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### Course: Math (NSDC) - English>Unit 3

Lesson 8: Multiplying fractions

# Multiplying fractions and whole numbers visually

Learn the concept of multiplying fractions and whole numbers. Watch how to visually represent this process and practice understanding the relationship between fractions and whole numbers in multiplication. Created by Sal Khan.

## Want to join the conversation?

• I'm just wanting to confirm and understand why:
2/5 = 2 x 1/5
and why isn't it like before with mixed numerals where this is done:

2 x 1/5 = ((2 x 5)+1)/5 = 11/5 ?

is there a conceptual difference i am missing? thanks in advance !! :)
• Yes there's a conceptual difference.

I believe you are confusing multiplication of a whole number and a fraction, with addition of a whole number and a fraction. Many students have difficulty in math, including higher levels such as algebra, ultimately because they confuse the fundamental concepts of addition and multiplication.

((2 x 5)+1)/5 is equivalent to the mixed number 2 and 1/5. This mixed number means 2 + 1/5, not 2 x 1/5.

2 x 1/5 can be thought of as the repeated addition 1/5 + 1/5, which is clearly 2/5.
• *why can't we just add it the normal way.like 1/5+3/4=4/9*
• You cant just add the denominators as well as adding the numerators, you need to find a common factor.
• If whatever happens to the denominator happens to the numerator why is the whole number only multiplied by the numerator and not the denominator? Are whole numbers +-x/ fractions only between the whole number and numerator?
• Technically, A whole number n is the same as n/1. Since anything multiplied by 1 is itself, The denominator doesn't change.
You only multiply both numbers by the whole number when you're finding a common denominator.
• If 1/2 x 5 is 5/2 does that mean 5 x 1/2 is the same?
• yes because 1/2 x 5 is the same as 1/2 x 5/1 (because 5 ones are five) and if you multipy 1 x 5 (the top) and 2 x 1( the bottom) you get 5/2 so you are correct
• I don't understand please help I am trying to get like what to do other than this fifths
• multiplying fractions are one of the hardest fractions but sometimes it can be easy for some people
• how would it be smaller instead of being bigger?
• this is because of the fact that the fraction is not equal to one, so it makes the number smaller. Think of these fractions as decimals, when you multiply a number by a decimal it becomes smaller. so 3 x 1/3 is 1, because it becomes 3/3 which is one
(1 vote)
• why is it that when you add denominators together, they aren't different. For example: 2 fourths + 2 fourths do not equal 4 eighths. it equals 4 fourths instead. Why is that true?
• Try imagining that the denominator is telling us how big the parts are. Adding parts together doesn't the size of those parts individually, but changes their amount over-all.

Hope this helps.
• what do you do if you like math to much :D