Answer :
To find out how many grains are in the box, we need to divide the total grain weight by the weight of one grain. Here’s how we can break it down step-by-step:
1. Total Grain Weight:
- The box contains a total grain weight of 512 grams.
2. Grain Weight:
- One grain weighs 56 grams.
3. Calculate Number of Grains:
- To find out how many grains are in the box, divide the total weight by the weight of one grain:
[tex]\[
\text{Total Grains} = \frac{512}{56} = 9.142857142857142
\][/tex]
This means there are 9 whole grains, and a fraction of a grain left.
4. Identify the Fraction:
- The decimal part, 0.142857..., is a repeating decimal equivalent to the fraction [tex]\(\frac{8}{56}\)[/tex] when simplified.
5. Simplify the Fraction:
- The fraction [tex]\(\frac{8}{56}\)[/tex] simplifies to [tex]\(\frac{1}{7}\)[/tex], but for the purpose here based on the options given, it’s shown as [tex]\(\frac{8}{56}\)[/tex].
Based on this calculation, the mixed number that represents the number of grains in the box is [tex]\(9 \frac{8}{56}\)[/tex].
Therefore, the correct answer is:
В) [tex]\(9 \frac{8}{56}\)[/tex]
1. Total Grain Weight:
- The box contains a total grain weight of 512 grams.
2. Grain Weight:
- One grain weighs 56 grams.
3. Calculate Number of Grains:
- To find out how many grains are in the box, divide the total weight by the weight of one grain:
[tex]\[
\text{Total Grains} = \frac{512}{56} = 9.142857142857142
\][/tex]
This means there are 9 whole grains, and a fraction of a grain left.
4. Identify the Fraction:
- The decimal part, 0.142857..., is a repeating decimal equivalent to the fraction [tex]\(\frac{8}{56}\)[/tex] when simplified.
5. Simplify the Fraction:
- The fraction [tex]\(\frac{8}{56}\)[/tex] simplifies to [tex]\(\frac{1}{7}\)[/tex], but for the purpose here based on the options given, it’s shown as [tex]\(\frac{8}{56}\)[/tex].
Based on this calculation, the mixed number that represents the number of grains in the box is [tex]\(9 \frac{8}{56}\)[/tex].
Therefore, the correct answer is:
В) [tex]\(9 \frac{8}{56}\)[/tex]
