answer: 2/3 (3/5 x 10/9).
4. Convert 0.75 into a fraction.
   Answer: 3/4 (75/100).
5. Convert 0.272727... into a fraction.
   Answer: 3/11 (27/99).
6. Find the value of 1.25 x 0.8.
   Answer: 1 (125 x 8 = 1000).
7. Which is the greatest: 3/4, 4/5 or 5/6?
   Answer: 5/6 (0.75, 0.8, 0.833).
8. Convert 0.666... into a fraction.
   Answer: 2/3 (6/9).
9. Find the value of 0.5 + 0.25 + 0.125.
   Answer: 0.875 (Add the decimals).
10. Find 7/8 of 64.
    Answer: 56 (7 x 8).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC fractions and decimals practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Simplification and BODMAS Notes
• Percentage Notes
• Ratio and Proportion Notes
• HCF and LCM Notes
• SSC Fractions and Decimals Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is a fraction?

A fraction is a part of a whole, written as numerator over denominator, such as 3/5.

What is a decimal?

A decimal is another way of writing a fraction whose denominator is 10, 100, 1000 and so on, such as 0.25 = 25/100.

How do I compare two fractions?

Cross-multiply: for a/b and c/d, compare ad with bc. The side with the larger product has the larger fraction.

How do I convert a recurring decimal into a fraction?

For a pure recurring decimal, write the recurring digits over as many 9s as there are digits, such as 0.37 recurring = 37/99.

How do I divide by a fraction?

Multiply by the reciprocal of the fraction.

What does "of" mean in maths?

"Of" means multiplication, such as 1/2 of 60 = 30.

How many questions come from fractions and decimals in SSC exams?

Several questions in simplification and approximation use fractions and decimals.

How should I practise fractions and decimals?

Learn the table of values, solve the examples here and attempt the fractions and decimals practice paper.