Identify the terms in the expression: $6x + 5y – 3$.
Write the factors of $8ab$.
Find the co-efficient of $x$ in $-7x$.
State whether the following are like or unlike terms: $4a$ and $9a$.
State whether the following are like or unlike terms: $5x$ and $5y$.
Add the like terms: $7a + 3a + 5a$.
Add the like terms: $4x + 6y + 2x$.
Subtract the like terms: $9m – 4m$.
Simplify: $12x – 5x + 3x$.
Simplify: $8a + 3b – 5a – b$.
1. The sum of $x$ and $y$
Expression: $x + y$
Explanation: The word “sum” is a mathematical keyword for addition. It indicates that you are totaling the two quantities together.
2. The subtraction of $m$ from $n$
Expression: $n – m$
Explanation: In subtraction, the word “from” determines the order. Since $m$ is being taken away from $n$, $n$ is the starting value and must come first in the expression.
3. The product of 3 and $a$
Expression: $3a$
Explanation: “Product” refers to multiplication. In algebra, placing a number (the coefficient) directly next to a letter (the variable) is the standard way to show they are being multiplied.
4. Divide $y$ by 5
Expression: $\frac{y}{5}$ or $y \div 5$
Explanation: This identifies $y$ as the number being divided and 5 as the divisor. Using a fraction bar is the most common way to represent this in algebra.
5. 8 more than $x$
Expression: $x + 8$
Explanation: The phrase “more than” signifies an increase, which translates to addition. You are starting with $x$ and adding 8 to it.
6. 7 decreased by $p$
Expression: $7 – p$
Explanation: “Decreased by” is a direct indicator of subtraction. It tells you to start with the first value (7) and reduce it by the second value ($p$).
7. 4 times $y$
Expression: $4y$
Explanation: The word “times” indicates multiplication. The number 4 is being multiplied by the variable $y$.
8. 36 divided by $z$
Expression: $\frac{36}{z}$ or $36 \div z$
Explanation: This identifies 36 as the starting total (the dividend) that is being split into $z$ equal parts.
9. 6 times $x$ added to 2 times $y$
Expression: $6x + 2y$
Explanation: This is a multi-step expression. You first represent the two multiplications (“6 times $x$“ and “2 times $y$“) and then combine them using addition.
10. The subtraction of $5a$ from 12
Expression: $12 – 5a$
Explanation: Similar to problem #2, the word “from” indicates that 12 is your starting point, and the entire term $5a$ is being subtracted from it.