# Use rounding to estimate solutions

Lesson

## Why work out an estimate?

If we have a simple problem, you may not think it is necessary to estimate the solution. As problems become trickier though, estimating helps to:

• give us an idea of how big or small our answer will be,
• compare our actual answer, to see if we are on track, or may have made an error, and
• make sure our digits are in the correct place columns.

There are different ways to estimate answers. For now, we are going to look at rounding, to the nearest multiple of $10$10.

Why $10$10? Oh boy! This is where it gets exciting. The number $10$10 has some terrific features that make solving problems much easier.

## Rounding to the nearest 10

When we round to the nearest $10$10, it means that we can calculate our estimate by multiplying by 10, or another multiple of $10$10. That means only the place value of our number changes, so it's a calculation we can do more easily.

The nearest $10$10 means we count:

• down, to the lower $10$10, if our number ends with a $1,2,3$1,2,3 or $4$4
• up, to the next $10$10, if our number ends with a $5,6,7,8$5,6,7,8 or $9$9

In Video 1, we can estimate how many apples we need to fill $12$12 boxes, if each box holds $44$44 apples, by rounding to the nearest $10$10. We also look at what this tells us about our final answer.

## Rounding up and down

In Video 1, we rounded both numbers down to the nearest $10$10. It means that at each step, our estimate was lower than our final answer would be. If we round both numbers up, then our estimate will be higher than the final answer. What happens if we round one number up, but the other down?

In Video 2, we will see what this means for our estimate.

## Does it matter?

In this short 'extra' video, we check out what would happen if we rounded both numbers up, or both numbers down. This is a great way to see just why rounding to the nearest gives us a more accurate estimate.

## Estimating with division

When we estimate in order to solve a division problem, rounding both numbers becomes even more important. Let's look at when you might need to round to the nearest $100$100 for one of the numbers. You will see how rounding to the nearest $10$10, $100$100, or even $1000$1000 can be useful, depending on the problem, especially if it involves division.

## The red truck

Did you wonder why it was possible to write $7200\div80$7200÷​80 as $720\div8$720÷​8 and get the same answer? Have a look at multiplying by $10$10 and $100$100, and you can work backwards to see how it helps with division.

If we increase or decrease the total amount and the size of each group by the same amount, then the answer will be the same. For example, $3500\div700=5$3500÷​700=5. If we make both numbers $100$100 times smaller, our question would be $35\div7$35÷​7 and we get the same answer, $5$5. It can be helpful to think of this the other way around:

• $5\times7=35$5×7=35
• $5\times7$5×7 hundred = $35$35 hundred or $3500$3500

#### Worked Examples

##### Question 1

Let’s estimate the solution to $224\times73$224×73 by rounding the digits first.

1. Rewrite the calculation, rounding the first number to the nearest $100$100 and the second number to the nearest $10$10.

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2. Calculate $200\times70$200×70.

3. Rewrite the calculation, but this time round both numbers to the nearest $10$10.

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4. Calculate $220\times70$220×70.

5. Which estimation will be closer to the actual result of $224\times73$224×73?

$220\times70$220×70

A

$200\times70$200×70

B

$220\times70$220×70

A

$200\times70$200×70

B
6. Is $15400$15400 going to be larger or smaller than the actual result of $224\times73$224×73?

Smaller

A

Larger

B

Smaller

A

Larger

B

##### Question 2

Let’s estimate the solution to $489\times58$489×58 by rounding the digits first.

1. Rewrite the calculation, rounding the first number to the nearest $100$100 and the second number to the nearest $10$10.

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2. Calculate $500\times60$500×60.

3. Rewrite the calculation, but this time round both numbers to the nearest $10$10.

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4. Calculate $490\times60$490×60.

5. Which estimation will be closer to the actual result of $489\times58$489×58?

$490\times60$490×60

A

$500\times60$500×60

B

$490\times60$490×60

A

$500\times60$500×60

B
6. Is $29400$29400 going to be larger or smaller than the actual result of $489\times58$489×58?

Smaller

A

Larger

B

Smaller

A

Larger

B

##### Question 3

Let’s estimate the solution to $1241\div62$1241÷​62 by rounding the digits first.

1. Rewrite the calculation, rounding the first number to the nearest $100$100 and the second number to the nearest $10$10.

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2. Calculate $1200\div60$1200÷​60.