Question

Write the following fractions as decimal fractions
(1) Two and a half.
(2) Two and a quarter.
(3) Ten and a half.
(4) Fourteen and three quarters.

Answer 1

Hint: In this question, first convert the given statement into numbers. Half means $\dfrac{1}{2}$ and quarter means $\dfrac{1}{4}$ . You should use this information to convert the given statement in fraction. After this next thing that you have to do is to convert the fraction into decimal.

Complete step-by-step answer:
In the question, it is given that we have to convert the given four fractions into decimal.
But the numbers are not directly given. They are given in terms of statements.
So, first we will convert these statements into fraction and then convert the fraction into decimal.
Two things that we should know before solving are:
Half means $\dfrac{1}{2}$ and quarter means $\dfrac{1}{4}$ .
(1)Two and a half
On converting it into number we get:
$2 + \dfrac{1}{2} = \dfrac{5}{2}$
Now, we will convert it into decimal which is given as:
$\dfrac{5}{2} = \dfrac{{5 \times 50}}{{2 \times 50}} = \dfrac{{250}}{{100}} = 2.5$
Here we have multiplied both numerator and denominator by 50 to get 100 in denominator so that we can easily convert the fraction into decimal.

(2)Two and a quarter
On converting it into number we get:
$2 + \dfrac{1}{4} = \dfrac{9}{4}$
Now, we will convert it into decimal which is given as:
$\dfrac{9}{4} = \dfrac{{9 \times 25}}{{2 \times 25}} = \dfrac{{225}}{{100}} = 2.25$
Here we have multiplied both numerator and denominator by 25 to get 100 in denominator so that we can easily convert the fraction into decimal.

(3)Ten and a half
On converting it into number we get:
$10 + \dfrac{1}{2} = \dfrac{{21}}{2}$
Now, we will convert it into decimal which is given as:
$\dfrac{{21}}{2} = \dfrac{{21 \times 50}}{{2 \times 50}} = \dfrac{{1050}}{{100}} = 10.5$

(4)Fourteen and three quarters
Quarter means $\dfrac{1}{4}$ .
$\therefore $ Three quarters means $\dfrac{{3 \times 1}}{4} = \dfrac{3}{4}.$
Now, on converting the given statement into fraction, we get:
$14 + \dfrac{3}{4} = \dfrac{{59}}{4}$ .
Now, we will convert it into decimal which is given as:
$\dfrac{{59}}{4} = \dfrac{{59 \times 25}}{{4 \times 25}} = \dfrac{{1475}}{{100}} = 14.75$
Here we have multiplied both numerator and denominator by 25 to get 100 in denominator so that we can easily convert the fraction into decimal.

Note: In such types of questions, you should proceed with converting the given numbers in words to the fraction. After this convert the fraction into decimal. There are two ways to convert the fraction into decimal. First one is that if the denominator of the fraction is convertible 100 by multiplying some number then in this case multiply both numerator and denominator by the same number to get 100 in denominator then simply convert the fraction into decimal. Another method is just divide the numerator by denominator to get the quotient in decimal.