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QuestionA franchise is owned by three people. If the first owns 13\frac{1}{3} and the second 37\frac{3}{7}, what fraction does the third own?

Studdy Solution

STEP 1

Assumptions1. The first person owns 13\frac{1}{3} of the business. . The second person owns 37\frac{3}{7} of the business.
3. The total ownership of the business sums up to1.

STEP 2

First, we need to find the total fractional part of the business owned by the first and the second person. We can do this by adding the fractions.
Total owned=Fraction owned by first person+Fraction owned by second personTotal\, owned = Fraction\, owned\, by\, first\, person + Fraction\, owned\, by\, second\, person

STEP 3

Now, plug in the given values for the fractions owned by the first and second person to calculate the total owned.
Total owned=13+37Total\, owned = \frac{1}{3} + \frac{3}{7}

STEP 4

To add fractions, we need a common denominator. The least common multiple of3 and7 is21, so we will use that as our common denominator.
13=721\frac{1}{3} = \frac{7}{21}37=921\frac{3}{7} = \frac{9}{21}

STEP 5

Now, add the fractions.
Total owned=721+921=1621Total\, owned = \frac{7}{21} + \frac{9}{21} = \frac{16}{21}

STEP 6

Now that we have the total fractional part owned by the first and second person, we can find the fractional part owned by the third person. This can be found by subtracting the total owned by the first and second person from1.
Fraction owned by third person=1−Total ownedFraction\, owned\, by\, third\, person =1 - Total\, owned

STEP 7

Plug in the value for the total owned to calculate the fraction owned by the third person.
Fraction owned by third person=1−1621Fraction\, owned\, by\, third\, person =1 - \frac{16}{21}

STEP 8

Subtract the fractions. Here,1 is equivalent to 2121\frac{21}{21}.
Fraction owned by third person=2121−1621=521Fraction\, owned\, by\, third\, person = \frac{21}{21} - \frac{16}{21} = \frac{5}{21}The fraction of the business owned by the third person is 521\frac{5}{21}.

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