Find the ratio of a to b

Question

Find the Ratio of a to b, that a≠0 and b≠0.

1- a=4b
2- 4a=b
3- 7a+5b=0
4- 2a-3b=0
5- a/6 =b/9
6- 17/a=11/b
7- 13/3a=2/7b

Answer 1

4) 2a-3b=0

    2a=3b

      a=(3/2)b

     a/b=3/2

 

5) a/6=b/9

    cross multiply

    9a=6b

      a=(6/9)b

    a/b=6/9  (a little trick: swap b and 6 in the original equation !!)

 

6) 17/a=11/b

    swap a and 11

   17/11=a/b

    or...

    cross multiply

    11a=17b

        a=(17/11)b

        a/b=17/11

 

7)  13/3a=2/7b

    cross multiply

     6a=91b

       a=(91/6)b

       a/b=91/6

 

Answer 2

To continue from where Kathy left off, some of them can be a little tricky.  This is because it requires a bit more algebra. 

 

 

2)

 

4a = b

 

 

Divide both sides of the equation by b.

 

4a/b = 1

 

 

Now multiply both sides of the equation by 1/4.

 

a/b = 1/4

 

This is like saying a=1  and   b=4.

 

 

3)

 

7a + 5b = 0

 

 

Subtract 5b on both sides of the equation.

 

7a = -5b

 

 

Divide both sides of the equation by b.

 

7a/b = -5

 

 

Multiply both sides of the equation by 1/7.

 

a/b = -5/7

 

 

This is like saying a=-5  and   b=7. 

 

 

The rest of the problems are similar to the previous. 

 

 

Answer 3

"ratio of a to b" can be written as "a/b"

 

So we want to change the equation around so we end up with a/b on one side by itself.

 

#1 a=4b

• we want the b on the bottom so divide both sides by b
• we get a/b = 4 or a/b = 4/1
• that can be read as "ratio of a to b is 4 to 1"

 

#2 4a=b

• again we want to get a on top and b on bottom
• so let's divide both sides by b and we'll have b on bottom
• now we have 4a/b=1
• we need to get rid of that 4 on the top
• so let's divide both sides by 4
• now we have a/b =1/4
• that can be read as "ratio of a to b is 1 to 4

 

#3 7a+5b=0

• as before we want to get a over b by itself on one side
• let's get rid of the +5b on the left
• so we can subtract 5b on both sides
• that gives us 7a=-5b
• now let's get the b on the bottom
• to do that we can divide both sides by b
• now we have 7a/b = -5
• next we need to get rid of that 7 on the top
• so divide both sides by 7
• and we are left with a/b = -5/7
• so the ratio of a to be is -5 to 7