Answer :
To find out how many grains are in a box containing a total weight of 512 grams, when each grain weighs 56 grams, you can follow these steps:
1. Understand the problem: We know the total weight of the grains in the box is 512 grams, and each grain has a weight of 56 grams. We need to determine the total number of grains in the box.
2. Set up the calculation: To find the number of grains, you need to divide the total weight of the grains by the weight of one grain.
[tex]\[
\text{Number of grains} = \frac{\text{Total weight of grains}}{\text{Weight of one grain}}
\][/tex]
3. Perform the division:
[tex]\[
\text{Number of grains} = \frac{512}{56}
\][/tex]
Carrying out this division gives you approximately 9.142857142857142.
4. Interpret the result: The result can be expressed as a mixed number. Since 9 is the integer part, and 0.142857142857142 can be converted into a fraction:
- Convert the decimal to a fraction: 0.142857... is equivalent to [tex]\(\frac{1}{7}\)[/tex].
- Since the mixed number choice closest to this in the given options is [tex]\(9 \frac{1}{8}\)[/tex], after rounding, this implies that for practical purposes (like choosing from the given options), 9 [tex]\(\frac{1}{8}\)[/tex] is the closest match.
5. Select the correct option: Look at the choices provided and compare them with your result. The correct answer matches with choice A) [tex]\(9 \frac{1}{8}\)[/tex].
6. Final check: Confirm that this choice accurately represents the division result (rounded and converted to a mixed number).
So, the correct answer is A) [tex]\(9 \frac{1}{8}\)[/tex].
1. Understand the problem: We know the total weight of the grains in the box is 512 grams, and each grain has a weight of 56 grams. We need to determine the total number of grains in the box.
2. Set up the calculation: To find the number of grains, you need to divide the total weight of the grains by the weight of one grain.
[tex]\[
\text{Number of grains} = \frac{\text{Total weight of grains}}{\text{Weight of one grain}}
\][/tex]
3. Perform the division:
[tex]\[
\text{Number of grains} = \frac{512}{56}
\][/tex]
Carrying out this division gives you approximately 9.142857142857142.
4. Interpret the result: The result can be expressed as a mixed number. Since 9 is the integer part, and 0.142857142857142 can be converted into a fraction:
- Convert the decimal to a fraction: 0.142857... is equivalent to [tex]\(\frac{1}{7}\)[/tex].
- Since the mixed number choice closest to this in the given options is [tex]\(9 \frac{1}{8}\)[/tex], after rounding, this implies that for practical purposes (like choosing from the given options), 9 [tex]\(\frac{1}{8}\)[/tex] is the closest match.
5. Select the correct option: Look at the choices provided and compare them with your result. The correct answer matches with choice A) [tex]\(9 \frac{1}{8}\)[/tex].
6. Final check: Confirm that this choice accurately represents the division result (rounded and converted to a mixed number).
So, the correct answer is A) [tex]\(9 \frac{1}{8}\)[/tex].
