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Answer :
Sure! Let's solve both parts of the question step-by-step.
### Part (1): What fraction of 1 minute is [tex]\(4^3\)[/tex] seconds?
1. Calculate [tex]\(4^3\)[/tex]: First, you need to calculate [tex]\(4^3\)[/tex], which means 4 raised to the power of 3.
- [tex]\(4^3 = 4 \times 4 \times 4 = 64\)[/tex].
2. Convert 1 minute to seconds: We know that 1 minute has 60 seconds.
3. Find the fraction: Now, find out what fraction 64 seconds is of 60 seconds.
- Fraction = [tex]\(\frac{64 \text{ seconds}}{60 \text{ seconds}}\)[/tex].
4. Simplified fraction answer: The fraction [tex]\(\frac{64}{60}\)[/tex] can be simplified if needed, or you can express it as a decimal, which is approximately 1.067.
So, [tex]\(4^3\)[/tex] seconds is about 1.067 times a minute.
### Part (2): What fraction of 600 g is 500 g?
1. Determine the quantities: You need to find the fraction of 500 grams out of 600 grams.
2. Calculate the fraction: Set up the fraction with 500 grams as the numerator and 600 grams as the denominator.
- Fraction = [tex]\(\frac{500 \text{ g}}{600 \text{ g}}\)[/tex].
3. Simplify the fraction: This fraction reduces to [tex]\(\frac{5}{6}\)[/tex] since both the numerator and the denominator can be divided by 100, or you can express it as a decimal, which is approximately 0.833.
So, 500 grams is [tex]\(\frac{5}{6}\)[/tex] or 0.833 (approximately) of 600 grams.
I hope this helps clarify the solution! If you have any more questions, feel free to ask.
### Part (1): What fraction of 1 minute is [tex]\(4^3\)[/tex] seconds?
1. Calculate [tex]\(4^3\)[/tex]: First, you need to calculate [tex]\(4^3\)[/tex], which means 4 raised to the power of 3.
- [tex]\(4^3 = 4 \times 4 \times 4 = 64\)[/tex].
2. Convert 1 minute to seconds: We know that 1 minute has 60 seconds.
3. Find the fraction: Now, find out what fraction 64 seconds is of 60 seconds.
- Fraction = [tex]\(\frac{64 \text{ seconds}}{60 \text{ seconds}}\)[/tex].
4. Simplified fraction answer: The fraction [tex]\(\frac{64}{60}\)[/tex] can be simplified if needed, or you can express it as a decimal, which is approximately 1.067.
So, [tex]\(4^3\)[/tex] seconds is about 1.067 times a minute.
### Part (2): What fraction of 600 g is 500 g?
1. Determine the quantities: You need to find the fraction of 500 grams out of 600 grams.
2. Calculate the fraction: Set up the fraction with 500 grams as the numerator and 600 grams as the denominator.
- Fraction = [tex]\(\frac{500 \text{ g}}{600 \text{ g}}\)[/tex].
3. Simplify the fraction: This fraction reduces to [tex]\(\frac{5}{6}\)[/tex] since both the numerator and the denominator can be divided by 100, or you can express it as a decimal, which is approximately 0.833.
So, 500 grams is [tex]\(\frac{5}{6}\)[/tex] or 0.833 (approximately) of 600 grams.
I hope this helps clarify the solution! If you have any more questions, feel free to ask.
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