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\( \begin{array}{l}\text { Write an expression: } \\ \text { Division } \\ \text { 1. The quotient of } \mathrm{r} \text { and } 19 \\ \text { 2. } x \text { divided by } \mathrm{d} \\ \text { 3. The ratio of } \mathrm{c} \text { to } \mathrm{d} \\ \text { 4. The price p per gallon } \mathrm{g}\end{array} \)

Ask by Knight Rogers. in the United States
Jan 24,2025

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Here are the division expressions: 1. \( \frac{r}{19} \) 2. \( \frac{x}{d} \) 3. \( \frac{c}{d} \) 4. \( \frac{p}{g} \)

Solución

Certainly! Here are the algebraic expressions for each of the given scenarios related to division: 1. **The quotient of \( r \) and 19** \[ \frac{r}{19} \] 2. **\( x \) divided by \( d \)** \[ \frac{x}{d} \] 3. **The ratio of \( c \) to \( d \)** \[ \frac{c}{d} \] 4. **The price \( p \) per gallon \( g \)** \[ \frac{p}{g} \] Each expression represents the division relationship as described: - **Quotient of \( r \) and 19**: This represents how many times 19 fits into \( r \). - **\( x \) divided by \( d \)**: This shows the division of \( x \) by \( d \). - **Ratio of \( c \) to \( d \)**: This expresses the relative size of \( c \) compared to \( d \). - **Price per gallon**: This calculates the cost for each gallon by dividing the total price \( p \) by the number of gallons \( g \). Feel free to use these expressions in your calculations or further mathematical work!

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The Deep Dive

The quotient of \( r \) and 19 can be expressed as \( \frac{r}{19} \). For \( x \) divided by \( d \), it becomes \( \frac{x}{d} \). The ratio of \( c \) to \( d \ is \frac{c}{d} \). Lastly, the price \( p \) per gallon \( g \) can be represented as \( \frac{p}{g} \). Did you know that ratios and quotients are foundational in fields like finance and science? Understanding how to express them accurately can help you manage budgets or analyze trends in data. Think of ratios as a way to compare sizes—like how many apples you can buy for every orange! Also, when working with division, be aware of common mistakes like overlooking the order of operations or misplacing parentheses. It's vital to keep the symbols clear—confusion can lead to unintended results! Always double-check your work to ensure you've expressed everything correctly.

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