# Algebraic expressions with fraction division | Introduction to algebra | Algebra I | Khan Academy

Let’s look at a few algebraic expressions, which involve multiplying fractions. We have a on b, a over b multiplied by c over d. How much will this be? I advise you to pause the video and try to calculate it yourself. When you multiply fractions, you just multiply the numerators, you also multiply the denominators. The numerators here are a and c, you multiply them. This is a multiplied by c, which we can write as ac, same as a over c, all over denominator b multiplied by d, b to d. Instead of multiplying what would happen, if we separate them? If we have a on b, a over b divided by … divided by c over d, how much will this be? I recommend you again to stop the video and find it yourself. When you divide by a fraction, this is equal to multiplication at its reciprocal value. This will be the same as a over b multiplied by the reciprocal value of this. Multiplied by d over … I will use the same color so as not to confuse you. d was in purple multiplied by d over c, and then becomes that task. I shouldn’t have used it this multiplication symbol as we are in the field of algebra and you can confuse it with x, so I will write it as multiplied, multiplied by d, d over c multiplied by d over c. What happens? The numerator is a over d, ad on … on bc, on b on c. Let’s look at a task that is perhaps more complex and see if you can solve it. Let’s say we have, … I don’t know, I’ll write 1 on a, minus 1 over b, all this on c, and let’s divide everything by 1 over d. Here is a more complex expression, from those we have already considered but know everything we need to solve it, so I advise you again to stop the video and try to simplify the expression on your own, to remove these operators and get a liver equal to that. Let’s solve the expression step by step, (1 / a) – (1 / b), I will only work on this part. We have (1 / a) – (1 / b), we know how to solve this, we find a common denominator, I will write it here. (1 / a) – (1 / b), will be equal to … we can multiply 1 / a by b / b, we will get b / ba, notice that I haven’t changed this value, I just multiplied by 1, b / b, minus, I will multiply numerator and denominator by a, minus a / ab, I can also write it as ba. I did it to get it the same denominator. This will be equal to b – a, on, I can write ba or ab. This will be equal to this numerator, b – a on ab, then if you divide it by c, it’s like multiplying on the reciprocal of c. If you divide by c, it’s like multiplying, it’s the same as multiplying by 1 / c. And if … I’ll just keep going, if divided by 1 / d, if you split … notice it’s the same like this division. If I divide by c, it’s the same as multiplying by the reciprocal of c. Finally divide by 1 / d, which is the same as multiplication on the reciprocal of 1 / d. The reciprocal of 1 / d is d / 1. What is the result? In the numerator I have (b – a) .1.d. We can write as d. (B – a), and in the denominator we have abc, ab and c. Finally, we can reveal the brackets, we can multiply by d and we will get … here we deserve the sound of drums :), we can write this as d over b, d by b minus d … oops, I want to write this down in the same green color to see how exactly does the multiplication, minus d over a, all this on abc. That is all! We’re ready! 