# 1/3 of the animals are dogs

by Mike
(PA)

1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter

### Comments for 1/3 of the animals are dogs

 Apr 08, 2011 Word Problem - Proportions by: Staff The question: by Mike (PA) 1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter The answer: 1/3 of the animals are dogs, 2/12 of the animals are cats, their are 19 other animals, how many are in the shelter To solve this problem, solve two equations with two unknowns 1st equation Fraction of animals which are dogs (= 1/3) + Fraction of animals which are cats (= 2/12) + Fraction of animals which are other animals (unknown value) = 1 (a total fraction of 1/1 = 100% of all animals) 2nd equation Total animals in shelter (unknown value) * Fraction of animals which are other animals (unknown value) = 19 Solving the 1st equation Fraction of animals in the shelter which are dogs: 1/3 Fraction of animals in the shelter which are cats: 2/12 Fraction of animals in the shelter which are other animals: F (unknown) The total of all three fractions must = 1 (a total fraction of 1/1 = 100% of all animals) Fraction of animals which are dogs + Fraction of animals which are cats + Fraction of animals which are other animals = 1 1/3 + 2/12 + F = 1 1/3 + (1 * 2)/(6 * 2) + F = 1 1/3 + (1/6) * (2/2) + F = 1 1/3 + (1/6) * 1 + F = 1 1/3 + 1/6 + F = 1 To convert the first fraction to a common denominator with the second fraction, multiply the first fraction by another fraction: 2/2 Note that 2/2 = 1, so the first fraction is only being multiplied by 1. Its value has not changed. (1/3)*(2/2) + 1/6 + F = 1 Multiply the numerators of the two fractions together, and multiply the denominators of the two fractions together. (1*2)/(3*2) + 1/6 + F = 1 2/6 + 1/6 + F = 1 Add the two fractions: 2/6 + 1/6 (2+1)/6 + F = 1 3/6 + F = 1 Reduce 3/6 to its lowest terms (1*3)/(2*3) + F = 1 (1/2)*(3/3) + F = 1 (1/2)*(1) + F = 1 (1/2)*1 + F = 1 1/2 + F = 1 Subtract ½ from each side of the equation 1/2 - 1/2 + F = 1 - 1/2 0 + F = 1 - 1/2 F = 1 - 1/2 F = 1/2 Fraction of animals in the shelter which are other animals = 1/2 Solving the 2nd equation Total animals in shelter * Fraction of other animals = total number of other animals Total animals in shelter * 1/2 = 19 Divide each side of the equation by ½ (Total animals in shelter * ½)/(1/2) = 19/(1/2) Reverse the ½ to the fraction 2/1, and then multiply. (Total animals in shelter * ½)*(2/1) = 19/(1/2) (Total animals in shelter)*(1/2)*(2/1) = 19/(1/2) (Total animals in shelter)*(1*2/2*1) = 19/(1/2) (Total animals in shelter)*(2/2) = 19/(1/2) (Total animals in shelter)*(1) = 19/(1/2) (Total animals in shelter)*1 = 19/(1/2) Total animals in shelter = 19/(1/2) Total animals in shelter = 19 * (2/1) Total animals in shelter = (19 * 2)/1 Total animals in shelter = 38/1 Total animals in shelter = 38 The final answer is: 38 animals are in the shelter Thanks for writing. Staff www.solving-math-problems.com

 Mar 04, 2013 1/3 dogs by: Anonymous It's impossible! How many dogs and how many cats? 19 other animals is 1/2. So 19 =1/2. 2/12..or 1/6 are cats which leaves 1/3 or 2/6 are dogs. Now try to figure out what 1/6 of 19 is......So you have 6.333333 cats and 12.6666666 dogs........imposible with the word problem the way it is stated.

 Mar 06, 2013 1/3 dogs by: Staff The original question does not ask how many dogs or cats are in the shelter. The question ONLY asks for the total number of animals in the shelter. The total number of animals in the shelter is 38. Everything is OK if you stop there. Once you try to calculate the number of cats and dogs, the problem falls apart. As you have correctly pointed out, 1/6 of 38 is indeed 6.333333 cats. 1/3 of 38 is 12.6666666 dogs. Whoever originally wrote the problem didn't think it through.