CBSE Class 7 Maths: Fractions and Decimals Ex 2.3

Understanding Multiplication of Fractions

Multiplying fractions might seem a little different from adding or subtracting them, but it's often simpler! When we say "multiplication of fractions," it's like asking for a "part of a part." For example, if you have half a cake and you want to eat half of that half, you're essentially multiplying 1/2 by 1/2. The word "of" often means multiplication in mathematics, especially when dealing with fractions. So, "half of a quarter" means 1/2 × 1/4.

The basic rule for multiplying two fractions is straightforward: multiply the numerators (top numbers) together, and multiply the denominators (bottom numbers) together. The product will be a new fraction. Sometimes, you might need to simplify this resulting fraction to its lowest terms. Unlike addition and subtraction, you don't need a common denominator to multiply fractions. This makes multiplication quite friendly! We'll explore how to handle fractions with whole numbers and mixed fractions in the upcoming sections.

Multiplying a Fraction by a Whole Number

1. Step 1: Convert the whole number to a fraction — Any whole number can be written as a fraction by placing it over 1. For example, 5 can be written as 5/1.
2. Step 2: Multiply the numerators — Multiply the top number of the first fraction by the top number of the second fraction (which is your whole number as a fraction).
3. Step 3: Multiply the denominators — Multiply the bottom number of the first fraction by the bottom number of the second fraction (which is always 1 when you convert a whole number).
4. Step 4: Simplify the result (if needed) — If your resulting fraction is an improper fraction (numerator is greater than or equal to the denominator), convert it to a mixed fraction. Also, reduce the fraction to its simplest form by dividing both numerator and denominator by their greatest common factor (GCF).

Multiplying a Fraction by Another Fraction

1. Step 1: Check for simplification (optional but recommended) — Before multiplying, you can often simplify by cross-cancelling. Look for common factors between any numerator and any denominator. Divide both by their common factor. This makes the numbers smaller and easier to multiply.
2. Step 2: Multiply the numerators — Multiply the top numbers of both fractions together. This will be the numerator of your answer.
3. Step 3: Multiply the denominators — Multiply the bottom numbers of both fractions together. This will be the denominator of your answer.
4. Step 4: Simplify the final fraction — If you didn't cross-cancel in Step 1, or if further simplification is possible, reduce the resulting fraction to its lowest terms. If it's an improper fraction, convert it to a mixed fraction.

Exam Tip: Avoiding Common Mistakes

When multiplying fractions, students often make a few common mistakes. One major error is trying to find a common denominator, which is only necessary for adding or subtracting fractions. Remember, for multiplication, you directly multiply numerator by numerator and denominator by denominator.

Another common mistake is forgetting to simplify the fraction to its lowest terms. Always check if the resulting fraction can be divided by a common factor. Cross-cancellation before multiplying can save you a lot of effort in simplifying at the end. Also, be careful when dealing with mixed fractions; always convert them to improper fractions before multiplying. A careless mistake here can lead to an incorrect final answer.

Practice Questions with Solutions

• Q: Find the product: (3/5) × 7 A: Step 1: Write the whole number as a fraction: 7 = 7/1. Step 2: Multiply the numerators: 3 × 7 = 21. Step 3: Multiply the denominators: 5 × 1 = 5. Step 4: Convert the improper fraction to a mixed fraction: 21/5 = 4 1/5. Final answer: 4 1/5
• Q: Multiply: (2/3) × (4/5) A: Step 1: Multiply the numerators: 2 × 4 = 8. Step 2: Multiply the denominators: 3 × 5 = 15. Step 3: The fraction 8/15 is already in its simplest form as there are no common factors other than 1. Final answer: 8/15
• Q: Find (1/2) of 18 A: Step 1: Understand "of" means multiplication: (1/2) × 18. Step 2: Write 18 as 18/1. The expression becomes (1/2) × (18/1). Step 3: Multiply numerators: 1 × 18 = 18. Step 4: Multiply denominators: 2 × 1 = 2. Step 5: Simplify the result: 18/2 = 9. Final answer: 9
• Q: Calculate: 2 (1/4) × 1 (1/3) A: Step 1: Convert mixed fractions to improper fractions. 2 (1/4) = (2×4 + 1)/4 = 9/4. 1 (1/3) = (1×3 + 1)/3 = 4/3. Step 2: The expression becomes (9/4) × (4/3). Step 3: Cross-cancel if possible. Here, 4 in the numerator and 4 in the denominator cancel out to 1. Also, 9 and 3 have a common factor of 3. 9/3 = 3, 3/3 = 1. Step 4: Multiply the remaining numerators: 3 × 1 = 3. Step 5: Multiply the remaining denominators: 1 × 1 = 1. Step 6: Simplify: 3/1 = 3. Final answer: 3

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