Learning Objectives
- Multiply fractions and mixed numbers
- Divide fractions by whole numbers and other fractions
- Multiply and divide decimal numbers
- Convert between fractions and decimals
Key Concepts
Multiplication of Fractions
Fraction × Fraction: (a/b) × (c/d) = (a×c)/(b×d)
Fraction × Whole Number: (a/b) × c = (a×c)/b
Mixed Numbers: Convert to improper fractions first, then multiply.
Division of Fractions
Reciprocal: The reciprocal of a/b is b/a
Division Rule: To divide by a fraction, multiply by its reciprocal.
(a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c)
Multiplication of Decimals
Multiply the numbers ignoring the decimal point. Then place the decimal point in the product so that the total decimal places equal the sum of decimal places in both numbers.
Example: 2.5 × 1.2 = 3.00 = 3.0
Division of Decimals
To divide by a decimal, convert the divisor to a whole number by multiplying both numbers by 10, 100, etc.
Example: 6.25 ÷ 0.5 = 62.5 ÷ 5 = 12.5
Summary
Fractions are multiplied by multiplying numerators and denominators separately. Division of fractions uses the reciprocal method. Decimal multiplication requires counting total decimal places. Decimal division converts the divisor to a whole number first.
Important Terms
- Proper Fraction
- A fraction where the numerator is less than the denominator (e.g., 3/4)
- Improper Fraction
- A fraction where the numerator is greater than or equal to the denominator (e.g., 7/4)
- Reciprocal
- The reciprocal of a/b is b/a; the product of a number and its reciprocal is 1
- Mixed Number
- A combination of a whole number and a proper fraction (e.g., 2¾)
Quick Revision
- To multiply fractions: multiply numerators, multiply denominators, simplify
- To divide fractions: multiply by the reciprocal of the divisor
- The reciprocal of 0 does not exist
- 0.1 × 0.1 = 0.01 (count total decimal places)
- Always simplify the final answer to lowest terms
Practice Tips
- Practice converting mixed numbers to improper fractions and back
- Use real-life situations like dividing a pizza or measuring ingredients
- Cross-check decimal multiplication by estimation