Fractions, Decimals and Percentages

Proper, improper, mixed fractions, operations using LCM, BODMAS, and percentage conversions.

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Curated Video Lesson

Visual explanation and practical step-by-step walk-through

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Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

Fractions represent equal parts of a whole quantity or collection. Whether measuring ingredients in cooking, calculating percentages of profits in business, or measuring land, fractions and decimals are central to applied mathematics. In the BECE exam, questions on fractions test your mastery of equivalent forms, the order of mathematical operations (BODMAS), and converting fluidly between fractions, decimals, and percentages.

What You Will Master in This Lesson (NaCCA Objectives):

Classify proper fractions, improper fractions, and mixed numbers.

Simplify fractions to lowest terms using the Highest Common Factor (HCF).

Add and subtract fractions with like and unlike denominators using the Lowest Common Multiple (LCM).

Multiply and divide fractions, including applying reciprocal rules.

Apply the BODMAS rule to complex multi-step fractional expressions.

Convert between fractions, terminating/recurring decimals, and percentages.

1. Types of Fractions & Conversions

A fraction is expressed as a/b, where a is the numerator and b is the non-zero denominator. • Proper Fraction: Numerator is smaller than denominator (e.g., 3/5, 7/10). Value is less than 1. • Improper Fraction: Numerator is greater than or equal to denominator (e.g., 9/4, 11/3). Value is 1 or greater. • Mixed Fraction: Consists of a whole number and a proper fraction (e.g., 2 ¾). Conversion Formula (Mixed to Improper): a (b/c) = (a × c + b) / c. Example: 3 ⅖ = (3 × 5 + 2) / 5 = 17/5.

2. Addition and Subtraction of Fractions

Rule: Fractions can ONLY be added or subtracted directly if they have the same denominator (like denominators). If denominators are different (unlike denominators): 1. Find the Lowest Common Multiple (LCM) of all denominators. 2. Convert each fraction into an equivalent fraction with the LCM as its denominator. 3. Add or subtract the numerators and keep the common denominator. 4. Reduce the final answer to its simplest form.

3. Multiplication and Division of Fractions

• Multiplication: Multiply numerators together and denominators together. Cancel common factors before multiplying. Formula: (a/b) × (c/d) = (a × c) / (b × d). • Division: Dividing by a fraction is the same as multiplying by its reciprocal (inverted fraction). Formula: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c).

4. The Order of Operations: BODMAS

Follow the strict hierarchy: B — Brackets first O — Of (multiplication evaluated immediately after brackets) D — Division M — Multiplication A — Addition S — Subtraction

5. Fractions, Decimals, and Percentages Triad

• Fraction to Percentage: Multiply by 100%. Example: ⅗ × 100% = 60%. • Percentage to Fraction: Write over 100 and simplify. Example: 45% = 45/100 = 9/20. • Fraction to Decimal: Divide numerator by denominator. Example: ⅜ = 3 ÷ 8 = 0.375. • Decimal to Percentage: Multiply by 100. Example: 0.085 × 100 = 8.5%.

Common Mistakes Students Make in BECE Examinations:

⚠️Adding denominators together: 1/3 + 1/4 = 2/7 is FALSE! Must find LCM (12) => 4/12 + 3/12 = 7/12.

⚠️Forgetting to invert the second fraction when dividing.

⚠️Ignoring BODMAS order.

Teacher's BECE Exam Pro-Tips:

⭐Convert all mixed numbers into improper fractions before multiplication or division.

⭐Cancel down common factors early to keep numbers small.

⭐Always present final answers in lowest terms.

Quick Revision Summary Checklist:

Add/Subtract: find LCM of denominators first.

Multiply: multiply numerators and denominators (cancel first).

Divide: invert second fraction and multiply.

BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction.

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Addition of Mixed Fractions

Problem StatementSimplify: 2 ⅓ + 1 ½

Step-by-Step Solution:

Step 1: Convert to improper fractions: 2 ⅓ = 7/3, 1 ½ = 3/2.

Step 2: Find LCM of 3 and 2: LCM = 6.

Step 3: Convert: 7/3 = 14/6 and 3/2 = 9/6.

Step 4: Add numerators: 14/6 + 9/6 = 23/6 = 3 ⅚.

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Key Takeaway / Exam Rule: Always find the LCM of denominators before adding or subtracting fractions.

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