Question

Edgar is putting toys into bags. One bag can hold 6 toys and Edgar has 53 toys. How many bags will Edgar fill? Write the answer as a mixed number AND an improper fraction.

Answer 1

`\textsf{Improper fraction}: \quad (53)/(6)`

`\textsf{Mixed number}: \quad 8(5)/(6)`

Explanation:

Definitions

• An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
• A mixed number is a number consisting of a whole number and a proper fraction.
• A proper fraction is a fraction where the numerator is less than the denominator.

If each bag holds 6 toys and Edgar has 53 toys, to find how many bags Edgar will fill, divide 53 by 6.

Improper fraction

To write this as an improper fraction, place 53 as the numerator and 6 as the denominator:

`\implies (53)/(6)`

As 53 is a prime number, its only factors are 1 and 53. Therefore, the improper fraction cannot be reduced any further.

Mixed number

Rewrite 53 as the sum of 48 and 5:

`\implies (53)/(6)=(48+5)/(6)`

`\textsf{Apply the fraction rule} \quad (a+b)/(c)=(a)/(c)+(b)/(c):`

`\implies (48)/(6)+(5)/(6)`

Divide 48 by 6:

`\implies (6 \cdot 8)/(6)+(5)/(6)`

`\implies 8+(5)/(6)`

Write as a mixed number:

`\implies 8(5)/(6)`