Fractions and decimals represent parts of a whole. Aptitude questions test conversion, comparison, arithmetic operations, recurring decimals, and efficient calculation using equivalent fractions.

Parts of a fraction

• Numerator: the top number, showing the number of parts considered.
• Denominator: the bottom number, showing the total equal parts.
• Proper fraction: numerator is smaller than denominator, such as 3/5.
• Improper fraction: numerator is at least the denominator, such as 7/4.
• Mixed number: a whole number and a proper fraction, such as 1 3/4.

Equivalent and simplest fractions

Equivalent fractions have the same value. Multiply or divide both the numerator and denominator by the same non-zero number to form an equivalent fraction. Reduce a fraction by dividing both terms by their HCF.

• 3/4 = 6/8 = 12/16.
• 18/24 reduces to 3/4 after dividing by 6.
• Convert mixed numbers to improper fractions before multiplication or division.

Fraction operations

• Addition and subtraction: use the LCM of denominators, then add or subtract numerators.
• Multiplication: multiply numerators and denominators; cancel common factors first where possible.
• Division: multiply by the reciprocal of the second fraction.
• For comparison, use a common denominator or cross multiplication.

Decimals and place value

A decimal uses powers of ten: tenths, hundredths, thousandths, and so on. For example, 0.375 means 375/1000, which reduces to 3/8.

• Align decimal points when adding or subtracting decimals.
• Count total decimal places in the factors when multiplying decimals.
• Make the divisor a whole number by multiplying both dividend and divisor by the same power of 10.

Converting fractions and decimals

• To convert a fraction to a decimal, divide numerator by denominator.
• To convert a terminating decimal to a fraction, write it over 10, 100, 1000, and simplify.
• A fraction in simplest form terminates only when the denominator has prime factors 2 and/or 5.
• For a recurring decimal, form an equation, multiply to align repeating digits, and subtract.

Useful fraction equivalents

• 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%.
• 1/3 = 0.333...; 2/3 = 0.666...; 1/5 = 0.2; 1/8 = 0.125.
• Use these values to estimate quickly and check calculations.

How to solve questions

1. Reduce fractions to simplest form when it makes the calculation easier.
2. Use an LCM before adding or subtracting unlike fractions.
3. Cancel common factors before multiplying large fractions.
4. Track decimal places carefully in multiplication and division.
5. Convert between fractions, decimals, and percentages when one form is easier to use.