Answer :
- 'divided by a number' translates to $\frac{{1}}{{x}}$.
- 'four-fifths more than three times a number' translates to $3x + \frac{{4}}{{5}}$.
- 'nine less than twice a number' translates to $2x - 9$.
- 'ninety-nine plus' translates to $99 + x$.
- 'the difference of eleven and five' translates to $11 - 5 = 6$.
### Explanation
1. Understanding the Problem
We need to match each verbal phrase to its corresponding mathematical expression. Let's use $x$ to represent the unknown number.
2. Translating the Phrases
1. 'divided by a number' translates to $\frac{{}}{{x}}$. Since the phrase is incomplete, we can assume it means 'one divided by a number', which is $\frac{{1}}{{x}}$.
2. 'four-fifths more than three times a number' translates to $3x + \frac{{4}}{{5}}$.
3. 'nine less than twice a number' translates to $2x - 9$.
4. 'ninety-nine plus' translates to $99 + $ (something). Since the phrase is incomplete, we can assume it means 'ninety-nine plus a number', which is $99 + x$.
5. 'the difference of eleven and five' translates to $11 - 5 = 6$.
3. Matching the Phrases
Therefore, the matches are:
- divided by a number: $\frac{{1}}{{x}}$
- four-fifths more than three times a number: $3x + \frac{{4}}{{5}}$
- nine less than twice a number: $2x - 9$
- ninety-nine plus: $99 + x$
- the difference of eleven and five: $11 - 5 = 6$
### Examples
Understanding how to translate verbal phrases into mathematical expressions is fundamental in algebra. For instance, if you're trying to calculate the total cost of items with a discount or additional fees, you need to translate the given information into an equation. This skill is also useful in everyday situations like budgeting, where you might need to express 'saving $5 more than last week' mathematically to track your progress.
- 'four-fifths more than three times a number' translates to $3x + \frac{{4}}{{5}}$.
- 'nine less than twice a number' translates to $2x - 9$.
- 'ninety-nine plus' translates to $99 + x$.
- 'the difference of eleven and five' translates to $11 - 5 = 6$.
### Explanation
1. Understanding the Problem
We need to match each verbal phrase to its corresponding mathematical expression. Let's use $x$ to represent the unknown number.
2. Translating the Phrases
1. 'divided by a number' translates to $\frac{{}}{{x}}$. Since the phrase is incomplete, we can assume it means 'one divided by a number', which is $\frac{{1}}{{x}}$.
2. 'four-fifths more than three times a number' translates to $3x + \frac{{4}}{{5}}$.
3. 'nine less than twice a number' translates to $2x - 9$.
4. 'ninety-nine plus' translates to $99 + $ (something). Since the phrase is incomplete, we can assume it means 'ninety-nine plus a number', which is $99 + x$.
5. 'the difference of eleven and five' translates to $11 - 5 = 6$.
3. Matching the Phrases
Therefore, the matches are:
- divided by a number: $\frac{{1}}{{x}}$
- four-fifths more than three times a number: $3x + \frac{{4}}{{5}}$
- nine less than twice a number: $2x - 9$
- ninety-nine plus: $99 + x$
- the difference of eleven and five: $11 - 5 = 6$
### Examples
Understanding how to translate verbal phrases into mathematical expressions is fundamental in algebra. For instance, if you're trying to calculate the total cost of items with a discount or additional fees, you need to translate the given information into an equation. This skill is also useful in everyday situations like budgeting, where you might need to express 'saving $5 more than last week' mathematically to track your progress.
