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# Multiplying fractions and whole numbers 2

## Video transcript

multiply 6 times one-fourth simplify your answer and write it as a mixed number so let's just do the multiplication so at first when you try to multiply 6 times 1/4 you'll be like what gee you know I know how to mow I know how to multiply a fraction times a fraction I know how to multiply a whole number times the whole number but what about a whole number times a fraction and kind of the key insight you need here is that any whole number can be written as a fraction we can rewrite 6 we can rewrite 6 as 6 over 1 right 6 divided by 1 is 6 6 ones is 6 depending how you think about it this is exactly the same thing as 6 so we just rewrote our whole number as a fraction you can do it for any number 10 is the same thing as 10 over 1 so this becomes 6 over 1 times 6 over 1 times 1/4 times 1/4 and then we just multiply the fraction so we multiply the numerators so this is equal to 6 times 1 is our numerator let me do that in another color so this becomes 6 times 1 for our numerator and 1 times 4 for our denominator for the number on the bottom and so this will become 6 over 4 and right now it's just as an improper fraction and it's also not in lowest terms you immediately see 6 and 4 are both divisible by 2 so let's divide them both by 2 if you divide 6 by 2 and I'll do it a new color again you divide 6 by 2 you get 3 you die divide 4 by 2 you get 2 so this is equal to 3 halves so it's still written as an improper fraction we now have to write it as a mixed number and the process for writing it is a mixed number you just divide the denominator into the numerator so this just becomes this just becomes 2 into 3 divided 2 into 3 it goes 2 goes into 3 one time 1 times 2 is 2 you subtract you have a remainder of 1 so this will become so this is this will become one whole one whole + 1 over 2 left over + 1 / - so this is 1 and 1/2 so that's alright and answer we've just simplified the answer and wrote it as a mixed number or we could simplify it at this stage we could say right here we'll look we could divide what's eventually going to be in the numerator by 2 and get a 3 there and divide what's eventually in the denominator by 2 and get a 2 there 3 times 1 is 3 1 times 2 is 2 so it's 3 halves and you do this exact same process say that 3 halves is the same thing as 1 and 1/2 either either one of those will work and let's think about why this makes sense let's think about what 6 times 1/4 is let's let's draw let me draw one for let's say that that is 1/4 right there and let's do 6 of them so that's 1/4 that's 2/4 that's 3/4 that's 4/4 which would be a whole and then you have 5/4 and then you have 6 4 so this is 6 times 1/4 6 times 1/4 this right here is 4/4 this right here is 4 over 4 which is equal to a 1 so this is equal to 1 and then this right here is to 1/4 it's or this right here is 2/4 and you could draw you can imagine this is 2 out of a potential if a whole has to have two more of them has to have four of them so this is 1 and 1 and let me do the same colors 1 and 1 and 1/2 right 2 out of 4 is the same thing as 1 over 2 so this right here is one out of a possible out of a possible one and then 2 so this is 1 and 1/2 1 and 1/2 which is exactly what we got before