Question

What is 3 1\2 divided by 2\3

Answer 1

Dividing Mixed Fractions

In this response, I will teach you a quick method to divide mixed fractions. The method we will be used is Keep Switch Flip (KSF) which will be later discussed in this response. The answer will be at the bottom if you wish to skip to the answer.

Step By Step Answer

The problem we will be solving is
`3 (1)/(2)` ÷
`(2)/(3)`. We will used the method KSF. KSF (Keep Switch Flip) is a method that is used to quickly solve division problems. To do the method, you must keep the first fraction, switch the division sign to multiplication sign, and flip the other fractions.

Lets step the problem out!

Keep

First,
`3(1)/(2)` is a mixed fraction, and we will be changing that to not be a mixed fraction. The way we do this is by multiplying the denominator and the whole number, then adding the numerator. So, 3 × 2 = 6. Then, 6 + 1, which is 7. Now, the mixed fraction turns into
`(7)/(2)`.

So, the equation is now
`(7)/(2)` ÷
`(2)/(3)`.

Switch

Next, we need to switch the division sign to a multiplication sign.

So, the equation is now
`(7)/(2)` ×
`(2)/(3)`.

Flip

Now, we have to flip
`(2)/(3)` to
`(3)/(2)`. This is called finding the reciprocal. Finding the reciprocal is very simple. When someone asks you to find the reciprocal of
`(2)/(4)` for example, the answer you should put is
`(4)/(2)`. Getting back on topic, the equation is now
`(7)/(2)` ×
`(3)/(2)`.

Answering the Problem

`(7)/(2)` ×
`(3)/(2)`

7 × 3 = 21

2 × 2 = 4

`(7)/(2)` ×
`(3)/(2)` =
`(21)/(4)`, however, we can reduce this. 4 can go into 21 5 times, so the answer is
`5(1)/(4)`.

Answer:

`3 (1)/(2)` ÷
`(2)/(3)` =
`5(1)/(4)`