How to Multiply and Divide Fractions #10

Summary

This educational video script explains the process of multiplying and dividing fractions. It simplifies the multiplication of fractions by demonstrating how to multiply numerators and denominators separately, followed by simplification if possible. The script also covers multiplying fractions by mixed numbers, emphasizing the conversion of mixed numbers to improper fractions for easier calculation. Dividing fractions is addressed by flipping the second fraction and converting division to multiplication. Examples are provided to illustrate each concept, ensuring a clear understanding of fraction operations.

Takeaways

• 🔢 Multiplying fractions involves multiplying the numerators together to get the new numerator and the denominators together to get the new denominator.
• 📉 After multiplying, it's important to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
• 📈 When multiplying fractions, if both fractions are less than one, the result is a fraction that represents a smaller portion of the whole.
• 🔄 To divide fractions, you flip the second fraction (divisor) upside down and change the division to multiplication.
• 🍕 An example given is multiplying one-half by one-third, which results in one-sixth, illustrating taking a portion of a portion.
• 📖 When dealing with mixed numbers, it's easier to first convert them to improper fractions before multiplying or dividing.
• 🔄 Converting a mixed number to an improper fraction involves multiplying the whole number by the denominator and then adding the original numerator.
• ✅ The video provides a step-by-step guide on how to multiply and divide fractions, including converting mixed numbers and simplifying results.
• 📉 Simplification of fractions is a necessary step to express the answer in its simplest form, which may involve dividing by common factors.
• 📝 The script concludes with a summary that reinforces the methods taught for multiplying and dividing fractions, ensuring understanding.

Q & A

What is the basic method for multiplying fractions?

To multiply fractions, you multiply the numerators together to get the new numerator and the denominators together to get the new denominator.

How do you simplify a fraction after multiplying?

After multiplying, you simplify the fraction by dividing the numerator and the denominator by their greatest common divisor.

What is the result when multiplying 7/15 by 3/4?

Multiplying 7/15 by 3/4 results in 21/60, which simplifies to 7/20 after dividing both the numerator and denominator by 3.

Can you multiply fractions without simplifying?

Yes, you can multiply fractions without simplifying, but it is common practice to simplify the result for clarity and to reduce the fraction to its simplest form.

What is the result of multiplying 4/7 by 9/5?

Multiplying 4/7 by 9/5 results in 36/35, which is already in its simplest form and cannot be simplified further.

How do you multiply a fraction by a mixed number?

To multiply a fraction by a mixed number, it's easier to first convert the mixed number to an improper fraction before multiplying.

What is the improper fraction form of two and three-quarters?

Two and three-quarters is converted to an improper fraction by multiplying the whole number (2) by the denominator (4) and adding the numerator (3), resulting in 11/4.

What happens when you multiply fractions that are less than one?

Multiplying fractions that are less than one results in a smaller number, as you are taking a portion of something that is already a fraction of the whole.

How do you divide fractions?

To divide fractions, you flip the second fraction upside down (invert it) and change the division to multiplication, then multiply the fractions as usual.

What is the result of dividing 3/4 by 5/9?

Dividing 3/4 by 5/9 results in 27/20, which cannot be simplified further.

How do you convert an improper fraction to a mixed number?

To convert an improper fraction to a mixed number, divide the numerator by the denominator, use the quotient as the whole number, and the remainder as the new numerator with the same denominator.