Question

Brad grew $4\dfrac{1}{4}$ inches this year and is now $56\dfrac{7}{8}$ inches tall. How do you write and solve an equation to find Brad’s height at the start of the year?

Answer 1

Hint: In this question we have been given how much Brad’s height has grown and the total height of Brad as of now. We will convert both the given mixed fractions into improper fractions and then we will subtract the value of height grown from the total height to get Brad’s height at the start of the year.

Complete step-by-step solution:
We know that Brad grew $4\dfrac{1}{4}$ inches this year. We will convert the mixed fraction to an improper fraction.
We have to multiply the denominator of the fraction with the whole number and add whatever there is in the numerator, it can be written as:
$\Rightarrow 4\dfrac{1}{4}=\dfrac{\left( 4\times 4 \right)+1}{4}$
On simplifying, we get:
$\Rightarrow 4\dfrac{1}{4}=\dfrac{17}{4}$.
Therefore, Brad grew $\dfrac{17}{4}$ inches this year.
Currently Brad is $56\dfrac{7}{8}$ inches tall. We will convert the mixed fraction to an improper fraction.
We have to multiply the denominator of the fraction with the whole number and add whatever there is in the numerator, it can be written as:
$\Rightarrow 56\dfrac{7}{8}=\dfrac{\left( 56\times 8 \right)+7}{8}$
On simplifying, we get:
$\Rightarrow 56\dfrac{7}{8}=\dfrac{455}{8}$.
Therefore, Brad is $\dfrac{455}{8}$ tall.
Now brads height at the start of the year will be the subtraction of the current height and the height grown.
It can be written as:
$\Rightarrow \dfrac{455}{8}-\dfrac{17}{4}$
On taking the lowest common multiple in the denominator, we get:
$\Rightarrow \dfrac{455}{8}-\dfrac{34}{8}$
On taking the denominator common, we get:
$\Rightarrow \dfrac{455-34}{8}$
On simplifying the terms in the numerator, we get:
$\Rightarrow \dfrac{421}{8}$, which is the height at the start of the year, which is the required solution.

Note: In this question we have converted mixed fraction to an improper fraction. An improper fraction is a fraction whose denominator is less than its numerator and a proper fraction has the numerator lesser than the denominator. A mixed fraction is a combination of a whole number and a fraction therefore, it has two parts to it.