Fill in the missing values. 151.5 cm =? m 151.5 cm = ? m (Type an integer or a decimal.)
1 answer:
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Answer:
Step-by-step explanation:
The greatest common divisor between 9 and 20 is 1, so we know the equation has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.
By inspection we just list some multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
and also list some mutiples of 20:
20, 40, 60, 80, 100, 120
And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.
For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:
20 = 9 * 2 + 2
Then we divide 9 by the remainder we got, which is 2:
9 = 2 * 4 + 1
we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:
9 - 2*4 = 1
And then we solve for 2 from the first equation, and plug that in into the previous equation:
20 - 9*2 =2
9 - ( 20 - 9*2)*4 = 1
which does give us the same solution:
We want to compute
The goal is to write it in the following form:
First step: How many "copies" of does
contain? We can write
, so the answer is
copies.
If we distribute to
, we get
If we were done, then this product would have matched the numerator at the start. But it doesn't; there are still some terms that need to vanish. In particular, we still have to account for
Second step: How many copies of can we find in
? Well,
, so the answer is
. Then
but this still doesn't match the original numerator. We still have to deal with
Third step: How many copies of can we get out of
?
. Then
This also doesn't match the original numerator. We have a difference between what we have and what we want of
But we also can't divide into chunks of
, and we can't continue the division algorithm.
Our final answer would be
For the second problem, you should find