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A large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, [tex][tex]$p$[/tex][/tex], was 342. Which statements can be used to write an expression and then find the number of peanuts that ended up in each bag? Check all that apply.

- The operation is division.
- The operation is multiplication.
- The variable is the number of bags.
- 342 divided by 6 equals 57.
- Write the division expression as a fraction, [tex]\frac{p}{6}[/tex].
- To evaluate, substitute 342 for the variable.
- Each bag will have 57 peanuts.
- The constant is 342.

Sagot :

GinnyAnswer
Alright, let's walk through the problem and the statements given step-by-step to identify which are useful in finding the number of peanuts in each bag.

We know the following:

- The total number of peanuts is [tex]\( p = 342 \)[/tex].
- The peanuts are divided equally into 6 small bags.

First, identify the operation we need to use:

1. The operation is division.
- This statement is correct. Since the peanuts are divided into smaller bags equally, we use division to find how many peanuts are in each bag.

Next, clarify which operation would be inappropriate:

2. The operation is multiplication.
- This statement is not correct in this context, as we are not combining quantities but rather dividing them.

Identify the variable involved:

3. The variable is the number of bags.
- This statement is incorrect here. The number of bags (6) is actually a given value, not a variable.

Construct the division expression:

4. 342 divided by 6 equals 57.
- This is a correct statement. If we divide the total number of peanuts (342) by the number of bags (6), we get 57 peanuts per bag.

Express the division operation as a fraction:

5. Write the division expression as a fraction, [tex]\(\frac{p}{6}\)[/tex].
- This is correct. Writing the division as a fraction [tex]\(\frac{p}{6}\)[/tex] helps in visualizing the division process.

Evaluating the expression by substitution:

6. To evaluate, substitute 342 for the variable.
- This statement is partially correct but needs clarification. The variable [tex]\( p \)[/tex] is being substituted by 342 in [tex]\(\frac{p}{6}\)[/tex].

Conclusion about the result:

7. Each bag will have 57 peanuts.
- This is correct. After performing the division, each bag indeed contains 57 peanuts.

Identify the constant:

8. The constant is 342.
- This statement is correct. In this scenario, 342 (the total number of peanuts) is the constant.

So, the statements you should check as correct are:

- The operation is division.
- 342 divided by 6 equals 57.
- Write the division expression as a fraction, [tex]\(\frac{p}{6}\)[/tex].
- Each bag will have 57 peanuts.
- The constant is 342.

These statements provide the necessary steps and information to correctly find the number of peanuts in each of the 6 bags.
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