x = 12 and y = 5, both to the nearest whole number. Find the lower… Step by Step

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The question

Question: x = 12 and y = 5, both to the nearest whole number.

Find the lower bound of x × y.

1 Bounds of each number

The number x is 12, to the nearest whole number.

Half a step is 0.5.

So it is from 11.5 up to 12.5.

11.5 ≤ x < 12.5

12 ± 0.5

The number y is 5, to the nearest whole number.

Half a step is 0.5.

So it is from 4.5 up to 5.5.

4.5 ≤ y < 5.5

5 ± 0.5

2 Choose the bounds

To make the answer as small as it can be, both numbers must be as small as they can be.

So we use 11.5 and 4.5.

lower bound = 11.5 × 4.5

smallest: smallest × smallest

Careful!

We do not change the answer by half a step.

We work it out again with the smallest numbers.

Careful: not 60 − 0.5 ✗

3 Work it out

That is 51.75.

lower bound = 51.75

To multiply decimals: first 115 times 45, as whole numbers.

That is 5175.

Then count the decimal places: 2.

115 × 45 = 5175

2 decimal places: 51.75

So the lower bound of the answer is 51.75.

4 Check

Let's check.

With the rounded numbers we get 60.

with the rounded numbers: 12 × 5 = 60

The lower bound, 51.75, is less than that, as it should be.

So the answer is right!

51.75 is less than 60

Let's look back.

First: bounds of each number.

Then: choose the bounds.

Then: work it out.

Last: check.

Answer