Evaluate each of the following expressions when y = 12.
9. 21 + y | 10. y – 7 | 11. |
12. 4y | 13. | 14. |
15. y + y + 3 | 16. 2y + 5 | 17. 30 – 2y |
Write an expression for each of the following situations.
1. Steve has $7 more than Duane. If Steve has $m, how much money does Duane have |
2. Steve has $7 more than Duane. If Duane has $m, how much money does Steve have Give answer in terms of m. |
3. A boy is x years old, and he is 4 years older than his younger brother is. How old is the younger brother |
4. A class has m students, but 5 students are absent today. a. How many students are present b. If m = 28, how many students are present |
5. Jamal is 12 years old. How old will he be x years from now |
6. Paula is 17 inches shorter than Randy. If Randy is h inches tall, how tall is Paula |
7. Which of the letters used in the above situations stand for values that could be a fraction or decimal |
Write an expression for each of the following situations.
1. Jamal is 12 years old. How old was he be x years ago |
2. Sammy and Tammy have $63 altogether. a. If Tammy has $d, the how much does Sammy have b. If d = 18, how much does Sammy have |
3. Two pieces of wood are laid end-to-end. What is the total length of the wood |
4. Two pieces of wood are laid end-to-end. Their total length is 23 cm. If the longer piece of wood is n cm, what is the length of the shorter piece |
5. Two numbers have a sum of 20. If the smaller number is n, what is the larger number |
6. Which of the letters used in the above situations stand for values that could be a fraction or decimal |
1. Imagine a stack of identical coins.
a. Each coin is 2 millimeters thick. What is the height of a stack of n coins
b. Each coin is t millimeters thick. What is the height of a stack of 7 coins
c. Each coin is t millimeters thick. What is the height of a stack of n coins
2. Each piece of the railroad track is 8 inches long. Several pieces of track together form one long, straight track.
a. Write an expression for the length of the track if there are p pieces.
b. Write an expression for the length of the track if there are p pieces and each piece is y inches long.
3. Five identical cookies cost a total of $m. How much does each cookie cost
4. One stick is x inches long. Another stick is half as long. How long is the shorter stick
Find the value of each of the following expressions when n = 6.
1. n + 4
2. 10 + n
3. 15 – n
4. n – 6
5. 4 n
6. 10 n
7.
8.
9.
10. n + n + n
11. 2n + 7
12.
[Hint: Start with the value of the variable, multiply by 3 then divide by 2.]
Write an expression for each situation.
1. You buy a pencil that costs 25 cents and a pen that costs n cents. What is the total cost | |||||
2. Anna and BrianÕs combined weight is 125 pounds. If Anna weighs h pounds, how heavy is Brian | |||||
3. A bowling ball weighs x pounds. How heavy is it if you have 6 of these bowling balls | |||||
4. A stack of 5 identical books measures w inches tall. How tall is each book | |||||
5. Peter is now 11 years old. How old will he be d years from now | |||||
6. A stick is 28 inches long. It is cut into two pieces. If one piece is k inches long, how long is the other | |||||
Write an expression for each situation.
1. Gumballs cost 12 cents each. What is the total cost if you buy g gumballs | |||||
2. A rope 24 feet long is cut into m pieces of equal length. How long is each piece |
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3. A tree is 20 feet tall. How tall will it be after it grows another y feet | |||||
4. A bicycle costs m dollars. If itÕs price is then reduced by $10, what will be its new price | |||||
5. What is the perimeter of a pentagon with each of its sides being k inches long | |||||
6. 6 girls equally share m dollars. How much does each girl get | |||||
Evaluate each of the following expressions for a = 3, b = 4, and c = 5.
2. a + bc =
3. abc =
4. (a + b) c =
5.
6. 8a =
7. b – (c – a) =
8. 2b + 5a =
Simplify each of the following expressions. Substitute a value into your new expression AND the original expression to verify that you have simplified correctly.
The given expression | My simplified expression |
5a + 4 – 2a + 1 | 3a + 5 |
To check, letÕs substitute a = 4 | |
5(4) + 4 – 2(4) + 1 20 + 4 – 8 + 1 24 – 8 + 1 16 + 1 17 |
3(4) + 5 12 + 5 17 |
Since both columns equal 17, we know that 3a + 5 is correct. |
The given expression | Simplified expression |
1) 5a + 4a | |
2) 8c – 5c | |
3) 7k – 2k + k | |
4) 3x + 6 – x | |
5) 7m + 7 – 2m | |
6) 5s + 10 + 2s |
Simplify each of the following expressions. Substitute a value into your new expression AND the original expression to verify that you have simplified correctly.
The given expression | My simplified expression |
5a + 4 – 2a + 1 | 3a + 5 |
To check, letÕs substitute a = 4 | |
5(4) + 4 – 2(4) + 1 20 + 4 – 8 + 1 24 – 8 + 1 16 + 1 17 |
3(4) + 5 12 + 5 17 |
Since both columns equal 17, we know that 3a + 5 is correct. |
The given expression | Simplified expression |
1) 2y + 5 + 3y – 2 | |
2) 9 + 4m – 3m – 8 | |
3) 8r + 6 – 2r – 6 | |
4) 8p – 3p – p + 2 | |
5) 8 + 8w + 5 – 2w | |
6) 7h + h – 4h – h |
Write an expression for each situation.
1. There are m marbles in a bag. They are separated into 4 equal groups. Write a variable expression to show the number of marbles in each group. | ||
2. You have $25 and then give d dollars of it to your brother. How much money do you have left | ||
Evaluate each of the following expressions if n = 8.
3. 8 + n
4. 20 – n
5. 4n
6.
7. 3(n + 4)
8. 33 – 3n
Simplify the following expressions.
1) x + x + x =
2) 3x + 4x =
3) 6p – 4p =
4) 2p + 2p – p =
5) 4r – 2r + 3r =
6) 5f – f – 3f =
7) 3c – 3c + c =
8) 5k + 7 – k =
9) 6n + 3 + n + 2 =
10) 7g – 2g + 2 =
11) 10x + 5 – 4x – 2 =
12) 3h + 8 – 3h + 2 =
Find the value of each of the following expressions when y = 4. Simplify all answers as fractions.
1) 21 – y
2) y + 25
3) 3y + 2
4) 3y
5)
6)
7)
8)
9)
10)
11)
12)
1. The admission fee to a bird park is y dollars. The admission fee to an amusement park is $1 more.
a. Express the admission fee to the amusement park in terms of y.
2. A rope is x meters long. An iron rod is 3 times as long as the rope.
a. Express the length of the iron rod in terms of x.
3. Henry is x years old. Betty is 3 times as old as Henry. Peter is 4 years older than Betty.
a. Express PeterÕs age in terms of x.
4. Stacy bought some candy bars at $2 each. She gave the cashier $50 and received $y change.
a. Express the number of candy bars Stacy bought in terms of y.
Simplify each of the following expressions.
1. 5a + 4a + 5a + 4a
2. 8c + 5 + 8c + 5
3. 7k + 2k +5 + k - 2
For each figure below, write an expression on one line that shows the perimeter. Then simplify the expression.
4.
5.
6.
For each figure below, write an expression on one line that shows the perimeter. Then simplify the expression.
1.
2.
Evaluate each of the following expressions if n = 9. Simplify all fractions rather than dividing.
3.
4.
5.
Write a variable expression for each of the following situations.
1. Gumballs cost 12 cents each. What is the total cost if you buy g gumballs |
2. A rope 24 feet long is cut into m pieces of equal length. How long is each piece |
3. A tree is 4 feet tall. How tall will it be after it grows another y feet |
4. A bicycle costs m dollars. If itÕs price is then reduced by $20, what will be its new price |
5. What is the perimeter of a pentagon with each of its sides being k inches long |
6. 5 girls equally share m dollars. How much does each girl get |
Simplify the following expressions. You must draw the bags and marbles.
1. x + x + x – x =
2. 3x + 3 + 4x =
3. 6p + p + 4 =
4. 6 + 3n – 2 – 2n =
5. 4r – 2r + 1 =
6. h + 6 – 4 + h =
Evaluate each of the following expressions when y = 4. Reduce all answers that are fractions.
1. 18 + y
2. y – 4
3.
4. 3y
5.
6.
Do you remember that to find the area of a rectangle, you need to multiply the base by the width
The area of this rectangle is 20 square units, because 4 x 5 = 20. |
Find the shaded area of each of the following rectangles. For some rectangles you will write an expression for the area instead of a numerical answer.
1. |
2. |
3. |
4. |
5. |