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Multiplication and Division 3 (Difficult)

Multiplication and division stretch your logical skills. In 11 Plus Maths, they’re used in puzzles, sequences, and real-world problems that test clear thinking and precision.

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Fascinating Fact:

Every human has about one hundred thousand hairs on their head, so in a class of thirty, there are roughly three million chances of a bad hair day.

In 11 Plus Maths, multiplication and division become more complex as problems involve patterns, scaling, and reasoning. These skills help pupils handle larger numbers and apply logical steps in unfamiliar contexts.

Key Terms

Power: The result of multiplying a number by itself one or more times, such as 3² meaning 3 × 3.
Inverse Operation: An operation that reverses the effect of another, such as division undoing multiplication.
Equation: A mathematical statement showing that two expressions are equal, often containing multiplication or division.

Parents can explore more in our 11 Plus sample questions guide for parents.

Frequently Asked Questions (Click to see answers)

How do powers relate to multiplication?

Powers are a way of expressing repeated multiplication, like 2? meaning 2 × 2 × 2 × 2, which equals 16.

What does it mean when division has no remainder?

It means one number divides exactly into another, showing that the divisor is a factor of the dividend.

How can I make fewer mistakes in long multiplication?

Work methodically, align digits correctly, and estimate your final answer before calculating to spot errors early.

Try These Related Quizzes

1 .

What is the correct answer to the given calculation?
27.83 x 105 = ?

2,922.15

2,783

3,162.83

3,227

To multiply a number by 105, first multiply the number by 10 and halve it, then multiply the original number by 100 and add your two answers together:
27.83 x 5 = (27.83 x 10) ÷ 2 = 278.3 ÷ 2 = 139.15
27.83 x 100 = 2,783
2,783 + 139.15 = 2,922.15

2 .

What is the correct answer to the given calculation?
96,000 ÷ 3,000 = ?

3.2

320

3,200

To divide a number by 3,000 just divide the number by 3, then by 1,000.
Another option, as both numbers end with “000” is to ignore them and divide 96 by 3 – simple!

3 .

What is the correct answer to the given calculation?
197.726 x 110 = ?

2,174,986

217,498.6

21,749.86

2,174.986

To multiply a number by 110: first multiply by 10, then multiply the original number by 100 and add the two answers together:
197.726 x 10 = 1,977.26
197.726 x 100 = 19,772.6
1,977.26 + 19,772.6 = 21,749.86

4 .

What is the correct answer to the given calculation?
8,300 ÷ 200 = ?

40.5

41.5

To divide a number by 200: just divide by 2, then divide by 100:
8,300 ÷ 200 = (8,300 ÷ 2) ÷ 100 = 4,150 ÷ 100 = 41.5

5 .

What is the correct answer to the given calculation?
68 x 95 = ?

6,460

6,350

6,240

6,130

To multiply a number by 95, first multiply the number by 100 and remember your answer. Next, times the original number by 10 and half it. Finally, subtract your second answer from your first:
68 x 95 = (68 x 100) - (68 x 10) ÷ 2 = 6,800 - (680 ÷ 2) = 6,800 - 340 = 6,460

6 .

What is the correct answer to the given calculation?
46,000 ÷ 99 = ?

466.466

464.646

462.462

460.46

To divide a number by 99, you can often just divide by 100 and repeat the number itself (ignoring any zeros): 46,000 ÷ 100 = 46 but 46,000 ÷ 99 = 464.64646464 etc…

7 .

What is the correct answer to the given calculation?
83 x 120 = ?

9,200

9,480

9,960

10,020

To multiply a number by 120, first multiply by 100 and remember your answer. Next, divide your answer by 5 and add this to your first answer:
83 x 120 = (83 x 100) + (83 x 100) ÷ 5 = 8,300 + (8,300 ÷ 5) = 8,300 + 1,660 = 9,960

8 .

What is the correct answer to the given calculation?
167.93628 x 10,000 = ?

167,936.28

1,679.3682

16,793,628

1,679,362.8

To multiply by 10,000 simply move the digits 4 places to the left: 167.93628 x 10,000 = 1,679,362.8

9 .

What is the correct answer to the given calculation?
16,714 ÷ 10,000 = ?

167.14

16.714

1.6714

0.16714

To divide by 10,000 simply move the digits 4 places to the right:
16,714 ÷ 10,000 = 1.6714

10 .

What is the correct answer to the given calculation?
75 ÷ 15 = ?

That was an easy one! Did you know, when asked to divide more difficult numbers by 15, you can use this trick - first divide by 10, then multiply by 2, and finally divide by 3:
75 ÷ 15 = ((75 ÷ 10) x 2) ÷ 3 = (7.5 x 2) ÷ 3 = 15 ÷ 3 = 5

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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