Write 23 as an improper fraction in its simplest form.
Work out 23 x 5. Give your answer as a fraction in its simplest form
The Correct Answer and Explanation is:
Part 1: Expressing 23 as an Improper Fraction
To express the whole number 23 as an improper fraction, we simply place it over 1. This is because any whole number can be written as a fraction with a denominator of 1. Thus, 23 as an improper fraction is:
[
23 = \frac{23}{1}
]
This fraction represents the whole number 23 divided by 1, which simplifies back to 23. There’s no further simplification needed because the fraction is already in its simplest form.
Part 2: Multiplying 23 by 5 and Expressing as a Fraction
Next, we are asked to multiply 23 by 5 and give the answer as a fraction in its simplest form.
Step 1: Write both numbers as fractions:
- 23 as a fraction is (\frac{23}{1}),
- 5 as a fraction is (\frac{5}{1}).
Now, we multiply these two fractions:
[
\frac{23}{1} \times \frac{5}{1} = \frac{23 \times 5}{1 \times 1} = \frac{115}{1}
]
Step 2: Simplification:
The fraction (\frac{115}{1}) is already in its simplest form because the denominator is 1, and there is no need for further simplification. So the final result is:
[
\frac{115}{1} = 115
]
Explanation:
- Improper Fraction: An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). When we express 23 as (\frac{23}{1}), it’s technically an improper fraction because the numerator (23) is greater than the denominator (1).
- Multiplication of Fractions: When multiplying fractions, the rule is to multiply the numerators together and multiply the denominators together. For this problem, multiplying (\frac{23}{1}) by (\frac{5}{1}) gives a new fraction (\frac{115}{1}).
- Simplest Form: After performing the multiplication, the result (\frac{115}{1}) is already simplified because it cannot be reduced further.
Thus, (23 \times 5 = \frac{115}{1}), and the answer is 115.