Dividing fractions example 2 | Fractions | Pre-Algebra | Khan Academy

TL;DR

Dividing a fraction by another fraction is the same as multiplying by the reciprocal of the second fraction.

Transcript

Divide and write the answer as a mixed number. And we have 3/5 divided by 1/2. Now, whenever you're dividing any fractions, you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal. So this thing right here is the same thing as 3/5 times-- so this is our 3/5 right here, and instead of a division sign,... Read More

Key Insights

• 🗂️ Dividing fractions by fractions can be solved by multiplying by the reciprocal of the divisor.
• ✖️ The process involves multiplying the numerators together and the denominators together.
• 😑 The result can be expressed as an improper fraction or a mixed number.
• 🗂️ Dividing fractions by fractions can be understood through the concept of grouping and the relationship between the dividend and the divisor.
• 🗂️ Dividing by 1/2 is the same as multiplying by 2, as demonstrated using objects divided into groups.
• 🗂️ Understanding the concept of dividing fractions helps in solving various mathematical problems efficiently.
• 🤝 Multiplying by the reciprocal is a useful strategy when dealing with complex fraction operations.

Questions & Answers

Q: What is the relationship between dividing fractions and multiplying by the reciprocal?

Dividing fractions by a fraction is equivalent to multiplying by the reciprocal of the second fraction. This can be understood by considering the concept of grouping.

Q: How do you calculate 3/5 divided by 1/2?

To determine 3/5 divided by 1/2, multiply 3/5 by the reciprocal of 1/2, which is 2/1. The result is 6/5.

Q: What is the process for expressing an improper fraction as a mixed number?

To convert an improper fraction like 6/5 into a mixed number, divide the numerator (6) by the denominator (5). The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part.

Q: Can the concept of dividing fractions by fractions be explained using a real-life example?

Yes, a real-life example is demonstrated by dividing a group of four objects into groups of 1/2. Each group contains half of an object. This results in eight groups, showing that dividing by 1/2 is the same as multiplying by 2.

Summary & Key Takeaways

• Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction.

• In the given example (3/5 divided by 1/2), the calculation involves multiplying 3/5 by 2/1.

• The result, when expressed as an improper fraction, is 6/5. When written as a mixed number, it is 1 and 1/5.