Find the difference by aligning the expressions vertically. Subtraction as adding the opposite Align like terms vertically and combine by addition Adding the opposite is equivalent to subtraction Students should recognize that the subtracted expression in Example 1(b) did not include a term containing the variable , so the from the first grouped expression remains unchanged in the answer. Example 3 (3 minutes): Using Expressions to Solve Problems Students write an expression representing an unknown real-world value, rewrite as an equivalent expression, and use the equivalent expression to find the unknown value. Example 3: Using Expressions to Solve Problems A stick is meters long. A string is times as long as the stick. Express the length of the string in terms of . The length of the stick in meters is meters, so the string is , or , meters long. If the total length of the string and the stick is meters long, how long is the string? The length of the stick and the string together in meters can be represented by , or . If the length of the stick and string together is meters, the length of the stick is meters, and the length of the string is meters. Example 4 (4 minutes): Expressions from Word Problems Students write expressions described by word problems and rewrite the expressions in standard form. Example 4: Expressions from Word Problems It costs Margo a processing fee of to rent a storage unit, plus per month to keep her belongings in the unit. Her friend Carissa wants to store a box of her belongings in Margo’s storage unit and tells her that she will pay her toward the processing fee and for every month that she keeps the box in storage. Write an expression in standard form that represents how much Margo will have to pay for the storage unit if Carissa contributes. Then, determine how much Margo will pay if she uses the storage unit for months. Let represent the number of months that the storage unit is rented. Original expression Subtraction as adding the opposite Opposite of the sum is the sum of its opposites Any order, any grouping Combined like terms This means that Margo will have to pay only of the processing fee and per month that the storage unit is used.
Find the difference by aligning the expressions vertically. Subtraction as adding the opposite Align like terms vertically and combine by addition Adding the opposite is equivalent to subtraction Students should recognize that the subtracted expression in Example 1(b) did not include a term containing the variable , so the from the first grouped expression remains unchanged in the answer. Example 3 (3 minutes): Using Expressions to Solve Problems Students write an expression representing an unknown real-world value, rewrite as an equivalent expression, and use the equivalent expression to find the unknown value. Example 3: Using Expressions to Solve Problems A stick is meters long. A string is times as long as the stick. Express the length of the string in terms of . The length of the stick in meters is meters, so the string is , or , meters long. If the total length of the string and the stick is meters long, how long is the string? The length of the stick and the string together in meters can be represented by , or . If the length of the stick and string together is meters, the length of the stick is meters, and the length of the string is meters. Example 4 (4 minutes): Expressions from Word Problems Students write expressions described by word problems and rewrite the expressions in standard form. Example 4: Expressions from Word Problems It costs Margo a processing fee of to rent a storage unit, plus per month to keep her belongings in the unit. Her friend Carissa wants to store a box of her belongings in Margo’s storage unit and tells her that she will pay her toward the processing fee and for every month that she keeps the box in storage. Write an expression in standard form that represents how much Margo will have to pay for the storage unit if Carissa contributes. Then, determine how much Margo will pay if she uses the storage unit for months. Let represent the number of months that the storage unit is rented. Original expression Subtraction as adding the opposite Opposite of the sum is the sum of its opposites Any order, any grouping Combined like terms This means that Margo will have to pay only of the processing fee and per month that the storage unit is used.