Answers (4)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
Given:
y = 7x
y - x = 18
Find x and y:
7x - x = 18
6x = 18
x = 3
y = 21
A number y is 1/7 of another number x :
1) y = 1/7 * x.
The difference of the numbers is 18 :
2) y = x - 18.
And as y=y,
1/7 * x = x - 18 ;; solve for x :
x = 7 (x - 18)
x = 7x - 126
-6x = -126
x = 21. Insert this in 1) or 2)
y = 3.
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Or,
1/7 * x = x - 18 ;; solve for x :
1/7x - x = -18
x (1/7 - 1) = -18
-6/7 = -18/x
We are allowed to multiply any term by 1 with k/k = 1 , k ≠ 0. Thus,
-6/7 * k/k = -18/x.
This tells you that
IF -6k = -18 THEN 7k = x.
-6k = -18
k = 3. Insert this into
7k = x
x = 21
And as y = k = x/7, it follows that
y = 3.