To convert the decimal [tex]\( 7.5 \)[/tex] into a fraction, follow these steps:
1. Understand the decimal:
The decimal number [tex]\( 7.5 \)[/tex] can be read as "seven and a half" or "seven point five."
2. Separate the integer and decimal parts:
Notice that [tex]\( 7.5 \)[/tex] can be split into two components: [tex]\( 7 \)[/tex] (the integer part) and [tex]\( 0.5 \)[/tex] (the decimal part).
3. Convert the decimal part to a fraction:
The decimal [tex]\( 0.5 \)[/tex] is equivalent to [tex]\( \frac{5}{10} \)[/tex]. Simplifying this fraction, divide both the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
So, [tex]\( 0.5 \)[/tex] is equivalent to [tex]\( \frac{1}{2} \)[/tex].
4. Combine the integer part with the fraction:
Now, combine the integer part [tex]\( 7 \)[/tex] with the fraction [tex]\( \frac{1}{2} \)[/tex]. To write this as a single fraction, first convert the integer into a fraction:
[tex]\[
7 = \frac{7}{1}
\][/tex]
5. Find a common denominator:
To add [tex]\( 7 = \frac{7}{1} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex], we first need a common denominator. The least common multiple of 1 and 2 is 2. So, convert [tex]\( \frac{7}{1} \)[/tex] to a fraction with a denominator of 2:
[tex]\[
\frac{7}{1} = \frac{7 \times 2}{1 \times 2} = \frac{14}{2}
\][/tex]
6. Add the fractions:
Now that both fractions have the same denominator:
[tex]\[
\frac{14}{2} + \frac{1}{2} = \frac{14 + 1}{2} = \frac{15}{2}
\][/tex]
Therefore, the decimal [tex]\( 7.5 \)[/tex] can be accurately expressed as the improper fraction [tex]\( \frac{15}{2} \)[/tex].
So, the final answer is:
[tex]\[
7.5 = \frac{15}{2}
\][/tex]
