NZ Level 5
topic badge
Make the statement true (mult/div)

How can I make this true?

When we looked at decimals with addition and subtraction, we saw that in order to make a statement true, we needed to make sure both sides of our number sentence were equal. We can think of it as a set of scales that is evenly balanced. We do exactly the same thing with statements containing multiplication or division.


How many more groups?

Remember that multiplication is the same as making groups of numbers. By looking at one side of our statement and seeing how many more groups we need, we can find the missing element.

Video 1 recaps how we do this with whole numbers, then shows you how we can apply the same principle using decimals. You might also see some similarities with how we use the area method for multiplication of whole numbers.


We can multiply a number with a decimal by breaking it into parts, just like we can with whole numbers.


Other ways to balance our statements

Sometimes we might find that one side of our statement has multiples of our decimal, but not as many. In Video 2, we look at ways in which we can balance our statement. We also look at an example where we may need to compare the total we have to share on each side and see what divisor will balance our statements. Again we can use the same processes that we use for whole numbers when we are balancing decimal statements.


Worked examples

Question 1

Complete the number sentence:

  1. $3.5\times4.5=\editable{}\times4+\editable{}\times0.5$3.5×4.5=×4+×0.5

Question 2

Complete the number sentence:

  1. $2.67\times8=2.67\times4\times\editable{}$2.67×8=2.67×4×

Question 3

Complete the number sentence:

  1. $10\div6=100\div\editable{}$10÷​6=100÷​



Understand operations on fractions, decimals, percentages, and integers

What is Mathspace

About Mathspace