Add and subtract fractions word problems

Question

The results of an election are shown in the table below.

candidate Fractions votes

Johnson 1/9

Smith 7/18

Dragovic 1/2

What is the difference between the fractions of votes received by Dragovic and Johnson?

Answer 1

1/2 - 1/9 = ?

In order to add and subtract fractions, they must have common denominators (the bottom number of a fraction).

Two strategies to find common denominators: quick common denominator (QCD) and least common multiple (LCM).

-To find the quick common denominator (QCD), multiply the denominators together. In this problem, 2 x 9 = 18.

OR

-To find the least common multiple (LCM), list the multiples of each denominator and find the lowest number they have in common. In this problem, multiples of 2 (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) and multiples of 9 (9, 18, 27, 36, 45). The LCM is 18.

Next, you must change 1/2 and 1/9 into equivalent fractions with the new common denominator. To do so, multiply the numerator (top number of the fraction) by the same number used to find the new denominator.

1/2: 2 x 9 =18 so 1 x 9 = 9. Equivalent fraction 1/2 = 9/18.

1/9: 9 x 2 = 18 so 1 x 2 = 2. Equivalent fraction 1/9 = 2/18.

Use the new equivalent fractions in place of the original fractions from the problem in the number model to solve for the answer.

1/2 - 1/9 = ?

9/18 - 2/18 - ?

And then solve by subtracting the numerators and keeping the denominator.

9/18 - 2/18 = 7/18

Solution: 7/18 votes (don't forget to include the unit in your answer!)

Answer 2

The results of an election are shown in the table below.

candidate Fractions votes

Johnson 1/9

Smith 7/18

Dragovic 1/2

What is the difference between the fractions of votes received by Dragovic and Johnson?

1/2-1/9

The first thing to do is to find a common denominator. To do this you need to find the least common multiple for both denominators. So in this case, the LCM is 18 because that is the lowest common multiple for 2 and 9.

Now to convert the fractions, you will multiply the numerator and denominator by the same number. So you want to ask yourself "2 times what number equals 18?" That answer is 9, so you would have 1/2 x9/9 which equals 9/18.

You would do a similar process for 1/9 by asking yourself "9 times what number equals 18?" The answer is 2, so you would have 1/9x2/2 which is 2/18.

Now you can solve 9/18-2/18.

Remember when subtracting fractions, leave the denominator alone once you find a common denominator. You just want to subtract the numerator.

Answer 3

Hello Itzy,

To find the difference between the fractions of votes received by Dragovic and Johnson, you would do a subtraction:

(1/2) - (1/9)

You need to give the same denominator to both fractions. One common denominator to 2 and 9 is 18

For 1/2, you would multiply the numerator and denominator by 9. You would get: 9/18

For 1/9, you would multiply the numerator and denominator by 2. You would get: 2/18

Now you can subtract both fractions: (9/18) - (2/18) = 7/18

So the difference between the fractions of votes received by Dragovic and Johnson is 7/18.