Question

One fruit salad recipe requires $\dfrac{1}{2}$ cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to $\dfrac{1}{16}$ cup, how much more sugar does the first recipe require?

Answer 1

Hint: Here, first to find the extra quantity of sugar for the first recipe, we have to find the difference between quantities of sugar required for the first and second recipe. Now, for that we have to convert tablespoons into parts of the cup. Using a unitary method, find the quantity of sugar for the second recipe by multiplying $\dfrac{1}{16}$ by 2. Now that both quantities are in terms of cups, subtract and find the answer.

Complete step by step answer:
From given information, we can write,
The first recipe requires $\dfrac{1}{2}$ cup of sugar.
The second recipe requires 2 tablespoons of sugar.
According to question, we have been given that
1 tablespoon of sugar = $\dfrac{1}{16}$ cup of sugar
We will now apply the unitary method here. This method is very helpful when we have to find the value of n items and the value of the unit item is known.
Here, we already know that value for 1 tablespoon. So, now let us find out the parts of a cup that 2 tablespoons of sugar would amount to.
Now, for 2 tablespoon, we have to multiply 2 with value for 1 tablespoon,
2 tablespoons =\[2\times \left( \dfrac{1}{16} \right)=\dfrac{1}{8}\]cup
Now, we have quantities of sugar for both recipes in terms of parts of a cup.
To derive how much more sugar the first recipe requires, we have to find the difference between the sugar required for the first recipe and the second recipe.
Hence, more amount of sugar the first cup requires \[=\left( \dfrac{1}{2} \right)-\left( \dfrac{1}{8} \right)\] cup
Taking LCM of terms, we get
\[=\left( \dfrac{4}{8} \right)-\left( \dfrac{1}{8} \right)\]
Again on simplification, we get,
\[=\dfrac{3}{8}\] cup

Thus, we have found that $\dfrac{3}{8}$ cup of extra sugar is required for the first recipe.

Note: This is a tricky question. With given information as 1 tablespoon is equivalent to $\dfrac{1}{16}$ cups, one can make mistakes while calculating 2 tablespoons of sugar. Instead of taking multiplication \[2\times \left( \dfrac{1}{16} \right)=\dfrac{1}{8}\], student by mistake, take division as \[\dfrac{\dfrac{1}{16}}{2}=\dfrac{1}{32}\]. This is the incorrect method. Students can also proceed by taking the unit in terms of tablespoons also. So, they will get that 16 tablespoons = 1 cup. Then, $\dfrac{1}{2}$ cup would be 8 tablespoons. Second recipe requires 2 tablespoons. So, we get that 8 – 2 = 6 tablespoons extra sugar is required for the first recipe.