# 2.6 To use a range of techniques to perform calculations

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## Memorandum

1.1 9 x 25 ÷9 x 100) ÷ 4

1.2 368 x 25 ÷368 x 100) ÷ 4

1.3 16 x 25 ÷16 x 100) ÷ 4

2. 2.1 ÷324 x 100) ÷ 4

32 400 ÷ 4

8 100

2.2 ÷1 436 x 100) ÷ 4

143 600 ÷ 4

35 900

2.3 ÷26 844 x 100) ÷ 4

2 684 400 ÷ 4

671 100

## Brain teasers

yes

÷1 436 ÷ 4) x 100

359 x 100

35 900

3.1

 375 625 1 125

3.2

 3 000 _______ 375 5 000 _______ 625 9 000 _______ 1 125

5. 1 000

8

divide

8

1 000

multiplication

6.1 36 x 1 000 1 056 000 ÷ 8

36 000 132 000

6.2 132 x 1 000 ÷1 056 x 1 000 ÷ 8

132 000 132 000

## Brain teasers

x 1 000  2 / x 5 x 100 / 2 x 1 000

## To determine output values for given input values [lo 2.3.3]

It is very important to develop strategies for arriving at answers quickly to make life easier in Grade 6. Let us take a look at some bright ideas to use when we do multiplication!

REMEMBER!

When you multiply by 25 you can first multiply by 100 and

then divide by 4!

1. Can you balance the following scales by filling in the correct number?

1.1

1.2

1.3

2. Use the above method to calculate:

2.1 324 x 25 =

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

2.2 1 436 x 25 =

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

2.3 26 844 x 25 =

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

BRAIN-TEASER!

Can I also first divide by 4 and then multiply by 100? _________________________

1 436 x 25 =_____________________________________

=___________________________________________

=___________________________________________

3. Look carefully at the following example and then complete the tables:

 3.1 1 × 125 125 3 × 125 _____ 5 × 125 _____ 9 × 125 _____
 3.2 1 × 1 000 1 000 ÷ 8 25 3 × 1 000 _____ ÷ 8 _____ 5 × 1 000 _____  8 _____ 9 × 1 000 _____  4 _____

4. Compare the answers in the tables. What do you realise?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

5. Complete the following:

REMEMBER:

If I have to multiply by 125 I can first multiply by ____________________________

and then __________________ the answer I get by ___________________________

OR I can first divide the number by_________________________________ and then

6. See if you can apply this method!

6.1 288 x 125 = ÷288  8) x 1 000

= _______________________

= _______________________

or

288 x 125 = ÷288 x 1 000) ÷ 8

= _______________________

= _______________________

6.2 1 056 x 125 = ÷1 056 ÷ 8) x 1 000 or _____________________

= _______________________

= _______________________

BRAIN-TEASER!

WITHOUT using a calculator, how would you multiply a number by 500 in two seconds?

## Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.10: We know this when the learner uses a range of techniques to perform written and mental calculations with whole numbers including:

1.10.3: building up and breaking down numbers.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.3: We know this when the learner determines output values for given input values, or input values for given output values, using:

2.3.3: tables.

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