Question

How many \[\dfrac{1}{4}\] pound bags of candy can be made from a \[3\dfrac{1}{2}\] pound bag of nuts?

Answer 1

Hint: Here we will firstly convert the given weight of nuts i.e. \[3\dfrac{1}{2}\] which is given in the mixed fraction into the normal fraction. Then we will simply divide the given weight of the bag of nuts with the given weight of the bag of candy to get the number of bags of candy.

Complete step by step solution:
It is given that the weight of the bag of nuts is equal to \[3\dfrac{1}{2}\] pound.
We will convert this weight into the normal fraction as it is given in the mixed fraction form. Therefore, we get
Weight of the bag of nuts \[ = 3\dfrac{1}{2} = \dfrac{{3 \times 2 + 1}}{2} = \dfrac{7}{2}pound\]
It is also given that the weight of the bag of candy is equal to \[\dfrac{1}{4}\] pound.
Now we will simply divide the given weight of the bag of nuts with the given weight of the bag of candy to get the number of bags of candy which can be made. Therefore, we get
Number of bags of candy \[ = \] Weight of nuts \[\div\] Weight of candy
Now we will put the values of the respective weights. Therefore, we get
Number of bags of candy \[ = \dfrac{{\dfrac{7}{2}}}{{\dfrac{1}{4}}} = \dfrac{{7 \times 4}}{2}\]
Now by solving the above equation, we get
Number of bags of candy \[ = 14\]

Hence the number of \[\dfrac{1}{4}\] pound bags of candy can be made from a \[3\dfrac{1}{2}\] pound bag of nuts is 14.

Note:
A pound is generally the weighing unit used in the foreign weighing system. A pound is generally not used as an Indian weighing system but a kilogram is the weighing unit that is generally used in the Indian weighing system.
We know the definition of three main types of fraction i.e. proper fractions, improper fractions and mixed fractions. Mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1. An improper fraction can be converted into a mixed fraction.