Here are the solutions to the problems on the worksheet, broken down step-by-step.
Part 1: Key Words and Definitions
First, let's fill in the blanks at the top to understand the rules.
* To translate statements into expressions and equations:
* Identify
key words (or operation words) that indicate the operation.
* Write the numbers/variables in the correct order.
The "KEY WORDS" Box:
* The SUM of \_\_\_ and \_\_\_:
Addition (+)
* The DIFFERENCE of \_\_\_ and \_\_\_:
Subtraction (-)
* The PRODUCT of \_\_\_ and \_\_\_:
Multiplication ($\times$ or just writing them together like $5b$)
* The QUOTIENT of \_\_\_ and \_\_\_:
Division ($\div$ or a fraction bar)
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Part 2: Basic Translations (Problems 1–4)
1) the sum of 8 and $t$
* "Sum" means add.
* Order doesn't matter for addition, but usually, we write it as it appears.
* Expression: $8 + t$
2) the quotient of $g$ and 15
* "Quotient" means divide.
* The first number mentioned goes on top (numerator), and the second goes on the bottom (denominator).
* Expression: $\frac{g}{15}$
3) the product of 5 and $b$
* "Product" means multiply.
* In algebra, we usually write the number first and don't use a multiplication sign.
* Expression: $5b$
4) the difference of 32 and $x$
* "Difference" means subtract.
* Order matters! The first number mentioned is the one you start with.
* Expression: $32 - x$
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Part 3: "Less Than" and "More Than" (Problems 5–10)
*Important Rule:* For phrases like "less than" and "more than," you must
switch the order.
* "5 less than $x$" means you start with $x$ and take away 5 ($x - 5$).
* "5 more than $x$" means you start with $x$ and add 5 ($x + 5$).
5) Eight more than $x$
* Start with $x$, then add 8.
* Expression: $x + 8$
6) Six less than $p$
* Start with $p$, then subtract 6.
* Expression: $p - 6$
7) 14 less than $f$
* Start with $f$, then subtract 14.
* Expression: $f - 14$
8) $p$ more than 10
* Start with 10, then add $p$.
* Expression: $10 + p$ (or $p + 10$)
9) 3 more runs than Pirates scored
* Let $P$ be the runs the Pirates scored.
* "3 more than" means we add 3 to their score.
* Expression: $P + 3$
10) 12 less than some number
* Let $n$ represent "some number."
* "12 less than" means we start with the number and subtract 12.
* Expression: $n - 12$
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Final Answer:
Top Section Blanks:
* Identify
key words
* The SUM:
Addition
* The DIFFERENCE:
Subtraction
* The PRODUCT:
Multiplication
* The QUOTIENT:
Division
Numbered Problems:
1) $8 + t$
2) $\frac{g}{15}$
3) $5b$
4) $32 - x$
5) $x + 8$
6) $p - 6$
7) $f - 14$
8) $10 + p$
9) $P + 3$ (assuming $P$ is the variable for Pirates' score)
10) $n - 12$ (assuming $n$ is the variable for "some number")
Parent Tip: Review the logic above to help your child master the concept of translate verbal expressions into algebraic expressions worksheet.
