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Multiplying fractions is an essential skill in mathematics, and it plays a crucial role in various real-life scenarios, such as cooking, scaling, and problem-solving. Understanding the process of multiplying fractions can sometimes be challenging, but with a systematic approach, it becomes much more manageable.
Step 1: Understanding Fraction Multiplication:
Before diving into the step-by-step process, it’s crucial to understand the fundamentals of fraction multiplication. Multiplying fractions involves multiplying the numerators (top numbers) and denominators (bottom numbers) separately. The product of the numerators becomes the new numerator, while the product of the denominators becomes the new denominator.
Step 2: Simplify Fractions (if necessary):
Before multiplying, simplify the fractions involved to make the calculation easier. To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF). This step ensures that the resulting product is in its simplest form.
Step 3: Multiply the Numerators:
Once you have simplified the fractions, multiply the numerators (the top numbers) together. The resulting product will become the new numerator of the final fraction.
Step 4: Multiply the Denominators:
Next, multiply the denominators (the bottom numbers) together. The product will become the new denominator of the final fraction.
Step 5: Combine the Results:
Now that you have the new numerator and the new denominator, combine them to form the final fraction. The numerator will be the product obtained from step 3, and the denominator will be the product obtained from step 4.
Step 6: Simplify the Result (if necessary):
If the resulting fraction can be simplified further, divide the numerator and denominator by their greatest common factor (GCF) to obtain the simplified form. This step ensures that the fraction is in its simplest form.
Example 1:
Let’s illustrate the steps with an example: multiplying 2/3 by 3/5.
Step 1: Understand Fraction Multiplication:
– Numerators: 2 × 3 = 6
– Denominators: 3 × 5 = 15
Step 2: Simplify Fractions (if necessary):
– Both fractions are already simplified.
Step 3: Multiply the Numerators:
– Numerator: 2 × 3 = 6
Step 4: Multiply the Denominators:
– Denominator: 3 × 5 = 15
Step 5: Combine the Results:
– Final fraction: 6/15
Step 6: Simplify the Result (if necessary):
– The fraction can be simplified by dividing both the numerator and denominator by their GCF.
– GCF(6, 15) = 3
– Simplified fraction: 6 ÷ 3 / 15 ÷ 3 = 2/5
Example 2:
Let’s illustrate the steps with an example: multiplying 3/4 by 2/5.
Step 1: Understand Fraction Multiplication:
Numerators: 3 × 2 = 6
Denominators: 4 × 5 = 20
Step 2: Simplify the Fractions (if necessary):
Both fractions are already in their simplest form.
Step 3: Multiply the Numerators:
Numerator: 3 × 2 = 6
Step 4: Multiply the Denominators:
Denominator: 4 × 5 = 20
Step 5: Combine the Results:
Final fraction: 6/20
Step 6: Simplify the Result (if necessary):
The fraction can be simplified by dividing both the numerator and denominator by their GCF.
GCF(6, 20) = 2
Simplified fraction: 6 ÷ 2 / 20 ÷ 2 = 3/10
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