Question
Write and solve the equation that represents the sentence below.
The quotient of a number and 18 is 109.8.
Which statements are correct? Check all that apply.
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be StartFraction x Over 18 EndFraction = 109.8.
The equation should be 18 x = 109.8.
The answer is 6.1.
The answer is 1,976.4.
The quotient of a number and 18 is 109.8.
Which statements are correct? Check all that apply.
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be StartFraction x Over 18 EndFraction = 109.8.
The equation should be 18 x = 109.8.
The answer is 6.1.
The answer is 1,976.4.
Answers
GPT-4o mini
To solve the problem, let's start by translating the sentence into an equation.
The sentence "The quotient of a number and 18 is 109.8" means that if we let the unknown number be \( x \), then we can express the statement as:
\[
\frac{x}{18} = 109.8
\]
Now, let's check the statements provided:
1. **It can be solved by using the division property of equality.**
**Correct.** You can use the division property to manipulate the equation. However, in this case, you generally would multiply both sides by 18 to isolate \( x \).
2. **It can be solved by using the multiplication property of equality.**
**Correct.** You would typically multiply both sides by 18 to eliminate the fraction.
3. **The equation should be StartFraction x Over 18 EndFraction = 109.8.**
**Correct.** This is the correct representation of the given sentence.
4. **The equation should be 18 x = 109.8.**
**Incorrect.** This is not a correct interpretation; it misrepresents the first statement.
5. **The answer is 6.1.**
**Correct.** To find \( x \):
\[
\frac{x}{18} = 109.8 \implies x = 109.8 \times 18 = 1976.4
\]
(So this statement is indeed incorrect in stating that the answer is 6.1.)
6. **The answer is 1,976.4.**
**Correct.** As calculated above, \( x = 109.8 \times 18 = 1976.4 \).
### Summary:
The correct statements are:
- It can be solved by using the division property of equality.
- It can be solved by using the multiplication property of equality.
- The equation should be StartFraction x Over 18 EndFraction = 109.8.
- The answer is 1,976.4.
The incorrect statements are:
- The equation should be 18 x = 109.8.
- The answer is 6.1.
The sentence "The quotient of a number and 18 is 109.8" means that if we let the unknown number be \( x \), then we can express the statement as:
\[
\frac{x}{18} = 109.8
\]
Now, let's check the statements provided:
1. **It can be solved by using the division property of equality.**
**Correct.** You can use the division property to manipulate the equation. However, in this case, you generally would multiply both sides by 18 to isolate \( x \).
2. **It can be solved by using the multiplication property of equality.**
**Correct.** You would typically multiply both sides by 18 to eliminate the fraction.
3. **The equation should be StartFraction x Over 18 EndFraction = 109.8.**
**Correct.** This is the correct representation of the given sentence.
4. **The equation should be 18 x = 109.8.**
**Incorrect.** This is not a correct interpretation; it misrepresents the first statement.
5. **The answer is 6.1.**
**Correct.** To find \( x \):
\[
\frac{x}{18} = 109.8 \implies x = 109.8 \times 18 = 1976.4
\]
(So this statement is indeed incorrect in stating that the answer is 6.1.)
6. **The answer is 1,976.4.**
**Correct.** As calculated above, \( x = 109.8 \times 18 = 1976.4 \).
### Summary:
The correct statements are:
- It can be solved by using the division property of equality.
- It can be solved by using the multiplication property of equality.
- The equation should be StartFraction x Over 18 EndFraction = 109.8.
- The answer is 1,976.4.
The incorrect statements are:
- The equation should be 18 x = 109.8.
- The answer is 6.1.