Make 3 into 3 1 :. What are the steps to divide fractions? In order, the steps are: Leave the first fraction in the equation alone. Turn the division sign into a multiplication sign. Flip the second fraction over find its reciprocal. Multiply the numerators top numbers of the two fractions together.
Multiply the denominators bottom numbers of the two fractions together. How do we divide decimals? To divide decimal numbers: Multiply the divisor by as many 10's as necessary until we get a whole number. Remember to multiply the dividend by the same number of 10's. What does it mean to divide fractions? A fraction is part of a whole number. It has two parts — a numerator and a denominator. Dividing a fraction.
Dividing a fraction by another fraction is the same as multiplying the fraction by the reciprocal inverse of the other.
We get the reciprocal of a fraction by interchanging its numerator and denominator. Why do we multiply fractions straight across? Multiplying Fractions. Did you notice that, when you take your original amount in this case, 20 and divide it by a number that continues to get smaller 10, then 5, then 2 , we end up with an answer that gets larger. Follow this logic into fractions, keeping in mind that fractions are not only less than 10, 5, and 2, but 1. Using this pattern, we determine that dividing the 20 screwdrivers by a number less than 1 would get us a larger answer than if we divided the 20 by 10, 5, or 2.
This does not mean that we end up with 40 screwdrivers, though. What it means is that we end up with 40 parts of screwdrivers.
You have to imagine that each of the screwdrivers were split into 2. Twenty screwdrivers split in half would give us 40 pieces in the end. The question now becomes, how do we do this mathematically? The answer lies in using what is known as a reciprocal. Here is the definition. Reciprocal : A number that has a relationship with another number such that their product is 1.
This means that, when you take a number such as 5 and then multiply it by its reciprocal, you will end up with an answer of 1. We could also write the number 5 as a fraction. To find the answer, we have to go back to multiplying fractions. Remember that, when we multiply fractions, we just multiply the numerators together and then multiply the denominators together. As far as I understand the reciprocal of a number the inverse of that number, that still doesn't clarify why it is needed.
For many years I've only ever done math like if I were a robot. I just did it and never understood what I was doing. So when I went and divided fractions I just used the reciprocal, because "that was the way to do it". I want to understand math at a deeper level, especially subjects like probability, statistics, calculus, and linear algebra. To do that I have to understand the fundamentals however. And I'm assuming that you're already comfortable with how to multiply fractions.
We need to go back to what division is supposed to achieve in the first place. This computation hopefully also gives some ides why it works, at least part way. But this memory trick itself then also serves as motivation for considering the reciprocal to be an interesting operation in its own right in higher algebra. There are already some excellent algebraic answers to this question, but I'd like to provide an answer based on the grade school meaning of division.
When we divide 20 by 4, we're asking for the answer to the question "Given 20 items distributed evenly to 4 piles, how many items are in each pile? When we divide 8 by a third, we're asking for the answer to the question "Given 8 items distributed evenly to a third of a pile, how many items are in each whole pile? Because each third of a pile has 8, and we want to know how much a whole pile 3 times larger has, we can use multiplication to compute the answer as
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