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### Course: Arithmetic>Unit 15

Lesson 5: Dividing fractions by fractions

# Dividing a whole number by a fraction

Dividing a whole number by a fraction involves multiplying the whole number by the fraction's reciprocal. For example, when dividing 4 by 2/3, multiply 4 by 3/2, resulting in 12/2, which equals 6. This method demonstrates how many sections of the fraction fit into the whole number.

## Want to join the conversation?

• What's a reciprocal? ()
• But, why does it work by using the reciprocal? How did he come to the conclusion he needs to use the reciprocal to find the correct answer?
• So reciprocal means to flip
• yes,a reciprocal means u flip.(in fractions)
• Am I supposed to multiply the numerators with the 4/1 ( )?
I'm VERY confused. How do I do this but in an easier way`?` (note: I am very new to this)
• Hey Neika!!

What do you mean by an easier way?

If you had a fraction like 5/6, you would multiply the "5" (as it is in the numerator) by the "4" in the fraction 4/1, as the 4, in this case, is in the numerator. Multiplying both numerators would give you 20/6, which cannot be simplified further. Did this help at all? Tell me if not.

P.S Just thought I'd like to mention that your grammar is better than almost any 10th grader I know, and education is definitely the key to freedom! Wise words from a wise person!
• how do you divide two whole numbers with fractions?
• You do the reciprocal of the second fraction but instead of dividing, you multiply.
• Ok I'm a bit confused about how to know what fraction to flip. In the video before this on Sal used the example of 2/3 divided by 5. he flipped the 5 to make it 1/5. So it was 2/3 X 5/1= 2/15's. In this video he flips the 2/3, which isn't the whole number. I'm a bit confused about why he didn't flip the whole number. Any help would be great thanks!
• You always flip the number that follows the division symbol. Some people use the phrase "keep change flip" to help them remember what to do.
"keep" means "keep the first number as is"
"change" means "change division to multiplication"
"flip" means "flip the next number".

Hope this helps.
• Whats a reciprocal?
• a rciprocal is like 1/3 is the reciprocal of 3 because 3*1/3=1 p.s might be confusing to you chase sorry if it is
• You explained by 2/3 fits into 4, 6 times but you never explained why it makes sense that 4 divided by 2/3 is the same thing as dividing 4 by the reciprocal. Can you please send me a video where I might have missed this explanation? Why does it make sense to multiply 4 by the reciprocal of 3/2, to solve 4 divided by 2/3?
• We multiply by the reciprocal while dividing because the division is basically inverse multiplication. For example, dividing by 4 is basically multiplying by 1/4. And it is the same for fractions. Dividing by 1/2 is the same thing as multiplying by 2. If you still feel confused, ask! I'll try explaining further and I bet some people on Khan might have a clearer answer.