Fractions and decimals form the backbone of numerical literacy at the primary and upper-primary levels. For MP TET, this topic tests both your conceptual clarity and your ability to perform quick, error-free calculations. Questions typically involve simplification, conversion between fractions and decimals, and word problems requiring operations on mixed numbers.
Mastery here is essential because fractions and decimals reappear in percentage, ratio-proportion, and mensuration problems. The pedagogy section may also ask how children develop fraction sense, so understanding the "why" behind procedures matters as much as the "how." Expect 3–5 direct questions plus indirect application in other arithmetic topics.
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Key Concepts
**Fraction as part of a whole**: A fraction a/b represents 'a' equal parts out of 'b' total parts. The numerator counts parts; the denominator names the size of each part.
**Types of fractions**: Proper (numerator < denominator), improper (numerator ≥ denominator), and mixed numbers (whole number + proper fraction).
**Equivalent fractions**: Multiplying or dividing both numerator and denominator by the same non-zero number gives an equivalent fraction. Example: 2/3 = 4/6 = 6/9.
**Lowest terms (simplest form)**: A fraction is in lowest terms when the HCF of numerator and denominator is 1.
**Decimal place value**: Each place to the right of the decimal point represents tenths, hundredths, thousandths, and so on—each place is 1/10 of the previous.
**Terminating vs non-terminating decimals**: A fraction in lowest terms gives a terminating decimal only if the denominator has no prime factors other than 2 and 5.
**Like and unlike fractions**: Like fractions share the same denominator; unlike fractions do not. Converting to like fractions is necessary before adding or subtracting.
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Formulas / Key Facts
| Operation | Rule | |-----------|------| | **Addition/Subtraction of fractions** | Convert to like fractions (common denominator), then add/subtract numerators. | | **Multiplication of fractions** | (a/b) × (c/d) = (a × c) / (b × d). Simplify by cancelling common factors first. | | **Division of fractions** | (a/b) ÷ (c/d) = (a/b) × (d/c). Multiply by the reciprocal of the divisor. | | **Fraction → Decimal** | Divide numerator by denominator. Example: 3/4 = 3 ÷ 4 = 0.75. | | **Decimal → Fraction** | Write decimal over the appropriate power of 10 and simplify. Example: 0.625 = 625/1000 = 5/8. | | **Mixed → Improper** | Whole × Denominator + Numerator, over the same denominator. Example: 2 3/5 = (2×5 + 3)/5 = 13/5. | | **Improper → Mixed** | Divide numerator by denominator; quotient is whole part, remainder is new numerator. |
A teacher divides a chocolate bar into 8 equal parts and gives 3 parts to Ravi and 2 parts to Sita. What fraction of the chocolate bar is left?
Q2 · Fractions and Decimals · EASY
Ramesh bought 2.5 kg of rice and 1.75 kg of wheat. What is the total weight of the grains he bought?
Q3 · Fractions and Decimals · MEDIUM
A student solved: (3/4 + 5/6) - 1/2. What is the correct answer in simplest form?
Q4 · Fractions and Decimals · MEDIUM
A water tank is 3/5 full. After adding 120 litres, it becomes 4/5 full. What is the total capacity of the tank in litres?
Q5 · Fractions and Decimals · MEDIUM
A student scored 3/5 of the total marks in Mathematics and 7/10 of the total marks in Science. If both subjects have the same maximum marks, what fraction more did the student score in Science than in Mathematics?