UPSSSC PET · Bite-size lessons
Whole Numbers, Fractions & Decimals
About 6 min · Elementary Arithmetic · English
Time worked out from the lesson's 334 words at 150 words a minute, plus a minute for each question.
Whole Numbers, Fractions & Decimals form the absolute foundation of Elementary Arithmetic in UPSSSC PET. Mastery here means speed and accuracy—two critical advantages in a competitive exam where every second counts.
Key ideas
- Whole numbers are the set {0, 1, 2, 3, ...}. They include zero and all positive integers. No fractions, no negatives. Operations follow standard arithmetic rules: commutative (a + b = b + a), associative ((a + b) + c = a + (b + c)), and distributive (a × (b + c) = a×b + a×c).
- Fractions represent parts of a whole, written as numerator/denominator. Proper fractions have numerator < denominator (⅗). Improper fractions have numerator ≥ denominator (⁷⁄₅). Mixed numbers combine a whole number and a proper fraction (1⅖ = ⁷⁄₅).
- Like fractions share the same denominator and can be added/subtracted directly. Unlike fractions require finding a common denominator (usually the LCM of denominators) before operations.
- Decimals are another way to represent fractions using base-10 place value. The decimal point separates the whole part from the fractional part. Each position right of the decimal is 1/10 of the previous: tenths (0.1), hundredths (0.01), thousandths (0.001).
- Terminating decimals end after a finite number of digits (0.75 = ¾). Non-terminating repeating decimals have a pattern that repeats forever (⅓ = 0.333..., ¹¹⁄₉₉ = 0.111...).
Quick reference
- Fraction → Decimal: Divide numerator by denominator.
- Decimal → Fraction: Write as numerator over place-value denominator, simplify.
- Mixed → Improper: Multiply whole part by denominator, add numerator.
- Improper → Mixed: Divide numerator by denominator; quotient = whole, remainder/denominator = fraction.
- Add/Subtract fractions: Convert to common denominator (LCM), then operate on numerators.
Check yourself: 3 questions
1. Arrange the following fractions in ascending order: 5/8, 3/4, 7/12, 2/3
2. A number when divided by 357 leaves a remainder 5. What will be the remainder when the same number is divided by 17?
3. What is the value of 3.75 + 2.8 - 1.625?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 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.
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