## 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. 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. 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 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:

• Subtracting and dividing typically make the answer SMALLER.

-and-

• 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 centimeters. 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! Move the red point up and down the number line and observe how the blue point moves in relation. What variable expression describes the blue point, if we consider the red point as $\large~x$? (The expression can include any of the four operations.)

# Self-Check

 Question 1 You have m marbles. You separate them into 4 equal piles. How many marbles are in each pile? [show answer]   $\large\frac{m}{4}$

 Question 2 Two pieces of wood are laid end-to-end. What is the total length of the wood? [show answer]   $\large~n+23$

 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? [show answer]   $\large18-n$

 Question 4 These five stamps cost a total of m cents. How much does each stamp cost? [show answer]   $\large\frac{m}{5}$

 Question 5 David has 9 bags. He places x coins in each bag. How many coins does he have total? [show answer]   $\large9x$

 Question 6 Anna and Brian's combined weight is 140 pounds. If Brian weighs h pounds, how heavy is Anna? [show answer]   $\large140-h$

 Question 7 Jenny has d dolls. If she buys 5 more dolls, how many will she have altogether? [show answer]   $\large~d+5$

 Question 8 There are m apples in each bag. If you buy 5 bags, how many apples will you have? [show answer]   $\large5m$

 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.) [show answer]   $\large3p+5k$