Download Chapter Audio Summary for McDougal Littell

Chapter Audio Summary for McDougal Littell
Pre-Algebra
Chapter 2 Solving Equations
In Chapter 2 you learned how to use the commutative, associative, and distributive properties to
evaluate expressions. You also learned how to use the distributive property to rewrite variable
expressions. You used all three properties to simplify variable expressions by combining like
terms. Next you used mental math to solve equations and then you solved equations using inverse
operations. Finally, you explored decimal operations and solved equations involving decimals.
Turn to the lesson-by-lesson Chapter Review that starts on p. 108 of the textbook.
Read the Vocabulary Review and answer the vocabulary questions. Now look at the review
sections that begin with the lesson numbers.
Lesson 2.1 Properties and Operations
Important terms to know are: additive identity and multiplicative identity.
The goal of Lesson 2.1 is to use properties of addition and multiplication.
Read the example.
"Evaluate the expression."
For part (a), use the order of operations by placing parentheses around the first two numbers.
Using the commutative property of addition, rearrange the order of the numbers within the
parentheses. Then use the associative property of addition to regroup the numbers that can be
more easily added; 57 and 13. 57 + 13 = 70. Then add 28 and 70 to get 98.
For part (b), use the order of operations by grouping the first two numbers. Using the
commutative property of multiplication, rearrange the order of the numbers within the brackets.
Then, using the associative property of multiplication, move the brackets to regroup numbers that
can be multiplied more easily; –5 and 20. –5 times 20 = –100. Finally, multiply 19 by –100. The
answer is –1900.
Now try Exercises 5 through 10. If you need help, go back to the worked-out examples on
pages 63 through 65.
Lesson 2.2 The Distributive Property
Important words and terms to know are: equivalent numerical expressions and equivalent
variable expressions.
The goal of Lesson 2.2 is to use the distributive property.
Read the first example.
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"Use the distributive property to evaluate 5(204)."
Begin by rewriting 204 as 200 + 4. Use the distributive property to rewrite the expression as
5(200) + 5(4). Multiply in each term; 5(200) = 1000 and 5(4) = 20. Add 1000 and 20 to get 1020.
Read the second example.
"Write an expression equivalent to 4(3x – 2)."
Using the distributive property, rewrite the expression as 4(3x) – 4(2). Then, multiply to simplify
each term; 4(3x) = 12x and 4(2) = 8. The equivalent expression is 12x – 8.
Now try Exercises 11 through 18. If you need help, go back to the worked-out examples on
pages 71 through 73.
Lesson 2.3 Simplifying Variable Expressions
Important words and terms to know are: term, coefficient, constant term, and like terms.
The goal of Lesson 2.3 is to simplify variable expressions.
Read the first example.
"Identify the terms, like terms, coefficients, and constant terms of the expression 7n – 5 – 3n + 2."
Remember that the parts of an expression that are added or subtracted are called terms. The terms
of this expression are 7n, –5, –3n, and 2. The like terms are 7n and –3n, and –5 and 2. The
coefficients are the numerical factors of the variable terms; they are 7 and –3. The constant terms
are –5 and 2.
Now read the second example.
"Simplify the expression 3p + 5 – 8(p + 2)."
First use the distributive property to rewrite –8(p + 2) as –8p – 16. Next group the like terms and
rewrite the expression as 3p – 8p + 5 – 16. Combine the like terms to get –5p – 11.
Now try Exercises 19 through 24. If you need help, go back to the worked-out examples on
pages 78 through 80.
Lesson 2.4 Variables and Equations
Important words and terms to know are: equation, solution of an equation, and solving an
equation.
The goal of Lesson 2.4 is to use mental math to solve equations.
Read the example.
"Solve the equation using mental math."
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To solve an equation using mental math, think of the equation as a question.
For part (a), ask yourself "What number plus 7 equals 11?" Think of what number you need to
add to 7 to get 11. That number, 4, is the solution. Then check the solution by substituting it for x
in the original equation. 4 + 7 = 11 is true, so 4 is the solution.
For part (b), ask yourself "What number minus 9 equals 5?" The solution is 14.
For part (c), ask yourself "3 times what number equals 21?" The solution is 7.
For part (d), ask yourself “–6 equals 30 divided by what number?" The solution is –5.
Now try Exercises 25 through 29. If you need help, go back to the worked-out examples on
pages 85 and 86.
Lesson 2.5 Solving Equations Using Addition or Subtraction
Important terms to know are: inverse operations and equivalent equations.
The goal of Lesson 2.5 is to use addition or subtraction to solve equations.
Read the first example.
"Solve x + 19 = 6."
First write the original equation. Then determine how to isolate the variable by using an inverse
operation. The inverse of addition is subtraction, so subtract 19 from each side. Then simplify
6 – 19 to get –13.
Read the second example.
"Solve m – 42 = –15."
First write the original equation. Then to isolate the variable m, add 42 to each side of the
equation. Simplify by adding –15 and 42. The solution is 27.
Now try Exercises 30 through 34. If you need help, go back to the worked-out examples on
pages 91 and 92.
Lesson 2.6 Solving Equations Using Multiplication or Division
The goal of Lesson 2.6 is to use multiplication or division to solve equations.
Read the example.
"Solve r = –5."
-13
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First write the original equation. Using the same inverse operation on each side of the equation,
multiply each side by –13. Multiply –13 and –5 to get the solution, 65.
Now try Exercises 35 through 39. If you need help, go back to the worked-out examples on
pages 97 and 98.
Lesson 2.7 Decimal Operations and Equations with Decimals
The goal of Lesson 2.7 is to use positive and negative decimals.
Read the first example.
"Perform the indicated operation."
For part (a), use the rule for different signs. Subtract the absolute values and use the sign of 9.74,
which is the number with the greater absolute value. The answer is 6.43.
For part (b), rewrite the expression as a sum, –4.2 + (–7.9). Because the numbers have the same
sign, add absolute values and use the common sign. The sum is –12.1.
For part (c), the numbers have different signs, so the product is negative. The product is –21.84.
For part (d), the numbers have the same sign, so the quotient is positive. The quotient is 5.7.
Now read the second example.
"Solve –1.9k = 0.76."
First write the original equation. Divide each side of the equation by –1.9 to isolate the variable.
Divide 0.76 by –1.9 to get the solution, –0.4.
Now try Exercises 40 through 47. If you need help, go back to the worked-out examples on
pages 102 through 104.
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