Question
Divide multi-digit whole _.
Estimate to predict _ and check for accuracy.
Divide multi-digit numbers to model real-world situations.
Estimate to predict _ and check for accuracy.
Divide multi-digit numbers to model real-world situations.
Answers
Answered by
GPT-4o mini
It seems you're looking for guidance on how to divide multi-digit whole numbers, estimate predictions, check for accuracy, and apply these skills to real-world situations. Here's a breakdown of each component:
### 1. Divide Multi-Digit Whole Numbers
To divide multi-digit numbers, you can use long division. Here's a step-by-step approach:
- **Step 1:** Set up the long division. Place the dividend (the number being divided) inside the division bracket and the divisor (the number you are dividing by) outside.
- **Step 2:** Determine how many times the divisor can fit into the first digits of the dividend.
- **Step 3:** Write that number above the division bracket. Multiply it by the divisor and write the result under the part of the dividend you are considering.
- **Step 4:** Subtract this result from the dividend segment you considered, and bring down the next digit of the dividend.
- **Step 5:** Repeat the process until you’ve brought down all digits of the dividend.
- **Step 6:** If there is a remainder, it can be expressed alongside the quotient.
**Example:**
Divide 348 by 12.
1. \( 12 \) goes into \( 34 \) \( 2 \) times (since \( 12 \times 2 = 24 \)).
2. Write \( 2 \) above the \( 4 \), subtract \( 24 \) from \( 34 \) (giving \( 10 \)), then bring down the \( 8 \) (making \( 108 \)).
3. \( 12 \) goes into \( 108 \) \( 9 \) times (since \( 12 \times 9 = 108 \)).
4. Write \( 9 \) above the line.
5. The result is \( 29 \) with no remainder.
### 2. Estimate to Predict
Estimation can help you quickly gauge what the answer might be, which is useful in determining if your answer is reasonable.
- **Step 1:** Round the dividend and the divisor to the nearest whole number.
- **Step 2:** Divide the rounded numbers to get a rough estimate.
**Example:**
Estimate \( 348 \div 12 \):
- Round \( 348 \) to \( 350 \) and \( 12 \) to \( 10 \).
- Estimate: \( 350 \div 10 = 35 \).
This gives you a rough idea of the actual answer being in the 30s.
### 3. Check for Accuracy
Once you have your quotient, you can check the accuracy of your division by multiplying the quotient by the divisor and adding any remainder, as follows:
**Example:**
Using our previous example:
- The quotient was \( 29 \) and the divisor is \( 12 \).
- Multiply: \( 29 \times 12 = 348 \).
- Since there's no remainder, our original division is correct!
### 4. Real-World Situations
You can apply division of multi-digit numbers to real-world problems such as:
- **Budgeting:** If you have a total budget of $348 to spend on 12 items, division can help you determine how much you can spend on each item.
- **Sharing:** If you are sharing something (like pizza or candy) between friends, dividing the total quantity by the number of friends can help figure out how much each person gets.
**Example:**
If you have 348 slices of pizza and want to share them equally among 12 people:
- You would use division: \( 348 \div 12 = 29 \).
- Each person receives 29 slices of pizza.
This methodological approach will help you confidently divide multi-digit numbers, make estimates, check for accuracy, and apply these skills in practical situations.
### 1. Divide Multi-Digit Whole Numbers
To divide multi-digit numbers, you can use long division. Here's a step-by-step approach:
- **Step 1:** Set up the long division. Place the dividend (the number being divided) inside the division bracket and the divisor (the number you are dividing by) outside.
- **Step 2:** Determine how many times the divisor can fit into the first digits of the dividend.
- **Step 3:** Write that number above the division bracket. Multiply it by the divisor and write the result under the part of the dividend you are considering.
- **Step 4:** Subtract this result from the dividend segment you considered, and bring down the next digit of the dividend.
- **Step 5:** Repeat the process until you’ve brought down all digits of the dividend.
- **Step 6:** If there is a remainder, it can be expressed alongside the quotient.
**Example:**
Divide 348 by 12.
1. \( 12 \) goes into \( 34 \) \( 2 \) times (since \( 12 \times 2 = 24 \)).
2. Write \( 2 \) above the \( 4 \), subtract \( 24 \) from \( 34 \) (giving \( 10 \)), then bring down the \( 8 \) (making \( 108 \)).
3. \( 12 \) goes into \( 108 \) \( 9 \) times (since \( 12 \times 9 = 108 \)).
4. Write \( 9 \) above the line.
5. The result is \( 29 \) with no remainder.
### 2. Estimate to Predict
Estimation can help you quickly gauge what the answer might be, which is useful in determining if your answer is reasonable.
- **Step 1:** Round the dividend and the divisor to the nearest whole number.
- **Step 2:** Divide the rounded numbers to get a rough estimate.
**Example:**
Estimate \( 348 \div 12 \):
- Round \( 348 \) to \( 350 \) and \( 12 \) to \( 10 \).
- Estimate: \( 350 \div 10 = 35 \).
This gives you a rough idea of the actual answer being in the 30s.
### 3. Check for Accuracy
Once you have your quotient, you can check the accuracy of your division by multiplying the quotient by the divisor and adding any remainder, as follows:
**Example:**
Using our previous example:
- The quotient was \( 29 \) and the divisor is \( 12 \).
- Multiply: \( 29 \times 12 = 348 \).
- Since there's no remainder, our original division is correct!
### 4. Real-World Situations
You can apply division of multi-digit numbers to real-world problems such as:
- **Budgeting:** If you have a total budget of $348 to spend on 12 items, division can help you determine how much you can spend on each item.
- **Sharing:** If you are sharing something (like pizza or candy) between friends, dividing the total quantity by the number of friends can help figure out how much each person gets.
**Example:**
If you have 348 slices of pizza and want to share them equally among 12 people:
- You would use division: \( 348 \div 12 = 29 \).
- Each person receives 29 slices of pizza.
This methodological approach will help you confidently divide multi-digit numbers, make estimates, check for accuracy, and apply these skills in practical situations.