February 8th
February 8th
Calculations with Hundreds and Thousands
Question: What is the value of 2000 × 300 ?
Misconception
There are several possible common incorrect answers
including
60 000
or
6 000 000
|
Correct
As
2 × 3 = 6
and
1000 × 100 = 100000
then
2000 300 600000
|
Further Explanation
As before there is only one answer and it is completely
logical! We will build on previous\par knowledge to get the
answer; you know, for example, that}\par }
10 × 10 = 100
10 × 100 = 1 000
10 × 1 000 = 10 000
10 × 10 000 = 100 000
and so on. Hence it is easy to see that}\par }
100 × 1 000 = 10 × 10
× 1 000 = 10 × 10 000 = 100 000
and similarly
1000 × 100 = 100 000
We can use this result, but we first note that we can write
2000 and 300 as
2 000 = 2 × 1 000 and 300 = 3 × 100
This gives
2 000 × 300 = (2 × 1 000) × (3 × 100)
= 2 × 1 000 × 3 × 100
and, as the order of multiplication does not matter, we can
rewrite this as
2 000 × 300 = 2 × 3 × 1 000 × 100
= (2 × 3) × (1 000 × 100)
= 6 × 100 000
= 600 000
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