# 12.04 Solve problems using an algorithm

Lesson

Do you know how to use an algorithm to describe a set of steps?  Try this one.

We want to order these three digit numbers from smallest to largest by following the algorithm below:

$705,281,106$705,281,106

 1 Order the numbers from the lowest to highest hundreds digit. 2 Is there more than one number with the same hundreds digit? If no - STOP If yes - Order them from the lowest to highest tens digit. 3 Is there more than one number with the same hundreds and tens digits? If no - STOP If yes - Order them from the lowest to highest units digit. 4 STOP
1. List the hundreds digit of each number from smallest to largest:

$\editable{},\editable{},\editable{}$,,

2. Will the algorithm STOP at step 2?

Yes

A

No

B

Yes

A

No

B
3. Using your answers above, put the numbers $705$705, $281$281 and $106$106 in order from smallest to largest.

$\editable{},\editable{},\editable{}$,,

## Learn

This video explores an example of an algorithm that is used to both setup and solve a problem.

### Apply

We are going to subtract these two numbers, using the subtraction algorithm below:

$91-26$9126

 1 Is the units digit of the first number less than the units digit of the second number? If no - GO TO step 2. If yes - regroup the tens from the first number to give a ten to the units, then GO TO step 2. 2 Subtract the units of the second number from the units of the first number. 3 Subtract the tens of the second number from the remaining tens of the first number. 4 Write the final answer by adding the results of steps 2 and 3.
1. Fill in the blanks below:

The units digit of the first number is $\editable{}$.

The units digit of the second number is $\editable{}$.

2. What do we need to do at step 1?

GO TO step 2.

A

Regroup the tens part of $91$91, then GO TO step 2.

B

GO TO step 2.

A

Regroup the tens part of $91$91, then GO TO step 2.

B
3. Fill in the blanks below:

We can regroup the tens part of $91$91 as $90=\editable{}+10$90=+10, in order to give $10$10 to the units part, which will become $1+10=\editable{}$1+10=.

4. Complete step 2: Subtract the units of the second number from the units of the first number.

5. Complete step 3: Subtract the tens of the second number from the remaining tens of the first number.

6. Complete step 4: Write the final answer by adding the results of steps 2 and 3.

Remember!

It's important when following algorithms to do each step one at a time and in order, this is the same as how computers read code. What would happen if we didn't follow the steps the way they were set out?

### Outcomes

#### VCMNA164

Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions