Decimals

Lesson

When you divide numbers in the hundreds, which we call three digit numbers, sometimes you'll find there is no remainder, and you can divide equally. An example of this is $624\div6$624÷6, where we can break our problem into smaller problems. Here, we might solve $600\div6=100$600÷6=100 and then $24\div6=4$24÷6=4, which means we know that $624\div6=104$624÷6=104.

We could also write this number as $104.0$104.0 if we need to express it as a decimal. What do we do though, when we end up with remainders? Let's find out.

In our earlier example, we had the problem $624\div6=104$624÷6=104.

Imagine we were putting $624$624 watermelons into$6$6 crates. We could put $104$104 watermelons into each crate. But if we had $627$627 watermelons, we will have $3$3 left over. You might write this as $104r3,$104`r`3, or $104\frac{3}{6}$10436. This is known as division with remainder. Now we will look at how to write an answer like this by expressing it as a decimal.

It's a good chance to refresh your memory on how to convert fractions to decimals too. Those $3$3 leftover watermelons represent half, or $\frac{1}{2}$12, so we express this as $0.5$0.5 in decimal form. In our first video we'll explore this further. We can use visual examples to help us imagine dividing or sharing into groups.

When we use short division, we use a mathematical expression to represent our division or sharing. When we work through our problem, we think of the place value of each digit. So, $824$824 has $8$8 hundreds, $2$2 tens and $4$4 units. Working through our problem, from left to right, we use regrouping of any remainders, until we get to the end. For our remainder at the end, we need to change our fraction to a decimal. In this next video, we look at how to do that. Money is a great help for us since we can use the facts that $1$1 dollar has $100$100 cents. This can help us when we are working with hundredths!

Is there one method you find easier? While we've looked at some ways to solve these problems, you could also use long division to solve division with a remainder expressed as a decimal. Perhaps you could try one problem a few different ways, to see which you prefer.

Remember!

We use the same process for division, but our remainder can be expressed as a decimal.

The remainder can be written as a fraction, and then we can express it in tenths, or hundredths.

Then we can express our answer as a decimal.

We are going to solve the division $477\div2$477÷2 by partitioning $477$477.

Complete the following number sentence:

$477=\editable{}+16+1$477=+16+1

Complete the following number sentence:

$477\div2=\editable{}\div2+16\div2+1\div2$477÷2=÷2+16÷2+1÷2

Complete the divisions:

$477\div2=\editable{}+\editable{}+\frac{1}{2}$477÷2=++12

Convert $\frac{1}{2}$12 into a decimal.

Use the answers to the previous parts to find $477\div2$477÷2.

We want to find $538\div4$538÷4.

Choose the most reasonable estimate for $538\div4$538÷4.

Greater than $150$150.

ABetween $130$130 and $140$140.

BBetween $13$13 and $14$14.

CLess than $120$120.

DGreater than $150$150.

ABetween $130$130 and $140$140.

BBetween $13$13 and $14$14.

CLess than $120$120.

DComplete the short division to find $538\div4$538÷4.

$\editable{}$ $\editable{}$ $\editable{}$ $.$. $\editable{}$ $4$4 $5$5 $\editable{}$ $3$3 $\editable{}$ $8$8 $.$. $\editable{}$ $\editable{}$

We want to find $377\div5$377÷5.

Choose the most reasonable estimate for $377\div5$377÷5.

Greater than $90$90.

ALess than $60$60.

BBetween $7$7 and $8$8.

CBetween $70$70 and $80$80.

DGreater than $90$90.

ALess than $60$60.

BBetween $7$7 and $8$8.

CBetween $70$70 and $80$80.

DComplete the short division to find $377\div5$377÷5.

$\editable{}$ $\editable{}$ $.$. $\editable{}$ $5$5 $3$3 $7$7 $\editable{}$ $7$7 $.$. $\editable{}$ $\editable{}$

Understand operations on fractions, decimals, percentages, and integers