Grade 6

2.12 Problem solving with decimals

Ideas

Problem solving with decimals

Problem solving with decimals

Once we know how to operations with decimals, we can think about how to work with decimals that we come across in the real world. Exchanging money, measuring lengths and weights, and recording times are all areas that use decimals.

We can use key words to help us work out which operation we need to use to solve the problem. Some key words in the problem could be:

addition	subtraction	multiplication	division
more	less	product	equally shared
add	subtract	by	in each
all together	how many left	times	per
total	difference	groups of	divided by

And reflecting on the following questions, can help ensure that our answer is reasonable:

What are the quantities that we need to work with?
What units do we expect the answer to have?
What operations will produce the expected units?
What do we estimate that a reasonable answer will be?
Does the answer we calculate seem appropriate in the context?

Examples

Example 1

Harry buys an item from the school canteen for \$ 3.20. If he pays for it with a five dollar note, how much change will he get back?

Worked Solution

Create a strategy

Identify the operation to perform by looking at the keywords in the problem. Reflect on the questions to ensure the reasonableness of answers.

Apply the idea

The question asks for the change Harry will get back. To find the change is similar to find how much money is left. This question requires subtraction.

Set up the subtraction: \begin{aligned} & &5 &.00 \\ &- &3&.20 \\ \hline \\ \hline \end{aligned}

0-0=0 so write a 0 below the last digit.

0 is less than 2 so we need to borrow from 5, to make it 10-2=8. \begin{aligned} & &4 &.{}^1 00 \\ &- &3&.20 \\ \hline & & &.80 \\ \hline \end{aligned}

Find 4-3=1. \begin{aligned} & &4 &.{}^1 00 \\ &- &3&.20 \\ \hline & & 1&.80 \\ \hline \end{aligned}

So the change due is \$ 1.80.

Example 2

How many 0.38 L bottles can be filled from a barrel which holds 41.8 L?

Worked Solution

Create a strategy

Understand the problem to identify the operation to be used to solve it.

Apply the idea

Each bottle holds 0.38 L and the container holds 41.8L, so to find out how many bottles can be filled we divide 41.8 L by 0.38 L.

Using long division:

Long division algorithm of 4180 divided by 38. Ask your teacher for more information.

We cannot divide 4 by 38 so we divide 41 by 38.

41 divided 38 is 1. So we put 1 in the hundreds place at the top.

Multiply 1 by 38 to get 38 and write this under the previous 41.

A long division algorithm of 4180 divided by 38 with a quotient of 110. ASk your teacher for more information.

Subtract 38 from 41 to get 3.

Bring down 8 from the tens place to have 38.

Divide 38 by 38. The answer is 1 so we write it beside 1 of the quotient's place.

Multiply 1 by 38 to get 38 and write this under 38

Subtract 38 from 38 to get 0.

We already have a difference of 0 and the last number to bring down is also 0. That means we can just fill the ones place value in the quotient by 0.

Same thing as we divide 0 by 38 which gives us zero, and then we multiply 0 by 38 we get 0 and finally subtract the zeroes to give us also zero.

The barrel can fill 110 bottles.

Idea summary

Key words can help identify which operation to use.

addition	subtraction	multiplication	division
more	less	product	equally shared
add	subtract	by	in each
all together	how many left	times	per
total	difference	groups of	divided by

Outcomes

6.NS.B.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.