# 5.08 Budgets

Lesson

## Are you ready?

In previous lessons we have  practiced addition and subtraction with large numbers  . Let's practice with the following problem.

### Examples

#### Example 1

Find the value of 6396 - 129.

Worked Solution
Create a strategy

Use the subtraction algorithm method.

Apply the idea

Write it in a vertical algorithm.\begin{array}{c} & & &6 &3 &9 &6 \\ &- & & &1 &2 &9 \\ \hline & \\ \hline \end{array}

Begin with the units column. We can see that 6 is less than 9, so we need to trade 1 ten from the tens place.

So we get 16 - 9 = 7 in the units column and 9 tens becomes 2 tens in the first row.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & & & &7 \\ \hline \end{array}

For the tens place: 8 - 2 = 6.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & & &6 &7 \\ \hline \end{array}

For the hundreds place: 3 - 1 = 2.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & & &2 &6 &7 \\ \hline \end{array}

For the thousands place: 6 - 0 = 6.\begin{array}{c} & & &6 &3 &8 &\text{ }^1 6 \\ &- & & &1 &2 &9 \\ \hline & & &6 &2 &6 &7 \\ \hline \end{array}

So 6396 - 129 = 6267.

Idea summary

We can use a vertical algorithm to add and subtract numbers.

## Money and change

How can we work out how much change we need to receive, when we buy something? Let's see some strategies to help.

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### Examples

#### Example 2

When out shopping Luigi buys some groceries for \$17.70 and pays with a \$20 note.

Which of the following could be the change he gets?

A
B
Worked Solution
Create a strategy

Count up from the cost to the amount given. Use this table of values to help you.

Apply the idea

To find the change we can count up from \$17.70 to \$20.

We would need to count up by another 30 cents to get to \$18. Then if we count up by 2 we get to 20. For option A, we have two 20 cents coins which make 40 cents and a \$1 coin. If we add them we would get:

For option B, we have two 50 cents coins which make \$1, a 20 cent coin, a 10 cent coin, and a \$1 coin. If we add them we would get:

This is equal to the change we found earlier so the answer is Option B.

Idea summary

To find change we can either:

• Subtract the price from the amount paid.

• Count up from the price to the amount paid.

## Bank accounts

How does a bank statement work? Let's find out in this video.

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### Examples

#### Example 3

A withdrawal is:

A
money taken out of a bank.
B
the amout of money in a bank account at any time.
C
money put into a bank account.
Worked Solution
Create a strategy

A withdrawal decreases your bank balance.

Apply the idea

A withdrawal is money taken out of a bank, option A.

Idea summary

A deposit is when we put money into our bank account.

A withdrawal is when we take money out of our bank account.

## Budgets and saving

In this video we work out if we have budgeted enough for the end of year party.

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### Examples

#### Example 4

Here is Sarah’s weekly budget.

a

Complete the table below:

Worked Solution
Create a strategy

Add up the values in the income column to get the total.

Apply the idea

Use a vertical algorithm. \begin{array}{c} & & &8 &0 &. &0 &0 \\ &+ & &3 &5 &. &0 &0 \\ \hline \\ \hline \end{array}

Add the numbers down each column starting from the hundredths column, then the tenths, units and tens column to get: \begin{array}{c} & & &8 &0 &. &0 &0 \\ &+ & &3 &5 &. &0 &0 \\ \hline & &1 &1 &5 &. &0 &0\\ \hline \end{array}

So the total income is \$115.00. b Sarah saves any money that she has not spent. How much does Sarah save each week? Worked Solution Create a strategy Find the difference between the total income and the total expenses. Apply the idea Write in a vertical algorithm. \begin{array}{c} & &1 &1 &5 &. &0 &0 \\ &- & &9 &0 &. &4 &5 \\ \hline \\ \hline \end{array} Begin with the hundredths column. We can see that 0 is less than 5, so we need to trade 1 tenth from the tenths place. But we have 0 tenth. So we need to trade 1 unit from the units place. So we get 10 - 5 = 5 in the hundredths column and 0 tenths becomes 9 tenths and 5 units becomess 4 units in the first row.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & & & & &5 \\ \hline \end{array} For the tenths place: 9 - 4 = 5.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & & & &5 &5 \\ \hline \end{array} For the units place: 4 - 0 = 4.\begin{array}{c} & &1 &1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & & &4 &. &5 &5 \\ \hline \end{array} For the tens column, we can see that 1 is less than 9, so we need to trade 1 hundred from the hundreds place. So we get 11 - 9 = 2 in the tens column and 1 hundred becomes 0 hundreds.\begin{array}{c} & &0 &\text{}^1 1 &4 &. &9 &\text{ }^10 \\ &- & &9 &0 &. &4 &5 \\ \hline & & &2 &4 &. &5 &5 \\ \hline \end{array} So Sarah saves \$24.55 each week.

Idea summary

When we need to work to a budget, we need to make sure our expenses (money we spend) are not more than our income (money we receive).

### Outcomes

#### MA3-5NA

selects and applies appropriate strategies for addition and subtraction with counting numbers of any size