How many pieces of length $1\dfrac{3}{4}m$ each can be cut from a cloth 84 m long?
ANSWER
Verified
Hint: We will convert mixed fraction to normal fraction first as we know that any mixed fraction like $a\dfrac{n}{b}$ can be converted into the normal form as $\dfrac{a\times b+n}{b}$. Then, convert to obtain the normal fraction into decimal form by just dividing it and in the final step we will divide the total length of the cloth with the obtained length of one piece in decimal to get the total number of pieces we can cut.
Complete step-by-step answer: It is given in the question that we have to cut out a piece of length $1\dfrac{3}{4}m$ each from a big piece of cloth 84 m long. First of all, we will convert the mixed fraction $1\dfrac{3}{4}m$ into the normal fraction form. We know that we can convert any mixed fraction $a\dfrac{n}{b}$ into its normal fraction form as $\dfrac{a\times b+n}{b}$. Thus, $1\dfrac{3}{4}$ can be written as $\dfrac{1\times 4+3}{4}=\dfrac{4+3}{4}=\dfrac{7}{4}$. So, we get a normal fraction of $1\dfrac{3}{4}m$ as $\dfrac{7}{4}m$. Now, we will convert $\dfrac{7}{4}$ into the decimal form as $\dfrac{7}{4}=1.75m$. Therefore, we will cut each piece of 1.75 m from the big cloth of 84 m length. Now, to get the total number of pieces we will use a unitary method. Unitary method is a mathematical approach to solve a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value. So, we will find the total number of pieces $\text{=}\dfrac{\text{total length}}{\text{size of 1 piece}}=\dfrac{84m}{1.75m}=48$. Therefore, we get that, 48 pieces of 1.75 m length can be cut from a cloth piece of 84 m.
Note: Whenever any mixed fraction is given in the question, it is better to convert it into the normal fraction. Then, it is not necessary to convert it to decimals. We can also find the final answer by diving 84 m by $\dfrac{7}{4}m$ directly. Also students must check if all the values are given in the same unit or not, if not convert all to one unit and then only proceed with the question.