Fractions and decimals for SSC GD

Fractions and decimals are rarely the whole question, but they are part of almost every question. A percentage is a fraction out of 100. A ratio is a fraction. A discount, a share of salary or a part of a tank is a fraction. If you handle them slowly, every topic feels slow.

The good news is that the rules are few and fixed. Learn them, learn the conversion table by heart, and practise for a week.

Types of fractions

Mixed to improper: multiply the whole by the denominator and add the top. 1¾ = (1 × 4 + 3)/4 = 7/4.

Improper to mixed: divide. 17/5 = 3 remainder 2, so 3⅖.

Simplifying: divide top and bottom by their HCF. 18/24: HCF is 6, so 3/4.

Adding and subtracting

Make the denominators the same, using their LCM, then add or subtract the tops. Our LCM and HCF guide shows how to find the LCM quickly.

1/3 + 1/4 = 4/12 + 3/12 = 7/12.

For mixed numbers, add wholes and fractions separately, then combine.

Multiplying and dividing

• Multiply: tops times tops, bottoms times bottoms. Cancel common factors first to keep numbers small.
• Divide: flip the second fraction and multiply. 4/5 ÷ 2/5 = 4/5 × 5/2 = 2.
• Always change mixed numbers to improper fractions before multiplying or dividing.

Comparing and ordering

There are three ways. Use whichever is quickest for the numbers in front of you.

1. Cross-multiply (for two fractions). For 3/5 and 4/7: 3 × 7 = 21 and 4 × 5 = 20. Since 21 > 20, 3/5 is bigger.
2. Convert to decimals (for three or more). This is usually fastest if you know the table below.
3. Same numerator: if the tops are equal, the smaller bottom gives the bigger fraction. 3/7 > 3/8.

Conversion table

Decimals

• Adding and subtracting: line up the decimal points. 2.5 + 1.25 = 3.75.
• Multiplying: multiply as whole numbers, then count the total decimal places in the question. 0.3 × 0.2: 3 × 2 = 6, two places, so 0.06.
• Dividing: move the decimal point in both numbers until the divisor is whole. 1.2 ÷ 0.4 = 12 ÷ 4 = 3.

Recurring decimals. When one digit repeats, put it over 9: 0.777… = 7/9. When two digits repeat, put them over 99: 0.3636… = 36/99 = 4/11.

Solved examples

Example 1. 2/3 + 3/4 − 5/6 = ?

1. LCM of 3, 4 and 6 is 12.
2. 8/12 + 9/12 − 10/12 = 7/12.

Example 2. 3⅓ × 1⅘ = ?

1. Improper: 10/3 × 9/5.
2. Cancel: 10 and 5 give 2 and 1; 9 and 3 give 3 and 1.
3. 2 × 3 = 6.

Example 3. 2⅔ ÷ 1⅓ = ?

1. Improper: 8/3 ÷ 4/3.
2. Flip and multiply: 8/3 × 3/4 = 24/12 = 2.

Example 4. Arrange 3/5, 2/3 and 5/8 in ascending order.

1. Decimals: 3/5 = 0.6, 2/3 ≈ 0.667, 5/8 = 0.625.
2. Order: 3/5 < 5/8 < 2/3.

Example 5. 0.25 × 0.4 ÷ 0.05 = ?

1. Left to right: 0.25 × 0.4 = 0.1.
2. 0.1 ÷ 0.05 = 10 ÷ 5 = 2.

Example 6. A candidate spends 1/4 of their monthly income on rent and 1/3 on food, and saves the remaining ₹5,000. Find the income.

1. Spent: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
2. Remaining: 1 − 7/12 = 5/12 of income = ₹5,000.
3. 1/12 = ₹1,000, so income = ₹12,000.
4. Check: rent ₹3,000, food ₹4,000, savings ₹5,000.

Common mistakes

Practice set

1. Change 3⅖ into an improper fraction.
2. Simplify 42/56.
3. 3/4 + 5/6 − 1/3
4. 2½ × 1⅗
5. 3¾ ÷ 1¼
6. Which is the largest: 4/7, 5/9 or 3/5?
7. 0.6 ÷ 0.015
8. A tank is 2/3 full. After 30 litres are used, it is 1/4 full. Find the capacity of the tank.

Answers:

1. 3 × 5 + 2 = 17, so 17/5.
2. HCF 14: 3/4.
3. 9/12 + 10/12 − 4/12 = 15/12 = 5/4, or 1¼.
4. 5/2 × 8/5 = 40/10 = 4.
5. 15/4 × 4/5 = 3.
6. 0.571, 0.556 and 0.6, so 3/5.
7. 600 ÷ 15 = 40.
8. 2/3 − 1/4 = 8/12 − 3/12 = 5/12 of the tank = 30 litres. 1/12 = 6 litres, so capacity = 72 litres.

What to do next

• Learn the conversion table until you can fill it in from memory.
• Solve 15 fraction lines a day for a week.
• Use these skills in simplification, then move on to percentage.