Question

What is $\dfrac{9}{16}+\dfrac{1}{2},$ simplified?

Answer 1

Hint: When we add two fractions with distinct denominators, we will use cross multiplication. We will find the sum of the product of numerator of one fraction and denominator of the other fraction and the product of numerator of the second fraction and the denominator of the first fraction. And then we will divide this sum by the product of denominators of both fractions.

Complete step by step solution:
Let us consider the given problem.
We are asked to find the sum $\dfrac{9}{16}+\dfrac{1}{2}.$
Here, we have two fractions, $\dfrac{9}{16}$ and $\dfrac{1}{2}.$
As we can see, the denominators of the fractions are distinct.
In this case, we need to do the cross multiplication.
We will first find the product of the numerator of the first fraction and the denominator of the second fraction. We will get $9\times 2=18.$
Then, we will find the product of the numerator of the second fraction and the denominator of the first fraction. By doing this, we will obtain $1\times 16=16.$
Now, we will add the two products we have obtained to get $18+16=34.$
Next, we will multiply the denominators of both fractions to find their product.
So, we will get $2\times 16=12.$
Now, we will divide the sum we have obtained by the product obtained above. We will get $\dfrac{34}{32}.$
Since $17\times 2=24$ and $16\times 2=32,$ we will get $\dfrac{34}{32}=\dfrac{17}{16}.$
Hence the sum of the given fractions is $\dfrac{3}{4}.$

Note: The basic idea behind the cross multiplication is the least common multiple. We want to make the denominators of both fractions the same. For that, we can multiply and divide the second fraction with $8.$ We will get $\dfrac{1\times 8}{2\times 8}=\dfrac{8}{16}.$ Now, the sum is $\dfrac{9}{16}+\dfrac{8}{16}=\dfrac{17}{16}.$