what is 45 and a half as a fraction in simplest form
The correct answer and explanation is:
Answer:
45 and a half as a fraction in simplest form is: 912\boxed{\frac{91}{2}}
Explanation (Approximately 300 words)
To convert a mixed number like 45 and a half into a fraction, we follow a straightforward process. Let’s break it down step-by-step and explain why each step is necessary.
Step 1: Understand the Mixed Number
A mixed number consists of a whole number and a fraction. In this case, “45 and a half” means 45 (the whole number) and ½ (the fractional part). Mathematically, it can be written as: 45+1245 + \frac{1}{2}
Step 2: Convert the Whole Number to a Fraction
To combine both parts into one fraction, we first express 45 as a fraction. Any whole number can be written as a fraction by placing it over 1: 45=45145 = \frac{45}{1}
However, since we are going to add it to ½, we want a common denominator. The denominator of ½ is 2, so we convert 45 into a fraction with denominator 2: 451=45×22=902\frac{45}{1} = \frac{45 \times 2}{2} = \frac{90}{2}
Step 3: Add the Fractions
Now add the two fractions: 902+12=912\frac{90}{2} + \frac{1}{2} = \frac{91}{2}
This is now an improper fraction, meaning the numerator (top number) is greater than the denominator (bottom number). Improper fractions are perfectly valid and are often used in mathematics for calculations.
Step 4: Simplify
The final step is to check whether the fraction can be simplified. A fraction is in simplest form if the numerator and the denominator have no common factors other than 1.
In this case, 91 and 2 have no common factors (91 is not divisible by 2), so: 912\boxed{\frac{91}{2}}
is already in simplest form.
So, 45 and a half as a fraction in simplest form is 912\frac{91}{2}.