Decimals

New Zealand

Level 5

Lesson

Sometimes, when we are dividing, we have remainder that need to be expressed as a decimal.

Thinking of our remainder as a fraction means we can find an equivalent fraction with tenths or hundredths as our denominator. Once we do this, we can then write our answer as a decimal. For example, we can write $\frac{5}{10}$510 as $0.5$0.5.

Have a look at how we do this, in Video 1, using long division. Don't worry, long division is not tricky. It just means we write out each step, so we can see what we are doing along the way.

Sometimes, you may have a number to divide, or share, that is less than the number you are sharing among. In other words, the total is less than the divisor. While it might seem we can't actually share the total, it's okay, we can! It just means we have to think of our total perhaps as tenths, rather than units. Once we do that, we can share our total, and continue on with our long division.

Video 2 shows you how to share a number, such as $3$3, between a larger number, such as $5$5.

Once you have solved long division of single digit numbers, you can use the same process to divide 2 digit numbers. This short video shows you how to do this, and also has a trick or two along the way that you may find useful!

We want to find $6\div5$6÷5.

Choose the most reasonable estimate for $6\div5$6÷5.

Between $0$0 and $1$1

ABetween $5$5 and $10$10

BBetween $1$1 and $5$5

CComplete the long division to find $6\div5$6÷5.

$\editable{}$ $.$. $\editable{}$ $5$5 $6$6 $.$. $0$0 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

We want to find $5\div4$5÷4.

Choose the most reasonable estimate for $5\div4$5÷4.

Between $0$0 and $1$1

ABetween $1$1 and $5$5

BBetween $5$5 and $10$10

CComplete the long division to find $5\div4$5÷4.

$\editable{}$ $.$. $\editable{}$ $\editable{}$ $4$4 $5$5 $.$. $0$0 $0$0 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

We want to find $21\div15$21÷15.

Choose the most reasonable estimate for $21\div15$21÷15.

$1$1

A$6$6

B$36$36

C$315$315

DFill in the multiplication table for $15$15.

$2$2 $30$30 $3$3 $45$45 $4$4 $\editable{}$ $5$5 $\editable{}$ $6$6 $\editable{}$ $7$7 $105$105 $8$8 $\editable{}$ $9$9 $\editable{}$ Complete the long division to find $21\div15$21÷15.

$\editable{}$ $.$. $\editable{}$ $15$15 $2$2 $1$1 $.$. $0$0 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Understand operations on fractions, decimals, percentages, and integers