How to Tell if Two Ratios Are in Proportion

Step-by-Step Guide

1. 1

   Step 1: Identify the denominator of each ratio.

   Ratios can be expressed using a colon (1:2{\displaystyle 1:2}), the word “to” (1 to 2{\displaystyle {\text{1 to 2}}}), or a fraction bar (12{\displaystyle {\frac {1}{2}}}).Set up your ratios as fractions.
   
   The denominator is the number below the fraction bar.
   
   For example, if one shelter’s ratio of cats to dogs is 6 to 4, and another shelter’s ratio of cats to dogs is 39 to 26, you would rewrite the ratios as 64{\displaystyle {\frac {6}{4}}} and 3926{\displaystyle {\frac {39}{26}}}.
   
   So, the denominators are 4{\displaystyle 4} and 26{\displaystyle 26}.
2. 2

   Step 2: Find the least common multiple for the two denominators.

   To find the least common multiple, look for the smallest multiple each denominator has in common.If there is no least common multiple, then the ratios cannot be in proportion and no further steps are required.
   
   For example, the denominators 4 and 26 are both multiples of
   52. , To find the equivalent fraction, divide the least common multiple by the denominator.
   
   Multiply the numerator by this quotient.
   
   This will give you the new numerator of your equivalent fraction.
   
   For example, if the first ratio is 64{\displaystyle {\frac {6}{4}}}, you would divide the least common multiple (52) by 4:52÷4=13{\displaystyle 52\div 4=13}.So, you will multiply the numerator (6) by 13:6×13=78{\displaystyle 6\times 13=78}.So, your new fraction becomes 7852{\displaystyle {\frac {78}{52}}}. , Follow the same steps you did to find the equivalent fraction for the first ratio.
   
   For example, if the second ratio is 3926{\displaystyle {\frac {39}{26}}}, you would divide the least common multiple (52) by 26:52÷26=2{\displaystyle 52\div 26=2}.So, you will multiply the numerator (39) by 2:39×2=78{\displaystyle 39\times 2=78}.So, your new fraction becomes 7852{\displaystyle {\frac {78}{52}}}. , If the two fractions are equal, then the two original ratios are in proportion.For example, 7852=7852{\displaystyle {\frac {78}{52}}={\frac {78}{52}}}, so 64=3926{\displaystyle {\frac {6}{4}}={\frac {39}{26}}}
3. 3

   Step 3: Write the equivalent fraction for the first ratio.

4. 4

   Step 4: Write the equivalent fraction for the second ratio.

5. 5

   Step 5: Compare the two equivalent fractions.

Detailed Guide

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