# Use Place Value in Given Calculations

In this worksheet, students will use their knowledge of place value to find the answer to a calculation which is based on a related calculation which has the answer given. A calculator is not allowed throughout this activity.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   OCR, AQA, Eduqas, Pearson Edexcel

Curriculum topic:   Number Operations and Integers, Number

Curriculum subtopic:   Whole Number Theory, Structure and Calculation

Difficulty level:

### QUESTION 1 of 10

If we are given the answer to a calculation, we can use this to find the answer to a related calculation in which the numbers have been multiplied or divided by a power of ten.

We can also use the fact that division is the inverse of multiplication.

e.g. If we know that 52.3 x 4.8 = 251.04 then we can find the answer to many related calculations such as:

a) 523 x 48 - Both numbers in the original calculation have been multiplied by 10 therefore the answer must be multiplied by 100.

So the answer is 25104.

b) 0.523 x 480 - One number has been divided by 100 and the other multiplied by 100 which cancel each other out.

So the answer remains unchanged as 251.04.

c) 251.04 ÷ 48 - The first number is the same as the answer of the original and the second has been multiplied by 10.

Since this is division, the answer will have the inverse operation applied, which is divide by 10.

So the answer is 5.23.

Note that when answering question like this, estimation is also a useful technique.

You can round the numbers to 1 or 2 significant figure and then estimate the answer, remembering that the digits will be the same as in the original calculation.

e.g. For c) above: 251.04 ÷ 48 ≈ 250 ÷ 50 = 5

So the answer must be 5.23 as it is close to our estimated guess of 5.

In this activity, you will use information given in a calculation to enable you to work out related calculations by applying your knowledge of place value.

Good luck, place value superstar!

In this question, use the fact:

86 x 73 = 6278

Below you will see four related calculations and four answers.

Match each calculation to their answer.

## Column B

8.6 x 730
627.8
8.6 x 7.3
6.278
0.86 x 730
6278
86 x 0.073
62.78

In this question, use the fact:

1924 ÷ 37 = 52

Below you will see four related calculations and four answers.

Match each calculation to their answer.

## Column B

1924 ÷ 3.7
0.52
19.24 ÷ 37
520
19.24 ÷ 370
0.052
19.24 ÷ 0.37
52

In this question, use the fact:

9.4 x 54 = 507.6

What is 94 x 54?

507.6

5076

50760

In this question, use the fact:

9.4 x 54 = 507.6

What is 94 x 5.4?

50.76

5076

507.6

In this question, use the fact:

9.4 x 54 = 507.6

What is 5.076 ÷ 9.4?

0.54

0.054

54

In this question, use the fact:

15.9 x 230.2 = 3660.18

366.018 is the answer to which of the other calculations below?

1.59 x 230.2

0.159 x 23020

159 x 23.02

In this question, use the fact:

15.9 x 230.2 = 3660.18

1.59 is the answer to which of the other calculations below?

0.366018 ÷ 0.2302

36.6018 ÷ 2.302

3660.18 ÷ 2302

Given that:

47 x 325 = 15275

Work out:

0.47 x 3250

Given that:

47 x 325 = 15275

Work out:

15.275 ÷ 3.25

Given that:

54 x 84.2 = 4546.8

Write down the exact value of the following:

4546.8 ÷ 5.4

• Question 1

In this question, use the fact:

86 x 73 = 6278

Below you will see four related calculations and four answers.

Match each calculation to their answer.

## Column B

8.6 x 730
6278
8.6 x 7.3
62.78
0.86 x 730
627.8
86 x 0.073
6.278
EDDIE SAYS
Option 1: One number has been divided by 10 the other multiplied by 10 so the answer is unchanged as these cancel each other out. Option 2: Both numbers have been divided by 10 so the answer is divided by 100 overall. To divide by 100, move the decimal point two places to the left. Option 3: One number has been divided by 100 the other multiplied by 10 so the answer is divided by 10 overall. To divide by 100, move the decimal point one place to the left. Option 4: One number is unchanged the other divided by 1000 so the answer is divided by 1000 overall. To divide by 1000, move the decimal point three places to the left. How did you find that first challenge?
• Question 2

In this question, use the fact:

1924 ÷ 37 = 52

Below you will see four related calculations and four answers.

Match each calculation to their answer.

## Column B

1924 ÷ 3.7
520
19.24 ÷ 37
0.52
19.24 ÷ 370
0.052
19.24 ÷ 0.37
52
EDDIE SAYS
Did you spot that all of these involved ÷? This means that we need to apply the inverse operation. Option 1: The first number is unchanged and the second has been divided by 10. So the answer is multiplied by 10 overall. Option 2: The first number is divided by 100 and the second is unchanged. So the answer is divided by 100 overall. Option 3: The first number is divided by 100 and the second is multiplied by 10. So the answer is divided by 1000 overall. Option 4: The first number is divided by 100 and the second is divided by 100. So the answer is unchanged. Great work!
• Question 3

In this question, use the fact:

9.4 x 54 = 507.6

What is 94 x 54?

5076
EDDIE SAYS
The first number has been multiplied by 10 and other is unchanged. So we need to multiply our original answer by 10 to find the answer to this new, related calculation: 507.6 x 10 = 5076
• Question 4

In this question, use the fact:

9.4 x 54 = 507.6

What is 94 x 5.4?

507.6
EDDIE SAYS
One number has been multiplied by 10 and the other divided by 10. These two processes cancel each other out overall, so our answer remains exactly the same. Did you spot that?
• Question 5

In this question, use the fact:

9.4 x 54 = 507.6

What is 5.076 ÷ 9.4?

0.54
EDDIE SAYS
The original answer is divided by 100 and the other number is unchanged. So overall the other input in the sum needs to be divided by 100: 54 ÷ 100 = 0.54 Hopefully that switch using the overall answer to using a number in the calculation didn't trip you up!
• Question 6

In this question, use the fact:

15.9 x 230.2 = 3660.18

366.018 is the answer to which of the other calculations below?

1.59 x 230.2
EDDIE SAYS
366.018 has been divided by 10 from our original answer (3660.18), so we need to find a calculation which has affected a change of ÷10 overall. Option 1 is correct, since the first number is divided by 10 and the second is unchanged, so the answer has been divided by 10 overall. Option 2 would result in a change of: (÷100) + (x100) = no change overall Option 3 would result in a change of: (x10) + (÷10) = no change overall
• Question 7

In this question, use the fact:

15.9 x 230.2 = 3660.18

1.59 is the answer to which of the other calculations below?

3660.18 ÷ 2302
EDDIE SAYS
The question asks for an answer of 1.59, which is a change of ÷10 from this. Therefore, we need to find a sum that affects a change of x10 in one of the contributing inputs. Option 3 is correct, since the answer is unchanged and the second input has been multiplied by 10, so the answer would be divided by 10 overall. Option 2 would result in a change of: (÷100) + (÷100) = ÷10,000 overall Option 1 would result in a change of: (÷1000) + (x10) = ÷100 overall Phew, this was a tricky one! Let's try another now...
• Question 8

Given that:

47 x 325 = 15275

Work out:

0.47 x 3250

1527.5
EDDIE SAYS
The first number has been divided by 100 and the second has been multiplied by 10. So the overall effect on the answer is to divide by 10. 15275 ÷ 10 = 1527.5
• Question 9

Given that:

47 x 325 = 15275

Work out:

15.275 ÷ 3.25

4.7
EDDIE SAYS
Using this sum, we can see that the first number has been divided by 1000 and the second has been divided by 100. The overall effect is therefore to divide the remaining input (47) by 10. 47 ÷ 10 = 4.7
• Question 10

Given that:

54 x 84.2 = 4546.8

Write down the exact value of the following:

4546.8 ÷ 5.4

842
EDDIE SAYS
The first number is unchanged and the second has been divided by 10. Since the question involves division, the remaining input (84.2) needs to have the inverse applied, which is multiplication by 10. 84.2 x 10 = 842 Amazing work - some of these were tricky! If you found this activity challenging, you may want to revise inverse operations or multiplying / dividing by 10, 100, 1000, etc.
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