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Y6 Level 5 Division with decimals January 2011

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Decimals and Place Value• A decimal is a number with a

decimal point in it (6.52, 0.5, 0.01)• The value of digits in a decimal is

based on the number 10• The digits to the left of the decimal

point represent whole number• The numbers to the right of the

decimal point represent some part of 1

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The strange story of:37.5 1.25

Dividing by a

Decimal Number

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FIRST…

Come up with a QUICK ESTIMATEQUICK ESTIMATE…

37.5 1.25 looks like it will be close to

37 1, which would equal just 37.

SO… we will be looking for an answer around 37 and REJECT an answer of

300-something or 3-something.

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37.5 1.25

3 7 51 2 5

To solve this problem using the “paper and pencil” procedure we would set it up like THIS.

BUT… the regular division procedure does not work comfortably with decimal

divisors… what can we do ?

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37.5 1.25

3 7 51 2 5

will give the same answer as 375 12.5

...since we multiplied BOTH Dividend and Divisor by 10.

…and we can do this multiplication by moving the decimal point one place to the right !

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and 375 12.5

3 7 51 2 5 0

will give the same answer as 3750 125

…since we multiplied BOTH Dividend and Divisor by 10 again.

…and we can do this multiplication by moving the decimal point one more place to the right !

and annexing a zero in the ones place.

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and 3750 125we can solve in the usual way

3 7 51 2 5 0

3

- 3 7 5

0

0

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Thousandths

2 1 6 4. 5 7 8– 2; thousands– 1; hundreds– 6; tens– 4; ones– 5; tenths– 7; hundredths– 8; thousandths

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Exercise

• Write the following numbers as decimals:

609

1000

•

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Exercise• Write the following numbers as decimals:

4602

1000

•

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Exercise

• Write the following number as a decimals:

• One hundred fifty-nine and twelve hundredths

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Changing Fractions to Decimals

• You can change a fraction to a decimal by dividing the numerator by the denominator

• Numerator; the top part of a fraction• Denominator; the bottom part of a

fraction– E.g. 4/5 = 4 ÷ 5 = 0.80– 5)4.00 = 0.8

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Now go on to the Website and do the XL exercise in Year 6

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LO: To understand the effects of division by decimals

I understand this idea fully.

I have some understanding but I need more practice.

I don’t understand this idea at all and need to work again on this unit of work.

A

B

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LO: To convert fractions into decimals

I understand this idea fully.

I have some understanding but I need more practice.

I don’t understand this idea at all and need to work again on this unit of work.

A

B

C Next pageNext page

LO: To be able to divide a whole number by a number that is a decimal or which has decimals e.g. 60 ÷ 1.5

I understand this idea fully – I could do the sum above.

I have some understanding but I need more practice.

I don’t understand this idea at all and need to work again on this unit of work.

A

B

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