Decimals

Lesson

We have looked at some division problems with numbers in the hundreds, where a decimal answer is needed. Now we can look at problems that have numbers in the thousands, and solve them using many of the same processes.

In Video 1, you can see we have a remainder, which we write as a fraction. So, if we are solving $2303$2303 divided by $4$4, we would express our remainder as $\frac{3}{4}$34. Next, we find an equivalent fraction in tenths or hundredths, and then we can express that as a decimal. This process is what we do each time we have a remainder to write as a decimal.

In our second video, we look at short division, which is just another way to solve our division problem. In our example, we can't share our units out evenly, so we see just how important our zero place holder is. We can then look at our remainder as a fraction, and use an equivalent fraction in hundredths, which then allows us to write our remainder as a decimal.

What about solving this using long division? You could do just that, using one of the problems above, and see if you get the same answer!

We are going to solve the division $2148\div8$2148÷8 by partitioning $2148$2148.

Complete the following number sentence:

$2148=1600+\editable{}+64+4$2148=1600++64+4

Complete the following number sentence:

$2148\div8=1600\div8+\editable{}\div8+64\div8+4\div8$2148÷8=1600÷8+÷8+64÷8+4÷8

Complete the divisions:

$2148\div8=\editable{}+\editable{}+\editable{}+\frac{4}{8}$2148÷8=+++48

Convert $\frac{4}{8}$48 into a decimal.

Use the answers to the previous parts to find $2148\div8$2148÷8.

We want to find $9878\div4$9878÷4.

Choose the most reasonable estimate for $9878\div4$9878÷4.

Less than $2300$2300.

ABetween $24$24 and $25$25.

BBetween $2400$2400 and $2500$2500.

CGreater than $2600$2600.

DLess than $2300$2300.

ABetween $24$24 and $25$25.

BBetween $2400$2400 and $2500$2500.

CGreater than $2600$2600.

DComplete the short division to find $9878\div4$9878÷4.

$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $.$. $\editable{}$ $4$4 $9$9 $\editable{}$ $8$8 $\editable{}$ $7$7 $\editable{}$ $8$8 $.$. $\editable{}$ $\editable{}$

We want to find $1173\div6$1173÷6.

Choose the most reasonable estimate for $1173\div6$1173÷6.

Between $100$100 and $200$200.

AGreater than $300$300.

BLess than $10$10.

CBetween $10$10 and $20$20.

DBetween $100$100 and $200$200.

AGreater than $300$300.

BLess than $10$10.

CBetween $10$10 and $20$20.

DComplete the short division to find $1173\div6$1173÷6.

$\editable{}$ $\editable{}$ $\editable{}$ $.$. $\editable{}$ $6$6 $1$1 $1$1 $\editable{}$ $7$7 $\editable{}$ $3$3 $.$. $\editable{}$ $\editable{}$

Understand operations on fractions, decimals, percentages, and integers