Divide. Simplify each quotient, if possible. (25)/(32) ÷(5)/(28)

Name: Problem 21, Chapter 4: Prealgebra
Uploaded: 2020-07-24T04:11:38-08:00
Duration: 4 min 18 s
Channel: Ann Douglas
Description: Divide. Simplify each quotient, if possible. (25)/(32) ÷(5)/(28)

step 1 Okay, we're dividing fractions. So the first thing you do when you're dividing fractions is to a

Divide. Simplify each quotient, if possible. (25)/(32)...

Key Concepts

Simplification

Simplification is the process of reducing a fraction to its simplest form by canceling any common factors between the numerator and denominator. This important mathematical technique ensures that the final answer is presented in the most reduced and understandable form.

Multiplication of Fractions

Multiplying fractions involves multiplying their numerators together and their denominators together. Once a division problem is converted into a multiplication problem using reciprocals, this straightforward operation is applied to calculate the product.

Division of Fractions

Division of fractions involves dividing one fraction by another. In mathematics, this process is transformed into multiplication by using the reciprocal of the divisor. This key concept is foundational in understanding how to approach any problem where one fraction is divided by another.

Reciprocal

The reciprocal of a fraction is obtained by swapping its numerator and denominator. This is a critical step in dividing fractions because it allows the division operation to be expressed as multiplication, thus simplifying the problem-solving process.

Transcript

00:01 Okay, we're dividing fractions.

00:03 So the first thing you do when you're dividing fractions is to always rewrite the problem as a multiplication problem.

00:09 So when we do that, our first fraction stays the same.

00:14 So 2428s, and i'm going to change my division sign to multiplication, and i'm going to take the reciprocal of my second fraction.

00:23 So that's always the first thing you do, and it doesn't matter what you're looking at fraction -wise.

00:29 Then we want to multiply these together.

00:34 And this is where intention comes in, because i've got a lot of numbers here, a lot of composite numbers that i'm sure i can probably simplify.

00:44 So i'm going to say i've got 24 times 16 on top, and i've got 28 times 3 on the bottom.

00:53 All right, so now i need to think about how am i going to factor these? so i know i've got a three right here and three can't be factored.

01:00 Three is a prime number.

01:03 But three is also a factor of 24.

01:07 So i'm going to rewrite my 24 as three times eight.

01:15 And then i need to think about how am i going to factor my 16? well, the three is going to be taken.

01:22 The three's already caught up with those, that one right there.

01:27 So i'm looking at 16 and 28 and what common factors do they have.

01:34 And the one that comes to mind is 4.

01:36 That's the biggest one i see right now.

01:39 So i'm going to rewrite my 16 using a factor of 4, and since 16 is a square number happens to be 4 times 4.

01:46 And now i'm going to do the, now i'm going to factor my bottom the same way with that same intention, that same thought.

01:54 So i'm going to take the 28, and i'm going to rewrite that...

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