Long Multiplication
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
Age
11 to 14
Challenge level
Problem
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown below.
Each star like this
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Apart from the zero shown the only digits which occur are 2, 3, 5 and 7.
Can you use this information to complete the whole multiplication?
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You might find this sheet useful for working on the problem,
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Student Solutions
Catherine, Rachel & Fiona from The Mount School, York, Sonia from Madras College, and the KS3 Maths Club from Strabane Grammar School all solved this. Everyone used trial and improvement but soon realised that there could not be a 2 in the two original numbers. James of Hethersett High School, Norwich gave the best explanation of the method. The answer is 775 multiplied by 33.
| 7 | 7 | 5 | ||
| x | 3 | 3 | ||
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| 2 | 3 | 2 | 5 | |
| 2 | 3 | 2 | 5 | 0 |
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| 2 | 5 | 5 | 7 | 5 |