Here are the algebraic expressions for each phrase on the worksheet.
1. 3 less than the product of 2 and x
* "Product of 2 and x" means $2x$.
* "3 less than" means we subtract 3 from that product.
* Expression:
$2x - 3$
2. 7 more than y
* "More than" means addition.
* Expression:
$y + 7$ (or $7 + y$)
3. The sum of e and 10 times 3
* "10 times 3" is $30$.
* "Sum of e and..." means we add $e$ to that number.
* Expression:
$e + 30$
4. -3 added to the product of 2 and v
* "Product of 2 and v" is $2v$.
* "-3 added to" means we add negative 3 (which is the same as subtracting 3).
* Expression:
$2v - 3$ (or $2v + (-3)$)
5. The quotient of 10 divided by a increased by 5
* "Quotient of 10 divided by a" is written as a fraction: $\frac{10}{a}$.
* "Increased by 5" means we add 5 to that fraction.
* Expression:
$\frac{10}{a} + 5$
6. 10 added to the difference between t and 8
* "Difference between t and 8" is $t - 8$.
* "10 added to" means we put the 10 in front with a plus sign.
* Expression:
$10 + (t - 8)$ which simplifies to
$t + 2$
7. 20 less than the product of 5 and k
* "Product of 5 and k" is $5k$.
* "20 less than" means we subtract 20 from the product.
* Expression:
$5k - 20$
8. 12 more than 2 times d
* "2 times d" is $2d$.
* "12 more than" means we add 12.
* Expression:
$2d + 12$
9. 2 times the sum of t and 3
* "Sum of t and 3" is $(t + 3)$. Because it says "2 times the sum," we must use parentheses to multiply the whole group.
* Expression:
$2(t + 3)$
10. 2 times the difference between y and 6
* "Difference between y and 6" is $(y - 6)$. We use parentheses because we are multiplying the whole result by 2.
* Expression:
$2(y - 6)$
11. The sum of 1 and 2 divided by c
* "Sum of 1 and 2" is $1 + 2$, which equals $3$.
* "Divided by c" means we put that sum over $c$.
* Expression:
$\frac{3}{c}$ (or $\frac{1+2}{c}$)
12. n and 8 multiplied by 3
* This usually implies adding $n$ and $8$ first, then multiplying the total by $3$.
* Expression:
$3(n + 8)$
Final Answer:
1. $2x - 3$
2. $y + 7$
3. $e + 30$
4. $2v - 3$
5. $\frac{10}{a} + 5$
6. $10 + t - 8$ (or $t + 2$)
7. $5k - 20$
8. $2d + 12$
9. $2(t + 3)$
10. $2(y - 6)$
11. $\frac{3}{c}$
12. $3(n + 8)$
Parent Tip: Review the logic above to help your child master the concept of addition of algebraic expressions worksheet.
