Question
mercury:35.9 million miles. venus:67.2 million miles earth:93million miles. mars:128.4 million miles Jupiter:483 million miles Saturn:885.5 million miles Uranus:32,000 miles Neptune:2.8 billion miles
Choose two of the distances of planets from the sun and add them. Show your work.
Choose two of the distances of planets from the sun and add them. Show your work.
Answers
GPT-4o mini
Let's choose the distances of Earth and Mars from the Sun to add them together.
1. Distance of Earth from the Sun: 93 million miles
2. Distance of Mars from the Sun: 128.4 million miles
Now, we will add the two distances:
\[
93 \text{ million miles} + 128.4 \text{ million miles} = 221.4 \text{ million miles}
\]
So, the total distance of Earth and Mars from the Sun is **221.4 million miles**.
1. Distance of Earth from the Sun: 93 million miles
2. Distance of Mars from the Sun: 128.4 million miles
Now, we will add the two distances:
\[
93 \text{ million miles} + 128.4 \text{ million miles} = 221.4 \text{ million miles}
\]
So, the total distance of Earth and Mars from the Sun is **221.4 million miles**.
Choose two of the distances of planets from the sun and subtract them.
GPT-4o mini
Let's choose the distances of Jupiter and Venus from the Sun to subtract them.
1. Distance of Jupiter from the Sun: 483 million miles
2. Distance of Venus from the Sun: 67.2 million miles
Now, we will subtract the distance of Venus from the distance of Jupiter:
\[
483 \text{ million miles} - 67.2 \text{ million miles} = 415.8 \text{ million miles}
\]
So, the result of subtracting the distance of Venus from Jupiter is **415.8 million miles**.
1. Distance of Jupiter from the Sun: 483 million miles
2. Distance of Venus from the Sun: 67.2 million miles
Now, we will subtract the distance of Venus from the distance of Jupiter:
\[
483 \text{ million miles} - 67.2 \text{ million miles} = 415.8 \text{ million miles}
\]
So, the result of subtracting the distance of Venus from Jupiter is **415.8 million miles**.
Choose two of the distances of planets from the sun and multiply them.
GPT-4o mini
Let's choose the distances of Mercury and Earth from the Sun to multiply them.
1. Distance of Mercury from the Sun: 35.9 million miles
2. Distance of Earth from the Sun: 93 million miles
Now, we will multiply the two distances:
\[
35.9 \, \text{million miles} \times 93 \, \text{million miles} = 3,344.7 \, \text{million miles}^2
\]
So, the product of the distances of Mercury and Earth from the Sun is **3,344.7 million miles²**.
1. Distance of Mercury from the Sun: 35.9 million miles
2. Distance of Earth from the Sun: 93 million miles
Now, we will multiply the two distances:
\[
35.9 \, \text{million miles} \times 93 \, \text{million miles} = 3,344.7 \, \text{million miles}^2
\]
So, the product of the distances of Mercury and Earth from the Sun is **3,344.7 million miles²**.
Choose two of the distances of planets from the sun and add them. Show your work. Just do the first on again you did but show work
GPT-4o mini
Sure! Let's choose the distances of Earth and Mars from the Sun again.
1. **Distance of Earth from the Sun**: 93 million miles
2. **Distance of Mars from the Sun**: 128.4 million miles
Now, let's show the addition step by step:
### Step 1: Write down the distances
\[
\text{Earth} = 93 \, \text{million miles}
\]
\[
\text{Mars} = 128.4 \, \text{million miles}
\]
### Step 2: Align the numbers for addition
```
93.0
+ 128.4
```
### Step 3: Add the numbers starting from the rightmost column
- **Thousandths**: \(0 + 4 = 4\)
- **Hundredths**: \(3 + 8 = 11\) (write down 1 and carry over 1)
- **Tenths**: \(9 + 2 + 1 (\text{carry}) = 12\) (write down 2 and carry over 1)
- **Units**: \(1 (\text{carry}) + 1 = 2\)
### Step 4: Write the result
Putting it all together, we perform the addition:
```
93.0
+ 128.4
--------
221.4
```
### Final Answer
So, the total distance of Earth and Mars from the Sun is **221.4 million miles**.
1. **Distance of Earth from the Sun**: 93 million miles
2. **Distance of Mars from the Sun**: 128.4 million miles
Now, let's show the addition step by step:
### Step 1: Write down the distances
\[
\text{Earth} = 93 \, \text{million miles}
\]
\[
\text{Mars} = 128.4 \, \text{million miles}
\]
### Step 2: Align the numbers for addition
```
93.0
+ 128.4
```
### Step 3: Add the numbers starting from the rightmost column
- **Thousandths**: \(0 + 4 = 4\)
- **Hundredths**: \(3 + 8 = 11\) (write down 1 and carry over 1)
- **Tenths**: \(9 + 2 + 1 (\text{carry}) = 12\) (write down 2 and carry over 1)
- **Units**: \(1 (\text{carry}) + 1 = 2\)
### Step 4: Write the result
Putting it all together, we perform the addition:
```
93.0
+ 128.4
--------
221.4
```
### Final Answer
So, the total distance of Earth and Mars from the Sun is **221.4 million miles**.
Choose two of the distances of planets from the sun and multiply them. Show your work.
GPT-4o mini
Let's choose the distances of Saturn and Neptune from the Sun to multiply.
1. **Distance of Saturn from the Sun**: 885.5 million miles
2. **Distance of Neptune from the Sun**: 2.8 billion miles (which is equivalent to 2800 million miles)
Now, we will show the multiplication step by step.
### Step 1: Write down the distances
\[
\text{Saturn} = 885.5 \, \text{million miles}
\]
\[
\text{Neptune} = 2800 \, \text{million miles}
\]
### Step 2: Set up the multiplication
\[
885.5 \times 2800
\]
### Step 3: Perform the multiplication
We'll multiply as follows:
\[
885.5 \times 2800
\]
To make the multiplication easier, we can separate it into smaller parts:
\[
885.5 \times 2800 = 885.5 \times (2000 + 800)
\]
Now we'll calculate each part:
1. **885.5 × 2000**:
\[
885.5 \times 2000 = 1771000 \, \text{(shift the decimal 3 places to the right)}
\]
2. **885.5 × 800**:
\[
885.5 \times 800 = 708400 \, \text{(shift the decimal 3 places to the right)}
\]
### Step 4: Add the two results
Now we sum them:
\[
1771000 + 708400 = 2479400
\]
### Step 5: Write the final result
The result of multiplying the distances of Saturn and Neptune from the Sun is:
\[
885.5 \, \text{million miles} \times 2800 \, \text{million miles} = 2479400 \, \text{million miles}^2
\]
### Final Answer
So, the product of the distances of Saturn and Neptune from the Sun is **2,479,400 million miles²** or **2.4794 billion million miles²**.
1. **Distance of Saturn from the Sun**: 885.5 million miles
2. **Distance of Neptune from the Sun**: 2.8 billion miles (which is equivalent to 2800 million miles)
Now, we will show the multiplication step by step.
### Step 1: Write down the distances
\[
\text{Saturn} = 885.5 \, \text{million miles}
\]
\[
\text{Neptune} = 2800 \, \text{million miles}
\]
### Step 2: Set up the multiplication
\[
885.5 \times 2800
\]
### Step 3: Perform the multiplication
We'll multiply as follows:
\[
885.5 \times 2800
\]
To make the multiplication easier, we can separate it into smaller parts:
\[
885.5 \times 2800 = 885.5 \times (2000 + 800)
\]
Now we'll calculate each part:
1. **885.5 × 2000**:
\[
885.5 \times 2000 = 1771000 \, \text{(shift the decimal 3 places to the right)}
\]
2. **885.5 × 800**:
\[
885.5 \times 800 = 708400 \, \text{(shift the decimal 3 places to the right)}
\]
### Step 4: Add the two results
Now we sum them:
\[
1771000 + 708400 = 2479400
\]
### Step 5: Write the final result
The result of multiplying the distances of Saturn and Neptune from the Sun is:
\[
885.5 \, \text{million miles} \times 2800 \, \text{million miles} = 2479400 \, \text{million miles}^2
\]
### Final Answer
So, the product of the distances of Saturn and Neptune from the Sun is **2,479,400 million miles²** or **2.4794 billion million miles²**.
Choose two of the distances of planets from the sun and divide them. Show your work.
GPT-4o mini
Let’s choose the distances of Jupiter and Earth from the Sun to divide.
1. **Distance of Jupiter from the Sun**: 483 million miles
2. **Distance of Earth from the Sun**: 93 million miles
We will divide the distance of Jupiter by the distance of Earth.
### Step 1: Set up the division
\[
\frac{483 \, \text{million miles}}{93 \, \text{million miles}}
\]
### Step 2: Perform the division
Now we divide 483 by 93. We can do this long division step by step.
1. **Divide the first two digits**: 93 into 483
- 93 goes into 483 approximately 5 times (since \( 93 \times 5 = 465 \)).
We write down 5 and subtract:
\[
483 - 465 = 18
\]
2. **Bring down the next digit**: Since there are no more digits in 483, we consider the next part. In decimal terms, we can treat this as 180 (considering two decimal places).
3. **Now divide again**: 93 into 180
- 93 goes into 180 approximately 1 time (since \( 93 \times 1 = 93 \)).
We write down 1 and subtract:
\[
180 - 93 = 87
\]
4. **Bring down another 0 to get 870**.
5. **Divide again**: 93 into 870
- 93 goes into 870 approximately 9 times (since \( 93 \times 9 = 837 \)).
We write down 9 and subtract:
\[
870 - 837 = 33
\]
6. **Bring down another 0 to get 330**.
7. **Divide again**:
- 93 goes into 330 approximately 3 times (since \( 93 \times 3 = 279 \)).
We write down 3 and subtract:
\[
330 - 279 = 51
\]
Now, putting this all together:
\[
\frac{483}{93} \approx 5.19
\]
### Final Result
The division of the distance of Jupiter by the distance of Earth is approximately:
\[
\frac{483 \, \text{million miles}}{93 \, \text{million miles}} \approx 5.19
\]
This means **Jupiter is approximately 5.19 times further from the Sun than Earth.**
1. **Distance of Jupiter from the Sun**: 483 million miles
2. **Distance of Earth from the Sun**: 93 million miles
We will divide the distance of Jupiter by the distance of Earth.
### Step 1: Set up the division
\[
\frac{483 \, \text{million miles}}{93 \, \text{million miles}}
\]
### Step 2: Perform the division
Now we divide 483 by 93. We can do this long division step by step.
1. **Divide the first two digits**: 93 into 483
- 93 goes into 483 approximately 5 times (since \( 93 \times 5 = 465 \)).
We write down 5 and subtract:
\[
483 - 465 = 18
\]
2. **Bring down the next digit**: Since there are no more digits in 483, we consider the next part. In decimal terms, we can treat this as 180 (considering two decimal places).
3. **Now divide again**: 93 into 180
- 93 goes into 180 approximately 1 time (since \( 93 \times 1 = 93 \)).
We write down 1 and subtract:
\[
180 - 93 = 87
\]
4. **Bring down another 0 to get 870**.
5. **Divide again**: 93 into 870
- 93 goes into 870 approximately 9 times (since \( 93 \times 9 = 837 \)).
We write down 9 and subtract:
\[
870 - 837 = 33
\]
6. **Bring down another 0 to get 330**.
7. **Divide again**:
- 93 goes into 330 approximately 3 times (since \( 93 \times 3 = 279 \)).
We write down 3 and subtract:
\[
330 - 279 = 51
\]
Now, putting this all together:
\[
\frac{483}{93} \approx 5.19
\]
### Final Result
The division of the distance of Jupiter by the distance of Earth is approximately:
\[
\frac{483 \, \text{million miles}}{93 \, \text{million miles}} \approx 5.19
\]
This means **Jupiter is approximately 5.19 times further from the Sun than Earth.**