Multiplying Fractions With Unlike Denominators

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Multiplying fractions with unlike denominators may seem challenging at first, but it is actually quite simple. Unlike adding or subtracting fractions, you do not need a common denominator to multiply them. Instead, you multiply the numerators and denominators directly.

In this guide, we will walk you through how to multiply fractions with different denominators, provide examples, and share tips to make the process easier.

Understanding Fractions

A fraction consists of two parts:

  • Numerator (the top number) – represents how many parts are taken.
  • Denominator (the bottom number) – represents the total number of equal parts.

For example, in the fraction 3/4, the numerator is 3, and the denominator is 4.

When multiplying fractions, the denominators do not need to be the same, making the process simpler compared to addition or subtraction.

Steps to Multiply Fractions with Unlike Denominators

Step 1: Multiply the Numerators

The first step in multiplying fractions is to multiply the numerators (top numbers) of both fractions.

For example:

frac{2}{3} times frac{4}{5}

Multiply the numerators:

2 times 4 = 8

Step 2: Multiply the Denominators

Next, multiply the denominators (bottom numbers) of both fractions.

3 times 5 = 15

Now, the fraction looks like this:

frac{8}{15}

Since 8/15 is already in its simplest form, no further simplification is needed.

Step 3: Simplify the Fraction (If Needed)

If the result is not in its simplest form, simplify it by dividing both the numerator and denominator by their greatest common factor (GCF).

For example:

frac{6}{8} times frac{2}{3}

Multiply the numerators:

6 times 2 = 12

Multiply the denominators:

8 times 3 = 24

Result:

frac{12}{24}

Since 12 and 24 have a common factor of 12, divide both by 12:

frac{12 div 12}{24 div 12} = frac{1}{2}

So, the simplified result is 1/2.

Examples of Multiplying Fractions with Unlike Denominators

Example 1: Simple Multiplication

frac{5}{7} times frac{2}{9}

Multiply numerators:

5 times 2 = 10

Multiply denominators:

7 times 9 = 63

Final fraction:

frac{10}{63}

Since 10 and 63 do not have common factors other than 1, this is already simplified.

Example 2: Multiplying with Whole Numbers

When multiplying a fraction by a whole number, convert the whole number into a fraction by placing it over 1.

For example:

frac{3}{5} times 4

Rewrite 4 as 4/1:

frac{3}{5} times frac{4}{1}

Multiply numerators:

3 times 4 = 12

Multiply denominators:

5 times 1 = 5

Result:

frac{12}{5}

Since this is an improper fraction, you can convert it to a mixed number:

12 div 5 = 2 text{ remainder } 2

So, 12/5 becomes 2 2/5.

Example 3: Multiplying Mixed Numbers

To multiply mixed numbers, first convert them into improper fractions.

For example:

2frac{1}{3} times 1frac{2}{5}

Convert to improper fractions:

frac{7}{3} times frac{7}{5}

Multiply numerators:

7 times 7 = 49

Multiply denominators:

3 times 5 = 15

Result:

frac{49}{15}

Convert to a mixed number:

49 div 15 = 3 text{ remainder } 4

Final answer: 3 4/15.

Common Mistakes to Avoid

1. Adding Instead of Multiplying Numerators and Denominators

A common mistake is adding the numerators and denominators instead of multiplying them.

Incorrect:

frac{2}{3} times frac{4}{5} = frac{2+4}{3+5} = frac{6}{8}

Correct:

frac{2}{3} times frac{4}{5} = frac{2 times 4}{3 times 5} = frac{8}{15}

2. Forgetting to Simplify the Answer

Always check if the final fraction can be simplified. If both numerator and denominator have a common factor, divide by their GCF.

For example:

frac{12}{18} Rightarrow frac{12 div 6}{18 div 6} = frac{2}{3}

3. Not Converting Mixed Numbers to Improper Fractions

Before multiplying mixed numbers, always convert them to improper fractions.

For example:

1frac{1}{2} times 2frac{2}{3}

Convert to improper fractions:

frac{3}{2} times frac{8}{3}

Multiply:

frac{24}{6} = 4

Real-Life Applications of Multiplying Fractions

Multiplying fractions is useful in everyday life, including:

  • Cooking & Baking – Adjusting recipes when changing portion sizes.
  • Construction & Carpentry – Measuring and cutting materials accurately.
  • Finance & Discounts – Calculating fractional percentages of amounts.

Multiplying fractions with unlike denominators is straightforward if you follow these steps:

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Simplify the fraction if necessary.

By practicing different types of fraction multiplication, including whole numbers and mixed numbers, you can master this skill and apply it in real-world situations.