Edgar will need 9 bags to hold all of his toys. This can be expressed as a mixed number as 9 1/6 bags, or as an improper fraction as 57/6 bags.
To determine the number of bags Edgar will need, we need to divide the total number of toys by the number of toys that each bag can hold. In this case, we have 53 toys and each bag can hold 6 toys, so we divide 53 by 6 to find the number of bags:
53 toys / 6 toys/bag = 8.83 bags
Since a bag cannot hold a fraction of a toy, we must round the result up to the nearest whole number. This means that Edgar will need 9 bags to hold all of his toys.
We can express this result as a mixed number as 9 1/6 bags, where 1/6 represents the fraction of a bag that is not filled with toys. Alternatively, we can express it as an improper fraction as 57/6 bags, where 57 represents the total number of toys and 6 represents the number of toys that each bag can hold.
Answer:
[tex]\textsf{Improper fraction}: \quad \dfrac{53}{6}[/tex]
[tex]\textsf{Mixed number}: \quad 8\frac{5}{6}[/tex]
Step-by-step explanation:
Definitions
If each bag holds 6 toys and Edgar has 53 toys, to find how many bags Edgar will fill, divide 53 by 6.
To write this as an improper fraction, place 53 as the numerator and 6 as the denominator:
[tex]\implies \dfrac{53}{6}[/tex]
As 53 is a prime number, its only factors are 1 and 53. Therefore, the improper fraction cannot be reduced any further.
Rewrite 53 as the sum of 48 and 5:
[tex]\implies \dfrac{53}{6}=\dfrac{48+5}{6}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}:[/tex]
[tex]\implies \dfrac{48}{6}+\dfrac{5}{6}[/tex]
Divide 48 by 6:
[tex]\implies \dfrac{6 \cdot 8}{6}+\dfrac{5}{6}[/tex]
[tex]\implies 8+\dfrac{5}{6}[/tex]
Write as a mixed number:
[tex]\implies 8\frac{5}{6}[/tex]
