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Multiplication and division (specifically) use remainders. Remainders are parts of a number that are left over. As an example, I have 4 cats and 10 cat treats. I can only give each cat 2 treats each, which means I will have 2 treats left over. The 2 left can't be divided by 4 as it is below 4, therefore the 2 is a 'remainder'. Remainders can be converted into fractions and decimals like so:

10 ÷ 4 = 2 r2 or 2.25 or 2^{1}⁄_{4}

1.

5.87 x 100 = ?

587

5870

0.587

0.0587

To multiply a number by 100 move its decimal point 2 places to the right

2.

Which strategy would be best to multiply 53 by 25?

Multiply by 100 then double

Multiply by 4 then 100

Multiply by 100 then divide by 4

Divide by 4 then double

Just as 0.25 is ^{1}⁄_{4}
of 1, 25 is ^{1}⁄_{4}
of 100

3.

2.43 x 10 = ?

2.430

24.3

243

0.243

To multiply a number by 10 move its decimal point 1 place to the right

4.

Which strategy would be best to multiply 93 by 101?

Multiply by 10 then add 93

Multiply by 100 then add 93

Multiply by 100 then subtract 93

Multiply by 10 then subtract 93

You can use this strategy for other numbers over 100, for example to multiply a number by 107 multiply by 100 and also by 7 then add the 2 results together

5.

Which gives the answer 91?

(6 + 5) x (8 - 3) + 6 =

(6 + 5 x 8) - (3 + 6) =

6 + 5 x (8 - 3) + 6 =

(6 + 5) x 8 - 3 + 6 =

Work out the calculations in brackets first

6.

On a calculator the answer to a division question is 5.25. What fraction is the remainder?

Half

Quarter

Third

Eighth

0.25 is the decimal equivalent of ^{1}⁄_{4}

7.

What is the best method of multiplying 81 by 99?

Multiply by 100 then subtract 81

Multiply by 10 then add 81

Multiply by 100 then add 81

Multiply by 10 then subtract 81

Multiplying by 100 is much easier than multiplying by 99

8.

Which of these methods would result in finding ^{1}⁄_{12}?

Half one third twice

Half one quarter twice

Double one quarter twice

Double one sixth

e.g. ^{1}⁄_{12} of 66. One third is 22, half of 22 is 11, half of 11 is 5.5

9.

How could we find an eighth of a number?

Multiply it by 4

Multiply it by 8

Divide it by 8

Divide it by 4

An eighth of a number is the same as saying divide it by 8

10.

What is the best method of multiplying 72 by 15?

Multiply by 10 then halve

Multiply by 10, halve the result, then add the two parts together

Multiply by 10, divide by 5, then add the two numbers

Divide by 10 then double

72 x 10 = 720; half of 720 = 360, so 720 + 360 = 1,080