Question

How many sixths are in $\dfrac{4}{3}$ ?

Answer 1

Hint: We are asked that in factor $\dfrac{4}{3}$ how many sixths are there. To answer this we will learn what does sixth mean. We will work on certain example like this then we will look how to find the number of sixth in $\dfrac{4}{3}$, we basically split $\dfrac{4}{3}$ in pieces where each pieces should be of magnitude sixth then we will find how many such pieces are there.

Complete step by step answer:
We are asked to find the sixth in $\dfrac{4}{3}$ , to do so we will first work on a certain example similar to this problem.
Now consider one is asking how many 2 are there in 6, so it means we have to look at how many 2 will be needed to make a 6.
So we will split 6 into pieces of length 2 and check how many pieces are there.
So, $6=2+2+2$
So there are 3 two’s which combine to give us ‘6’.
So in ‘6’ there are 3 two.
Easy way to solve such a problem is to divide the 6 by 2. So $6\div 2=3$
Similarly if one asks how many 3 are there in 39, it means that how many 3 combine to form 39.
So here also we just divide the 39 by 3 and get $\dfrac{39}{3}=13$
Hence 13 three are needed to make 39.
Now we work on our problem, we are asked how many sixths are in $\dfrac{4}{3}$ .
As we know that tenth means $\dfrac{1}{10}$ similarly sixth means $\dfrac{1}{6}$ .
So, how many sixth in $\dfrac{4}{3}$ , to find this we will divide $\dfrac{4}{3}$ by $\dfrac{1}{6}$
So, $\dfrac{4}{3}\div \dfrac{1}{6}=\dfrac{4}{3}\times \dfrac{6}{1}$
By simplifying we get –
$=\dfrac{4\times 6}{3}$
Solving further we get –
$=8$

Note:
Remember that while we divide by fraction then $\div $ changes to $\times $ and second fraction will always get reciprocal. Also we can check that our answer is correct by adding 8 times $\dfrac{1}{6}$ so we get $\dfrac{4}{3}$ then our answer is correct.
Now we add 8 times $\dfrac{1}{6}$ to check.
So, $\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}$ we get –
$\dfrac{8}{6}$
Simplifying we get –
$\dfrac{4}{3}$ so our solution is correct.