We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent $\displaystyle .8$

Because we are dividing$\displaystyle .8$ by $\displaystyle .4$, we need to split up our $\displaystyle .8$  into groups of $\displaystyle 4$

As you can see, we have $\displaystyle 2$ groups. Thus the answer is $\displaystyle 2$. 

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent $\displaystyle .4$

Because we are dividing $\displaystyle .4$ by $\displaystyle .2$ , we need to split up our $\displaystyle .4$ into groups of $\displaystyle 2$

We can see that we have 2 groups of 2, thus the answer is 2. 

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent .2

Because we are dividing .2 by .2, we need to split up our .2 into groups of .2:

We can see that we have 1 group, thus our answer is 1. 

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent $\displaystyle .9\textup:$

Because we are dividing $\displaystyle .9$ by $\displaystyle .3$, we need to split up our $\displaystyle .9$ into groups of $\displaystyle .3$:

As you can see, we have $\displaystyle 3$ groups; thus, $\displaystyle .9\div.3=3$

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent $\displaystyle .8\textup:$

Because we are dividing $\displaystyle .8$ by $\displaystyle .2$, we need to split up our $\displaystyle .8$ into groups of $\displaystyle .2$:

As you can see, we have $\displaystyle 4$ groups; thus, $\displaystyle .8\div.2=4$

We can use base ten blocks to help us solve this problem. First, we want to use base ten blocks to represent $\displaystyle .6\textup:$

Because we are dividing $\displaystyle .6$ by $\displaystyle .3$, we need to split up our $\displaystyle .6$ into groups of $\displaystyle .3$

As you can see, we have $\displaystyle 2$ groups; thus, $\displaystyle .6\div.3=2$ 

The problem that you are challenged to solve is $\displaystyle 7.8 \div 2=?$. 

$\displaystyle 7.8$ is the dividend, this is what is being broken up into groups. $\displaystyle 2$ is our divisor which is the number of groups you are making. We need to split $\displaystyle 7.8$ in half to see how many are in each group.

The first step is to place your decimal above your equation in the same place. It will line up with the decimal inside of your "long-division house". 

Next, we need to use or multiplication facts to determine what $\displaystyle 2$ can be multiplied by to make $\displaystyle 7$ or get close to it without going over. $\displaystyle 2\times 3=6$ is the fact that works best ($\displaystyle 2\times 4=8$ is too large). We will place the numeral $\displaystyle 3$ directly above the $\displaystyle 7$ in the ones place to indicate that $\displaystyle 3$ groups of $\displaystyle 2$ fit into the $\displaystyle 7$. We will put the product of $\displaystyle 2\times 3$ which was $\displaystyle 6$ underneath the $\displaystyle 7$ in the ones place and subtract the difference. The numbers above the "house" are our quotient or answer to the division problem.

Next, we will carry the $\displaystyle 8$ in the tenths place down and put it next to the $\displaystyle 1$. We will work with the numbers as if they were $\displaystyle 18$ when thinking of multiplication facts, but it should be noted this is actually $\displaystyle 1.8$ when you consider the decimal placement. $\displaystyle 2\times 9=18$ so we place the $\displaystyle 9$ above the "house" in the tenths place of our quotient and subtract the $\displaystyle 18$. We are left with $\displaystyle 0$ remaining so there is no remainder. 

Our final answer is $\displaystyle 3.9$, which means that half of $\displaystyle 7.8$ is $\displaystyle 3.9$

The problem that you are challenged to solve is $\displaystyle 13.71 \div 3=?$.

$\displaystyle 13.71$ is the dividend, this is what is being broken up into groups. $\displaystyle 3$ is our divisor which is the number of groups you are making. We need to split $\displaystyle 13.71$ in thirds to see how many are in each group.

The first step is to place your decimal above your equation in the same place. It will line up with the decimal inside of your "long-division house".

Next, we need to use or multiplication facts to determine what $\displaystyle 3$ can be multiplied by to make $\displaystyle 13$ or get close to it without going over. $\displaystyle 3\times 4=12$ is the fact that works best ($\displaystyle 3\times 5=15$ is too large). We will place the numeral $\displaystyle 4$ directly above the $\displaystyle 3$ in the ones place to indicate that $\displaystyle 4$ groups of $\displaystyle 3$ fit into the $\displaystyle 13$. We will put the product of $\displaystyle 3\times 4$ which was $\displaystyle 12$ underneath the $\displaystyle 13$ and subtract the difference. The numbers above the "house" are our quotient or answer to the division problem.

Next, we will carry the $\displaystyle 7$ in the tenths place down and put it next to the $\displaystyle 1$. We will work with the numbers as if they were $\displaystyle 17$ when thinking of multiplication facts, but it should be noted this is actually $\displaystyle 1.7$ when you consider the decimal placement. $\displaystyle 3\times 5=15$ so we place the $\displaystyle 5$ above the "house" in the tenths place of our quotient and subtract the $\displaystyle 15$. We are left with $\displaystyle 2$ remaining.

Finally, we carry down the $\displaystyle 1$ from the hundredths place and place it next to the $\displaystyle 2$ giving us $\displaystyle 2.1$ (or $\displaystyle 21$ for the purpose of our multiplication facts.) $\displaystyle 3\times 7=21$ so we place the $\displaystyle 7$ above the $\displaystyle 1$ in the hundredths place on top of our "house" and subtract the $\displaystyle 21$ leaving us with a remainder of $\displaystyle 0$.

Our final answer is $\displaystyle 4.57$

The problem that you are challenged to solve is $\displaystyle 16.84 \div 4=?$. 

$\displaystyle 16.84$ is the dividend, this is what is being broken up into groups. $\displaystyle 4$ is our divisor which is the number of groups you are making. We need to split $\displaystyle 16.84$ in quarters to see how many are in each group.

The first step is to place your decimal above your equation in the same place. It will line up with the decimal inside of your "long-division house".

Next, we need to use or multiplication facts to determine what $\displaystyle 4$ can be multiplied by to make $\displaystyle 16$ or get close to it without going over. $\displaystyle 4\times 4=16$ is the fact that works best. We will place the numeral $\displaystyle 4$ directly above the $\displaystyle 6$ in the ones place to indicate that $\displaystyle 4$ groups of $\displaystyle 4$ fit into the $\displaystyle 16$. We will put the product of $\displaystyle 4\times 4$ which was $\displaystyle 16$ underneath the $\displaystyle 16$ and subtract the difference. The numbers above the "house" are our quotient or answer to the division problem.

Next, we will carry the $\displaystyle 8$ in the tenths place down and put it next to the $\displaystyle 0$. $\displaystyle 4\times 2=8$ so we place the $\displaystyle 2$ above the "house" in the tenths place of our quotient and subtract the $\displaystyle 8$. We are left with $\displaystyle 0$ remaining.

Finally, we carry down the $\displaystyle 4$ from the hundredths place and place it next to the $\displaystyle 0$. $\displaystyle 4\times 1=4$ so we place the $\displaystyle 1$ above the $\displaystyle 4$ in the hundredths place on top of our "house" and subtract the $\displaystyle 4$ leaving us with a remainder of $\displaystyle 0$.

Our final answer is $\displaystyle 4.21$