Decimals and Fractions
About 6 min · Elementary Mathematics · English
Time worked out from the lesson's 311 words at 150 words a minute, plus a minute for each question.
Decimals and fractions are two different ways to represent parts of a whole, and mastery of both is essential for SSC GD Elementary Mathematics.
Key ideas
- Fraction basics: A fraction a/b has numerator a (top) and denominator b (bottom). Proper fractions have a < b; improper fractions have a ≥ b. A mixed number combines a whole number and a proper fraction (e.g. 2 1/3).
- Decimal place value: In 45.678, the 6 is in the tenths place (6/10), 7 in hundredths (7/100), and 8 in thousandths (8/1000). Understanding place value prevents errors when adding or comparing decimals.
- Equivalent fractions: Multiplying or dividing both numerator and denominator by the same nonzero number gives an equivalent fraction. Example: 2/3 = 4/6 = 6/9. Simplification means reducing to lowest terms by dividing by the greatest common divisor.
- Conversion fraction to decimal: Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions give terminating decimals (like 1/2 = 0.5), others give recurring decimals (like 1/3 = 0.333...).
- Conversion decimal to fraction: Write the decimal as a fraction over the appropriate power of 10, then simplify. Example: 0.36 = 36/100 = 9/25 after dividing numerator and denominator by 4.
Quick reference
- Common conversions: 1/2 = 0.5; 1/4 = 0.25; 3/4 = 0.75; 1/5 = 0.2; 1/8 = 0.125; 1/10 = 0.1
- To add/subtract fractions: Same denominator? Add/subtract numerators. Different? Find LCM first.
- To multiply fractions: Multiply straight across (numerators together, denominators together), then simplify.
- To divide fractions: Flip the second fraction (reciprocal) and multiply.
- Decimal to fraction: Write over power of 10 matching decimal places, then simplify → 0.75 = 75/100 = 3/4.
Check yourself: 3 questions
1. What is the value of 0.75 + 1/4?
2. Convert 3.625 into a fraction in its simplest form.
3. What is the result of (2/5 × 0.35) + (3/4 ÷ 0.5)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.