What is Multiplying Two Fractions?

S1-SA2-1111

Grade Level:

Class 5

Maths, Computing, AI, Physics, Probability

Definition

What is it?

Multiplying two fractions means finding a 'part of a part'. You combine two fractions to get a new fraction that represents a portion of the original portion. It tells you what fraction of the whole you get when you take a fraction of another fraction.

Simple Example

Quick Example

Imagine you have half (1/2) a pizza. If your friend eats one-third (1/3) of *your half*, how much of the whole pizza did your friend eat? You would multiply 1/2 by 1/3 to find out.

Worked Example

Step-by-Step

Let's multiply 2/3 by 1/4.

Step 1: Multiply the numerators (the top numbers) together.
2 x 1 = 2

---Step 2: Multiply the denominators (the bottom numbers) together.
3 x 4 = 12

---Step 3: Write the new fraction with the new numerator and denominator.
The new fraction is 2/12.

---Step 4: Simplify the fraction if possible. Both 2 and 12 can be divided by 2.
2 ÷ 2 = 1
12 ÷ 2 = 6

---Answer: So, 2/3 multiplied by 1/4 is 1/6.

Why It Matters

Understanding fraction multiplication is crucial in fields like engineering and science for calculating proportions and scaling. Computer programmers use it when dealing with data compression or image resizing. Even physicists use fractions to describe parts of a whole in experiments.

Common Mistakes

MISTAKE: Adding the denominators instead of multiplying them. For example, multiplying 1/2 and 1/3 and getting 1/5. | CORRECTION: Always multiply the numerators together and the denominators together separately.

MISTAKE: Cross-multiplying or finding a common denominator like you do for adding/subtracting fractions. | CORRECTION: Common denominators are not needed for multiplication. Just multiply numerator by numerator and denominator by denominator.

MISTAKE: Forgetting to simplify the final answer. For example, leaving 6/12 instead of 1/2. | CORRECTION: Always check if the resulting fraction can be simplified by dividing both the numerator and denominator by their greatest common factor.

Practice Questions

Try It Yourself

QUESTION: What is 1/2 multiplied by 3/4? | ANSWER: 3/8

QUESTION: A recipe calls for 3/4 cup of sugar. If you only want to make half (1/2) of the recipe, how much sugar do you need? | ANSWER: 3/8 cup

QUESTION: Riya completed 4/5 of her homework. Of the completed homework, 1/2 was Maths. What fraction of her total homework was Maths? Simplify your answer. | ANSWER: 2/5

MCQ

Quick Quiz

Which of these is the correct way to multiply 2/5 by 3/7?

(2+3) / (5+7)

(2x3) / (5x7)

(2x7) / (5x3)

Find a common denominator first

The Correct Answer Is:

To multiply fractions, you multiply the numerators together and the denominators together. Option B correctly shows (2x3) as the new numerator and (5x7) as the new denominator.

Real World Connection

In the Real World

Imagine a tailor in India has 5/6 of a roll of fabric left. If he uses 1/2 of that remaining fabric to make a kurta, he's multiplying 5/6 by 1/2 to find out what fraction of the original roll he used. This helps him manage his inventory and order more fabric.

Key Vocabulary

Key Terms

NUMERATOR: The top number in a fraction, showing how many parts are being considered. | DENOMINATOR: The bottom number in a fraction, showing the total number of equal parts the whole is divided into. | SIMPLIFY: To reduce a fraction to its lowest terms by dividing both numerator and denominator by their greatest common factor. | PRODUCT: The result of multiplying two or more numbers.

What's Next

What to Learn Next

Next, you can explore 'Dividing Fractions'. It's closely related and builds on your understanding of multiplication. Once you master both, you'll be ready for more complex fraction problems!