Welcome to Math with Mr. J. In this video, I'm going to cover how to divide a fraction by a fraction. Now, when working with fractions and division, we need to remember three steps. Keep, switch, flip. We can also think multiply by the reciprocal.
When we flip a fraction, that's called the reciprocal. So this means we're going to use multiplication to solve these. This actually makes the process simpler. Now how and why this works is a topic for another video. I'll drop that link down in the description.
Let's jump into number one where we have three-fourths divided by one-seventh. So we are seeing how many one-sevenths we can make out of three fourths or how many one sevenths are in three fourths, so to speak. So let's start by rewriting this problem using keep, switch, flip. So we always keep the first fraction or number. So we keep 3 fourths as is.
We switch to the opposite or inverse of division, which is multiplication. And since we switched to the opposite or inverse of division, we're going to flip the second fraction. So the 7 is going to be our numerator and the 1 is going to be our denominator.
So we end up with 7 over 1. Once we get to this point, it's a multiplying fractions problem. So we can multiply straight across. 3 times 7 is 21. And then 4 times 1 is 4. And we end up with 21 fourths.
Now that's an... improper fraction, so we do not want to leave it. We need to divide our numerator of 21 by 4. How many whole groups of 4 are in 21? Well, 5. That gets us to 20. So 5 whole groups of 4, that's our whole number of the mixed number here. Now that doesn't hit 21 exactly.
We have a remainder of 1, so that's our numerator in our fractional part of the mixed number. and we keep our denominator of 4 the same. Always look to see if you can simplify the fractional part of a mixed number.
1 fourth is in simplest form, so we are done. 5 and 1 fourth is our answer for number 1. So 3 fourths divided by 1 seventh equals 5 and 1 fourth. Let's move on to number 2, where we have 2 thirds divided by two fifths.
Keep, switch, flip. So keep two thirds here. Switch the multiplication and then flip that second fraction. So five over two.
And now we can multiply straight across. Two times five is ten. Three times two is six. So we get ten sixths. So That's an improper fraction.
We need to convert to a mixed number. So 10 divided by 6. How many whole groups of 6 out of 10? Well, 1. And we get a remainder of 4. Keep our denominator of 6 the same.
We can simplify 4 sixths. We have a common factor of 2. So let's divide each of these by 2 here. and we get 1. and two thirds. So our answer for number two is one and two thirds.
Two thirds divided by two fifths equals one and two thirds. So there you have it. There's how you divide a fraction by a fraction.
I hope that helped. Thanks so much for watching. Until next time, peace.