Collecting Rational Number Like Terms

Videos and solutions to help Grade 7 students learn how to rewrite rational number expressions by collecting like terms and combining them by repeated use of the distributive property.

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Common Core For Grade 7

New York State Common Core Math Module 3, Grade 7, Lesson 6

Lesson 6 Student Outcomes

• Students rewrite rational number expressions by collecting like terms and combining them by repeated use of the distributive property.

Lesson 6 Summary

• Combining like terms is much harder to do when the coefficients and constant terms are not integers because there are usually more steps, including finding common denominators, converting mixed numbers to improper fractions, etc.

Classwork

Opening Exercise
Do the computations, leaving your answers in simplest/standard form. Show your steps.
1. Terry weighs 40 kg. Janice weighs 2 3/4 kg less than Terry. What is their combined weight?
2. 2 2/3 - 1 1/2 - 4/5
3. 1/5 + (-4)
4. 4 (3/5)
5. Mr. Jackson bought 1 3/5 lb. of beef. He cooked 3/4 of it for lunch. How much does he have left?
6. 2/3 n - 3/4 n + 1/6 n + 2 2/9 n

Example 1
Rewrite the expression in standard form by collecting like terms.

Exercise 1
For the following exercises, predict how many terms the resulting expression will have after collecting like terms. Then, write the expression in standard form by collecting like terms.

Example 2
At a store, a shirt was marked down in price by ten dollars. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half. Write two different expressions that represent the new cost of the items, using for the cost of each shirt and p for the cost of a pair of pants. Explain the different information each one shows.

Exercise 2
Continuing with Example 2, write two different expressions that represent the total cost of the items if tax was 1/10 of the original price. Explain the different information each shows.

Example 3
As a class, write each expression in standard form by collecting like terms. Justify each step.

Exercise 3
Rewrite the following expressions in standard form by finding the product and collecting like terms.

Example 4
Model how to write the expression in standard form using rules of rational numbers.

Exercise 4
Rewrite the following expression in standard form by finding common denominators and collecting like terms.

Example 5
Rewrite the following expression in standard form.

Exercise 5
Write the following expression in standard form.