Review and Practice
It is time to review how to write expressions with addition, subtraction, multiplication, and division.
The situation | The model | The answer |
Two sticks are joined together with tape. One stick is 5 centimeters long and the other is x centimeters long. What is the total length of the two sticks | The total length of the two sticks is centimeters. |
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A stick is x centimeters long. It is cut into two pieces. If the shorter piece is 5 centimeters long, what is the length of the longer piece | The length of the longer piece is centimeters. |
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A stick is x centimeters long. If it is cut into 5 equal pieces, what is the length of each piece | The length of each piece is |
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Five identical sticks are taped together to form one long stick. If each of the smaller sticks is x centimeters long, what will be the total length of the combined stick | The total length of the sticks will be |
Assuming x stands for a number that is larger than 1, there are four things we can say about the above algebraic expressions:
- Adding and multiplying typically make the answer LARGER.
- Subtracting and dividing typically make the answer SMALLER.
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- Adding and subtracting typically involve things that are NOT EQUAL in length, size, weight, etc.
- Multiplying and dividing typically involve things that are EQUAL in length, size, weight, etc.
These four statements can be arranged into a grid to help you know whether a situation involves addition, subtraction, multiplication, or division.
The objects get bigger or smaller | |||
Bigger | Smaller | ||
The objects in the situation are equal of NOT equal in size. | Not equal |
Addition Two sticks are joined together with tape. One stick is 5 centimeters long and the other is x centimeters long. What is the total length of the two sticks? The total length of the two sticks is centimeters. |
Subtraction A stick is x centimeters long. It is cut into two pieces. If the shorter piece is 5 centimeters long, what is the length of the longer piece? The length of the longer piece is |
Equal |
Multiplication Five identical sticks are taped together to form one long stick. If each of the smaller sticks is x centimeters long, what will be the total length of the combined stick? The total length of the sticks will be |
Division A stick is x centimeters long. If it is cut into 5 equal pieces, what is the length of each piece? The length of each piece is |
Remember x must represent a number larger than 1 in order for these statements to be true!.
EXPLORE! |
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Self-Check
Question 1 You have m marbles. You separate them into 4 equal piles. How many marbles are in each pile?
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Question 2 Two pieces of wood are laid end-to-end. What is the total length of the wood?
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Question 3 Two pieces of wood are laid end-to-end. Their total length is 18 cm. If the shorter piece of wood is n cm, what is the length of the longer piece?
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Question 4 These five stamps cost a total of m cents. How much does each stamp cost?
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Question 5 David has 9 bags. He places x coins in each bag. How many coins does he have total?
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Question 6 Anna and Brian's combined weight is 140 pounds. If Brian weighs h pounds, how heavy is Anna?
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Question 7 Jenny has d dolls. If she buys 5 more dolls, how many will she have altogether?
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Question 8 There are m apples in each bag. If you buy 5 bags, how many apples will you have?
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Question 9 At a movie cinema, adult tickets cost p dollars and child tickets cost k dollars. If 3 adults and 5 children go to the movies, how much is the total price for tickets? (Write a variable expression.)
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