Fractions and Decimals Primary Questions for CTET PAPER I

Understanding Fractions — The Basics

A fraction represents a part of a whole. The bottom number (denominator) tells how many equal parts the whole is divided into. The top number (numerator) tells how many parts we are talking about. For primary classes (1-5), fractions are introduced using concrete objects like chapati, pizza, or a strip of paper folded into equal parts. The key word is EQUAL parts — children often divide shapes into unequal parts and still call it a fraction, which is a classic misconception CTET tests.

• Numerator = parts taken; Denominator = total equal parts
• Proper fraction: numerator less than denominator (3/5)
• Improper fraction: numerator greater than or equal to denominator (7/4)
• Mixed number: whole + proper fraction (1 and 3/4)
• Equivalent fractions: same value, different look — 1/2 = 2/4 = 3/6
• Unit fraction: numerator is 1, e.g., 1/3, 1/5 — simplest fractions taught first in primary

Comparing and Ordering Fractions

Children (and many exam aspirants) confuse bigger denominator with bigger fraction. This is a top PYQ trap. When denominators are the same, bigger numerator means bigger fraction. When numerators are the same, bigger denominator means SMALLER fraction (the whole is cut into more pieces, so each piece is smaller). To compare unlike fractions, convert to a common denominator (LCM method) or cross-multiply.

• Same denominator: compare numerators directly — 3/7 > 2/7
• Same numerator: bigger denominator = smaller fraction — 1/3 < 1/2
• Unlike fractions: find LCM of denominators, convert, then compare
• Cross multiplication shortcut: a/b vs c/d — compare a x d with b x c
• On a number line, fractions between 0 and 1 increase as you move right

Addition and Subtraction of Fractions

Same denominator: just add or subtract numerators, keep the denominator. Different denominators: find LCM, convert to equivalent fractions, then add or subtract. CTET Paper I often gives a word problem where a child makes an error like adding denominators too (1/2 + 1/3 = 2/5 is a classic wrong answer). Identifying such errors is as important as solving correctly.

• Same denominator: a/c + b/c = (a+b)/c
• Different denominators: find LCM, rewrite, then add numerators
• Never add denominators — 1/4 + 1/4 is NOT 2/8, it is 2/4 = 1/2
• Simplify the final answer to lowest terms always
• For mixed numbers: add whole parts and fraction parts separately, regroup if needed

Decimals — Place Value and Conversion

Decimals are just another way to write fractions with denominators 10, 100, 1000 and so on. The decimal point separates whole number part from the fractional part. At primary level (Class 4-5), children learn tenths and hundredths. CTET questions often check if you can identify place value in decimals and convert between fraction and decimal form. The link between decimals and the metric system (money, measurement) is a common context for word problems.

• 0.1 = 1/10 (one tenth), 0.01 = 1/100 (one hundredth)
• 0.25 = 25/100 = 1/4 — very common conversion in PYQs
• To convert fraction to decimal: divide numerator by denominator
• To convert decimal to fraction: write digits over appropriate power of 10, simplify
• Comparing decimals: line up decimal points, compare digit by digit from left
• 0.5 = 0.50 = 0.500 — adding trailing zeros does NOT change value

Pedagogical Angle — Teaching Fractions in Primary Classes

CTET always includes 1-2 questions on HOW to teach fractions to young children, not just what fractions are. The NCF and NCERT approach emphasizes concrete-pictorial-abstract (CPA) progression. Start with real objects (folding paper, cutting fruits), then move to diagrams, then symbols. Children should explore fractions as part of a whole AND as part of a collection (e.g., 3 out of 6 mangoes = 1/2). Common child errors must be recognized by the teacher.

• Concrete to Pictorial to Abstract (CPA) — the right teaching order
• Use fair-sharing activities: divide 1 chapati equally among 4 children
• Fraction of a collection: 2 out of 8 balls are red = 2/8 = 1/4
• Number line is a key visual tool for understanding fraction size
• Do NOT rush to algorithms — let children discover equivalence through folding/shading
• Error to watch: child says 1/4 is bigger than 1/2 because 4 is bigger than 2

• Adding both numerators AND denominators: writing 1/2 + 1/3 = 2/5. This is the most-tested child error in CTET — you must identify it as wrong and explain why.
• Thinking bigger denominator means bigger fraction: confusing 1/8 > 1/4 because 8 > 4. Always remind yourself: more pieces = smaller each piece.
• Not simplifying final answer: leaving 4/8 instead of writing 1/2. CTET may mark the unsimplified form as an error.
• Comparing decimals by ignoring place value: thinking 0.9 < 0.75 because 75 > 9 as whole numbers. Always align decimal points and compare column by column.
• Confusing mixed number conversion: writing 2 and 3/5 as 23/5 instead of the correct 13/5 (forgetting to multiply the whole number by denominator first).

• DENOMINATOR = DOWN below the line — D for Down. It tells how many equal parts DOWN the whole is split into.
• Same numerator? BIGGER bottom = SMALLER fraction. Think: more people sharing one pizza = less for each person.
• CPA order for teaching: Chapati, Picture, Algebra (Concrete, Pictorial, Abstract) — the desi memory hook.
• 0.25 = quarter = 1/4. Remember: 25 paise = one-quarter of a rupee. Links decimal to everyday Indian money context.

• CTET Paper I typically has 1 pure calculation question (compare, convert, or operate on fractions/decimals) and 1-2 pedagogy questions (identify child error, choose best teaching activity, or select correct teaching sequence).
• Pedagogy questions are usually easier marks — if a question says 'a student wrote X, what error did the student make?', look for the typical adding-denominators or bigger-denominator-bigger-fraction trap.
• Word problems often use context of money (rupees and paise) or measurement (metres, kilometres) to test decimals — practice reading these quickly.
• Questions on equivalent fractions and simplification are almost always present. Know your LCM and HCF methods cold — do not waste time on these.
• When stuck, eliminate options: in MCQs on fraction comparison, cross-multiply quickly in the margin rather than finding LCM for all options. Saves 30-40 seconds per question.