Patterns — Practice

Question 1

Circle the multiples of 9: 25, 27, 35, 36, 45, 46, 54, 55.

Accepted Answer

27, 36, 45 and 54. Each has digits reducing to 9.

Question 2

Find 47 x 100.

Accepted Answer

Attach two zeros: 4700.

Question 3

Complete: 90, 180, 270, ___, ___, ___.

Accepted Answer

360, 450, 540. The rule is add 90.

Question 4

In the magic square 2 9 4 / 7 5 3 / 6 1 8, what do both diagonals add to?

Accepted Answer

2 + 5 + 8 = 15 and 4 + 5 + 6 = 15. Both give 15.

Question 5

Use casting out nines to decide whether 13476 is a multiple of 9.

Accepted Answer

1 + 3 + 4 + 7 + 6 = 21, and 2 + 1 = 3. The result is 3, not 9, so 13476 is not a multiple of 9.

Question 6

Is 23769 a multiple of 9?

Accepted Answer

Cast out the 9. Then 2 + 3 + 7 + 6 = 18, and 1 + 8 = 9. So yes, it is a multiple of 9.

Question 7

Reverse 62, subtract the smaller from the larger, and check whether the difference is a multiple of 9.

Accepted Answer

62 - 26 = 36, and 3 + 6 = 9. Yes, it is a multiple of 9.

Question 8

Complete the letter-and-number pattern: A9, B18, C27, D36, ___, ___.

Accepted Answer

E45 and F54. Letters run in order while the numbers are multiples of 9.

Question 9

A magic square reads 2 9 4 in the top row, 7 __ 3 in the middle and 6 1 8 at the bottom. Its total is 15. Find the missing centre and explain how you know.

Accepted Answer

The middle row must also total 15, and 7 + 3 = 10, so the centre is 15 - 10 = 5. In any 3x3 magic square built from 1 to 9, the centre is always 5.

Question 10

Given 9 x 6 = 54, 9 x 66 = 594 and 9 x 666 = 5994, predict 9 x 66666.

Accepted Answer

599994. Each extra 6 pushes one more 9 into the middle of the answer.

Practice — Patterns

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