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Multiplication and Division illustration | Caesar
"Divide and conquer" said Caesar. Will you be victorious in this quiz?

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.

  • 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.
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.

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
32
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
40.5
41
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 = ?
4
5
6
7
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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