Converting mixed numbers to improper fractions | Fractions | Pre-Algebra | Khan Academy

TL;DR

To convert a mixed number to an improper fraction, multiply the whole-number part by the denominator, add the original numerator, and place the result over the original denominator. For 5 and 1/4, calculate 5 × 4 + 1 = 21, giving 21/4. Read on to see why rewriting five wholes as 20 fourths makes this method work.

Transcript

Write 5 and 1/4 as an improper fraction. So just as a reminder, an improper fraction is one where the numerator is greater than or equal to the denominator. So improper fraction means that the numerator-- and actually, I should say the absolute value of the numerator-- is greater than or equal to the absolute value of the denominator. I could have ... Read More

Key Insights

• 🟰 An improper fraction has a numerator that is greater than or equal to the denominator.
• #️⃣ Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.
• #️⃣ The method of converting mixed numbers to improper fractions is based on representing the whole number as a fraction and combining it with the fraction part.
• #️⃣ The numerator of an improper fraction is obtained by adding the product of the whole number and the denominator to the numerator of the mixed number.
• ❓ The resulting improper fraction can be simplified if possible.
• 🎭 Understanding the concept of improper fractions helps in performing operations like addition, subtraction, multiplication, and division with fractions.
• 💨 Converting mixed numbers to improper fractions provides a way to compare and order fractions.

Questions & Answers

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

Multiply the whole-number part by the denominator, then add the numerator. Use that sum as the new numerator and keep the original denominator.

Q: How do you convert 5 and 1/4 to an improper fraction?

Multiply 5 by 4 to get 20, then add 1 to get 21. Keep the denominator 4, so 5 and 1/4 equals 21/4.

Q: What is an improper fraction?

An improper fraction is one in which the absolute value of the numerator is greater than or equal to the absolute value of the denominator. In 21/4, the numerator 21 is greater than the denominator 4.

Q: Why does multiplying the whole number by the denominator work?

Each whole can be expressed using the mixed number’s denominator. With denominator 4, one whole is 4/4, so five wholes are 5 × 4/4, or 20/4.

Q: Why is 5 equal to 20/4?

Each whole equals 4/4. Therefore, five wholes equal five groups of 4/4, which is 20/4.

Q: Why do you add 1 after multiplying 5 by 4?

The five wholes account for 20 fourths, and the mixed number also contains 1/4. Because both quantities have denominator 4, their numerators can be added: 20 + 1 = 21.

Q: Does the denominator change when converting 5 and 1/4?

No, the denominator remains 4. The five wholes are rewritten in fourths, and the existing fractional part is already measured in fourths.

Q: What formula represents the conversion of 5 and 1/4?

The conversion is written as (5 × 4 + 1)/4. Evaluating the numerator gives 21, so the resulting improper fraction is 21/4.

Summary & Key Takeaways

• An improper fraction has a numerator that is greater than or equal to the denominator.

• Mixed numbers can be written as improper fractions by multiplying the whole number by the denominator and adding the numerator.

• 5 and 1/4 can be written as 21/4 by multiplying 5 by 4 and adding 1.