1) The three expresssions, F / 0.15; 15 F / 100; 3F / 20; are equivalent.
2) The number of figurines Kat owned last year may be expressed in terms of the number the of figurines purchased, F, this year, and the 15%, following this procedure:
Call n the amount of figurines owned last year.
F is the number of figurines purchased: F = 15%n = 0,15n
Hence, you just need to clear F from the expression F = 0.15n
Divide both sides by 0.15:
F / 0.15 = n or n = F / 0.15 (reflexive property)
To prove the equialavence of the other expresssions you just have to use the properties of multiplication or division:
The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.
The Euclidean algorithm solves the problem:
<em> Given integers </em><em>, find </em><em />
Here is an outline of the steps:
Let , .
Given , use the division algorithm to write .
If , stop and output ; this is the gcd of .
If , replace by . Go to step 2.
The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.
Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:
Step 1: Subtract D from N repeatedly.
Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.
(a) To find we apply the Euclidean algorithm:
The process stops since we reached 0, and we obtain .
(b) To find we apply the Euclidean algorithm:
The process stops since we reached 0, and we obtain .
(c) To find we apply the Euclidean algorithm:
The process stops since we reached 0, and we obtain .