Monday, October 17, 2016

Equivalent Ratios | Algebra 1 (High School Algebra)

Equivalent Ratios
                               If there simplification of two ratios are equal then it is called equivalent ratios.

Example-
               First ratio is 1:3 and second is 3:9 then simplification of first is 1:3 and simplification of second is 1:3 then both simplification are of same so these are equivalent ratios.

Short Trick for  Equivalent Ratios:
                                                             Let us consider there are two ratios one is 1:3 and second is 3:9 (above example)

  --[Step 1] Firstly write these in fractional form
      1/3=3/9 

 --[Step 2] Now multiply numerator of first ratio and denominator of second ratio as 1x9=9

--[Step 3] And denominator of first ratio and numerator of second ratio as 3x3=9

If Step 2 and Step 3 are equal then these are equivalent ratios else not.so here 9=9
then these are equivalent ratios.

Solved Problems
                             There are two ratios one is 4:8 and second is 1:2 . Are these equivalent ratios ?
     Solution
                  -Simplification of 4:8 is 1:2 and second is also 1:2 then both are of same so these are equivalent ratios.
                  
                  -Now we use short trick so here 4x2=8
                                                             and 1x8=8
                        then both are of same these called equivalent ratios.


Problems
                 
   1) Are 1:3 and 2:8 equivalent ratios?
   2) Are  4:12 and 8:24 equivalent ratios?
   3) Simplify - 25:100
   4) Are 2:10 and 1:5 equivalent ratios?
   5) Are 20:2 and :5 equivalent ratios?

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TagsMathematics for High School, High School Math, Algebra 1, Ratio, Numbers, High School Mathematics Curriculum , High School Algebra, Equivalent Ratios

Ratio | Algebra 1 (High School Algebra)

Ratio
         Ratio is basically relationship between two numbers that how many times first number contains second. 

Example- there are two numbers first is 4 and second is of 1 so here 4 is four time of 1.
In ratio we represent these as 4:1

So in simply form we can say that ratio is compassion of two numbers or more.


  • If there are 2:3 means there is comparison between 2 & 3 so here we  
              2x5:3x5
       (If we multiply same number of both side than ratio will not change)


  • In same manner for division if there are 3:9
         3/: 9/

   (If we divide by same number of both side than ratio will not change)

Ratio Simplification
                                    If there is 3:9
         so we can write these as 3x1:3x3
             Means 3=3x1
                         9=3x3

so now we divide both side by 3
then       3x1/3x3/3           

              Now it will be  1:3

Explain:
               In above there are two numbers 3 and 9 so we divide both of by 3 (because ratio will remain same then new numbers will be 1 and 3 then ratio will be 1:3

Ratio Problems
                           
1) Simplify following ratio-
       5:15

2) Simplify ?
      4:16

3) If there is 24:8 then how many times 8 of 24 ?

4) Simplify?
    100:10

5) Simplify ?
     12:15

Solutions
1) 1:3
2) 1:4
3)  3
4) 10:1
5) 4:5

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Tags- Mathematics for High School, High School Math, Algebra 1, Ratio, Numbers, High School Mathematics Curriculum , High School Algebra