Decimal and Fractions Questions for AFCAT

Understanding Fractions

A fraction represents a part of a whole. It has two parts: the numerator (top number — how many parts you have) and the denominator (bottom number — how many equal parts the whole is divided into). A proper fraction has numerator less than denominator (like 3/4). An improper fraction has numerator greater than or equal to denominator (like 7/4). A mixed number combines a whole number and a proper fraction (like 1 and 3/4). In AFCAT, you must be comfortable switching between these forms instantly.

• Proper fraction: numerator is less than denominator. Example: 5/9
• Improper fraction: numerator is greater than or equal to denominator. Example: 11/4
• Mixed number: whole part plus proper fraction. Example: 2 and 3/7
• To convert mixed number to improper fraction: multiply whole number by denominator, add numerator, keep denominator. So 2 and 3/7 = (2 x 7 + 3)/7 = 17/7
• Equivalent fractions: multiply or divide both numerator and denominator by same number. 2/3 = 4/6 = 8/12
• Always simplify (reduce) fractions by dividing by HCF of numerator and denominator

Understanding Decimals

A decimal is just another way to write a fraction whose denominator is a power of 10 (10, 100, 1000, etc.). Each digit after the decimal point has a place value: tenths, hundredths, thousandths, and so on. For AFCAT, the key skill is fast conversion between decimals and fractions, and being able to compare or simplify decimal expressions without a calculator.

• 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000
• To convert decimal to fraction: write digits after decimal over appropriate power of 10, then simplify. 0.75 = 75/100 = 3/4
• To convert fraction to decimal: divide numerator by denominator. 3/8 = 0.375
• Recurring decimals: 1/3 = 0.333..., 2/3 = 0.666..., 1/6 = 0.1666...
• Terminating decimals come from fractions whose denominator has only 2 and 5 as prime factors
• Non-terminating recurring decimals come from all other denominators like 3, 6, 7, 9

Comparison of Fractions and Decimals

AFCAT frequently asks you to arrange fractions in ascending or descending order, or identify the largest or smallest among a set. The fastest method depends on the fractions given. If denominators are the same, compare numerators. If numerators are the same, larger denominator means smaller fraction. For unlike fractions, convert to decimals or find LCM of denominators.

• Cross multiplication trick: to compare a/b and c/d, compare a x d with b x c. Larger product side wins
• Same denominator: bigger numerator = bigger fraction
• Same numerator: bigger denominator = smaller fraction (think dividing a pizza into more pieces — each piece is smaller)
• Quick decimal conversion is fastest for comparing 3 or more fractions
• Memorise common fractions as decimals: 1/8=0.125, 1/6=0.1667, 1/4=0.25, 1/3=0.333, 3/8=0.375, 1/2=0.5, 5/8=0.625, 2/3=0.667, 3/4=0.75, 7/8=0.875

Operations on Fractions and Decimals

AFCAT questions often wrap a fraction or decimal operation inside a word problem or simplification. For addition and subtraction of fractions, you must find the LCM of denominators first. For multiplication, multiply straight across. For division, flip and multiply. With decimals, align decimal points for addition and subtraction, and count total decimal places for multiplication.

• Add or subtract fractions: find LCM of denominators, convert, then operate on numerators
• Multiply fractions: (a/b) x (c/d) = ac/bd — simplify before multiplying if possible to keep numbers small
• For decimals in multiplication: count total decimal places in both numbers — place that many in the answer
• For decimal division: shift decimal point in both numerator and denominator equally to make denominator a whole number
• In complex simplification questions, work from innermost bracket outward using BODMAS

• Forgetting to find LCM before adding fractions — students directly add numerators and denominators, giving a completely wrong answer
• In division of fractions, flipping the first fraction instead of the second. Always flip the divisor (the one after the division sign)
• Misplacing the decimal point in multiplication — for example 0.2 x 0.3 = 0.06, not 0.6. Count decimal places carefully
• Confusing same-numerator comparison — students think 3/7 is greater than 3/5 because 7 is bigger, but it is actually smaller
• Not simplifying recurring decimals using the 9-trick — students do long division instead and waste 2-3 minutes

• FLIP IT TO DIVIDE IT: in fraction division, flip the second fraction and multiply. Think of it as flipping a fraction upside down to remove the division.
• PETE'S DECIMAL TABLE (Pin to memory): 1/4=0.25, 1/3=0.33, 1/2=0.5, 3/4=0.75, 1/8=0.125, 3/8=0.375, 5/8=0.625, 7/8=0.875. These 8 values cover 80 percent of AFCAT decimal questions.
• SAME NUMERATOR = SMALLER DENOMINATOR WINS. Analogy: sharing a chocolate between 3 friends gives bigger pieces than sharing between 7 friends.
• 9-TRICK FOR RECURRING DECIMALS: count repeating digits, put that many 9s in denominator. 0.7777 = 7/9. 0.142857142857 (6 digits repeat) = 142857/999999 = 1/7.

• AFCAT typically places 1 to 2 direct decimal or fraction questions per paper, usually in simplification or comparison form. They are solvable in under 60 seconds if conversions are memorised.
• A common AFCAT pattern is: which of the following fractions is the largest? with 4 options that look similar — use decimal conversion from memory to solve in 20 seconds flat.
• Recurring decimal to fraction conversion has appeared in multiple AFCAT papers as a standalone question. The 9-trick is your fastest weapon here.
• Complex fraction questions like (a/b + c/d) divided by (e/f - g/h) require BODMAS discipline. Write each bracket result separately before dividing — do not rush and skip steps.
• If you are stuck, eliminate options by approximation — convert all fractions to rough decimals and compare. Even if your mental arithmetic is off slightly, wrong options are usually far enough away to eliminate.