Getting Confused Dividing Fractions

[rstratton11]

I was making a recipe and wanted to halve everything. Everything was easy until I got to 3/4. I got a little confused and instead of dividing by 2 I thought I should divide by 1/2. I know when dividing fractions you’re supposed to flip the dividing number so I flipped 1/2 and made it 2/1. I ended up multiplying 3/4 by 2/1 which made 6/4 and I could tell it was wrong because 6/4 is larger than 3/4 and I was trying to halve it. I realized after that I should’ve multiplied 3/4 by 1/2 getting 3/8 but it didn’t feel intuitive to me. Do you know of any way to remember when you’re trying to halve a fraction you don’t divide by half but you multiply?

 

[tkhunny]

Divide by 2
Multiply by 1/2
Same thing.

There is no such thing as "flip".

Divide by 2
Multiply by 2
NOT the same thing.

3/4 divided by 2 ==> (3/4) / 2 = (3/4)*(1/2) <== I'm guessing this is what you mean by "flip".

(3/4)*(1/2) = (3*1)/(4*2) = 3/8

This is why we teach mathematics, so that when something correct doesn't feel intuitive, you ignore that feeling and use the correct operation, anyway.

 

[Steven G]

half of 8/17 is 4/17since half of 8 is 4.
half of 12/19 is 6/19 since half of 12 is 6.

half of 3/4 is 1.5/4 = 3/8 (after doubling numerator and denominator)