The word "algorithm" is used in computer science, mathematics, and many other areas, to describe a process or set of steps we can follow to complete a task or problem.
Here is an algorithm:
| Algorithm Steps | Example |
|---|---|
| Think of any two numbers from $1$1 to $9$9. | $3$3 and $5$5 |
| Make two $2$2-digit numbers by putting them in either order. | $53$53 and $35$35 |
| Subtract the smaller number from the larger number. | $53-35=18$53−35=18 |
| Divide the result by $9$9. | $18\div9=2$18÷9=2 |
| Finally, add the smaller starting number. | $2+3=5$2+3=5 |
In the example, we chose the numbers $3$3 and $5$5 to start with. In the last step of the algorithm, we added the smaller of these numbers, $3$3, and got a result which was the larger number, $5$5.
Does this always happen? Try it yourself with two different numbers!
Worked Examples
Question 1
We are going to add these two numbers together, using the addition algorithm below:
$37+46$37+46
| 1. | Add the units. |
| 2. | Is the result at least $10$10?
|
| 3. | Add the tens. |
| 4. | Is the result at least $100$100?
|
| 5. | Write the final answer by adding the hundreds, tens and units. |
Which two numbers will be added in step 1?
$7$7$\text{and}$and$6$6
A$3$3$\text{and}$and$4$4
BComplete step 1: Add the units.
What do we need to do at step 2?
GO TO step 3.
AFirst regroup into tens and units, then GO TO step 3.
BRegroup $13$13 into tens and units:
$13=\editable{}+\editable{}$13=+
Now complete step 3: Add the tens.
What do we need to do at step 4?
GO TO step 5.
AFirst regroup into hundreds and tens, then GO TO step 5.
BComplete step 5: Write the final answer by adding the hundreds, tens and units.
Question 2
We are going to add these two numbers together, using the addition algorithm below:
$89+65$89+65
| 1. | Add the units. |
| 2. | Is the result at least $10$10?
|
| 3. | Add the tens. |
| 4. | Is the result at least $100$100?
|
| 5. | Write the final answer by adding the hundreds, tens and units. |
Complete step 1: Add the units.
What do we need to do at step 2?
GO TO step 3.
AFirst regroup into tens and units, then GO TO step 3.
BRegroup $14$14 into tens and units:
$14=\editable{}+\editable{}$14=+
Now complete step 3: Add the tens.
What do we need to do at step 4?
GO TO step 5.
AFirst regroup into hundreds and tens, then GO TO step 5.
BRegroup $150$150 into hundreds and tens:
$150=\editable{}+\editable{}$150=+
Now complete step 5: Write the final answer by adding the hundreds, tens and units.
Question 3
We are going to subtract these two numbers, using the subtraction algorithm below:
$91-26$91−26
| 1. | Is the units digit of the first number less than the units digit of the second number?
|
| 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. |
Fill in the blanks below:
The units digit of the first number is $\editable{}$.
The units digit of the second number is $\editable{}$.
What do we need to do at step 1?
GO TO step 2.
ARegroup the tens part of $91$91, then GO TO step 2.
BFill 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=.
Complete step 2: Subtract the units of the second number from the units of the first number.
Complete step 3: Subtract the tens of the second number from the remaining tens of the first number.
Complete step 4: Write the final answer by adding the results of steps 2 and 3.