The sum of $x$ and $y$.
The subtraction of $m$ from $n$.
The product of 3 and $a$.
Divide $y$ by 5.
8 more than $x$.
7 decreased by $p$.
4 times $y$.
36 divided by $z$.
6 times $x$ added to 2 times $y$.
The subtraction of $5a$ from 12.
1. The sum of $x$ and $y$
Expression: $x + y$
Explanation: “Sum” is the result of addition. It indicates that the two variables should be joined with a plus sign.
2. The subtraction of $m$ from $n$
Expression: $n – m$
Explanation: The word “from” is a “turn-around” word. It means you start with the second value ($n$) and take away the first value ($m$). Writing $m – n$ would be incorrect here.
3. The product of 3 and $a$
Expression: $3a$
Explanation: “Product” indicates multiplication. In algebra, we usually write the number (coefficient) next to the letter (variable) without needing a $\times$ symbol.
4. Divide $y$ by 5
Expression: $\frac{y}{5}$ or $y \div 5$
Explanation: This identifies $y$ as the number being split (dividend) and 5 as the number of groups (divisor).
5. 8 more than $x$
Expression: $x + 8$
Explanation: “More than” means you are increasing an existing amount ($x$) by a specific value (8).
6. 7 decreased by $p$
Expression: $7 – p$
Explanation: “Decreased by” tells you to start with the first number and reduce it by the second.
7. 4 times $y$
Expression: $4y$
Explanation: The word “times” is a direct indicator of multiplication between the constant 4 and the variable $y$.
8. 36 divided by $z$
Expression: $\frac{36}{z}$ or $36 \div z$
Explanation: This identifies 36 as the starting total that is being divided by the variable $z$.
9. 6 times $x$ added to 2 times $y$
Expression: $6x + 2y$
Explanation: This involves two multiplication operations ($6x$ and $2y$) that are then combined using addition.
10. The subtraction of $5a$ from 12
Expression: $12 – 5a$
Explanation: Just like problem #2, the word “from” indicates that you begin with the 12 and then subtract the $5a$ portion.