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Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
How many weeks in 363 days?
51 weeks67
Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
Complete each equation.
1. 1 week = days 2. 1 foot = inches
3. 1 nickel = cents 4. 1 gallon = quarts
5. 1 yard = feet
Check Skills You’ll Need
1-1
Solutions
1. 1 week = days 2. 1 foot = inches
3. 1 nickel = cents 4. 1 gallon = quarts
5. 1 yard = feet
Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
7 12
5 4
3
1-1
Identify each expression as a numerical expression or a
variable expression. For a variable expression, name the variable.
Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
numerical expression
variable expression; t is the variable.
a. 7 3
b. 4t
Quick Check
1-1
Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
Write a variable expression for the cost of p pens
priced at 29¢ each.
= number of pens.
Words times
Let
29¢ number of pens
p
The variable expression 29 • p, or 29p, describes the cost of p pens.
Expression 29 p•
Quick Check
1-1
Variables and ExpressionsVariables and ExpressionsPRE-ALGEBRA LESSON 1-1PRE-ALGEBRA LESSON 1-1
Write a variable expression for each word phrase.
1. the total of h and 56 2. three less than d
3. p decreased by three 4. a divided by 7
p – 3
h + 56 d – 3
a ÷ 7
1-1
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Divide. Round answers to the nearest tenth.
a. 75 ÷ 8 b. 740 ÷ 7
9.4 105.7
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
(For help, go to Skills Handbook p. 760.)
Find each quotient.
1. 164 ÷ 2 2. 344 ÷ 8 3. 284 ÷ 4
4. 133 ÷ 7 5. 182 ÷ 13 6. 650 ÷ 25
Check Skills You’ll Need
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Solutions
1. Estimate: 2. Estimate: 3. Estimate:160 ÷ 2 = 80 360 ÷ 8 = 45 280 ÷ 4 = 70 82 43 712 164 8 344 4 284 –16 –32 –28 4 24 4 – 4 – 24 – 4 0 0 0
4. Estimate: 5. Estimate: 6. Estimate:140 ÷ 7 = 20 195 ÷ 13 = 15 625 ÷ 25 = 25 19 14 267 133 13 182 25 650 –7 –13 –50 63 52 150 –63 – 52 –150 0 0 0
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Simplify 8 – 2 • 2.
8 – 2 • 2
8 – 4 First multiply.
Then subtract.4
Quick Check
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Simplify 12 ÷ 3 – 1 • 2 + 1.
12 ÷ 3 – 1 • 2 + 1
Add and subtract from left to right.2 + 1
4 – 2 + 1 Multiply and divide from left to right.
3 Add.
Quick Check
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Simplify 20 – 3[(5 + 2) – 1].
20 – 3[(5 + 2) – 1]
20 – 3[ 7 – 1] Add within parentheses.
Subtract within brackets.20 – 3 [6]
20 – 18 Multiply from left to right.
Subtract.2
Quick Check
1-2
The Order of OperationsThe Order of OperationsPRE-ALGEBRA LESSON 1-2PRE-ALGEBRA LESSON 1-2
Simplify each expression.
1. 7(3) – 2 • 4 2. 6 ÷ 2 + 1 • 5
3. 10 ÷ (4 + 1) 4. 3[9 • 2 ÷ (10 – 4)]
2
13 8
9
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1-3
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
Evaluate each expression.
a. 8 + 6 – 2 b. 16 – 8 + 2 c. 12 + 9 • 2
12 10 30
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
(For help, go to Lesson 1-2.)
Simplify each expression.
1. 6(9 + 1) 2. 17 – 2 + 3
3. 9 + 8 • 2 + 4 4. [3(5) + 1] • 2
Check Skills You’ll Need
1-3
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
Solutions
1. 6(9 + 1) 2. 17 – 2 + 3 6(10) 15 + 3
60 18
3. 9 + 8 • 2 + 4 4. [3(5) + 1] • 2
9 + 16 + 4 [15 + 1] • 2
29 16 • 2
32
1-3
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
Evaluate 18 + 2g for g = 3.
18 + 2g = 18 + 2(3) Replace g with 3.
= 18 + 6 Multiply.
= 24 Add.
Quick Check
1-3
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
Evaluate 2ab – for a = 3, b = 4, and c = 9.
= 2 • 3 • 4 – 3 Work within grouping symbols.
= 6 • 4 – 3 Multiply from left to right.
= 24 – 3 Multiply.
= 21 Subtract.
c3
2ab – = 2 • 3 • 4 – Replace the variables.c3
93
1-3
Quick Check
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
The Omelet Café buys cartons of 36 eggs.
a. Write a variable expression for the number of cartons the Café should buy for x eggs.
b. Evaluate the expression for 180 eggs.
a. x eggs
b. 180 eggs
x36 = Evaluate for x = 180.180
36
x36
= 5 Divide.
The Omelet Café should buy 5 cartons to get 180 eggs.
1-3
Quick Check
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
The One Pizza restaurant makes only one kind of pizza, which costs $16. The delivery charge is $2. Write a variable expression for the cost of having pizzas delivered. Evaluate the expression to find the cost of having two pizzas delivered.
$2 delivery charge
= number of pizzas.
Words for each
Let
$16
p
pizza plus
Evaluate the expression for p = 2.
16 • p + 2 = 16 • 2 + 2 = 32 + 2 = 34
It costs $34 to have two pizzas delivered.
Expression 16 p• 2+
1-3
Quick Check
Writing and Evaluating Expressions Writing and Evaluating Expressions PRE-ALGEBRA LESSON 1-3PRE-ALGEBRA LESSON 1-3
Evaluate.
1. 7(b) – 4 for b = 3 2. h ÷ 2 + 1 for h = 12
3. 3c + 4 ÷ d for c = 8, d = 2 4. fg – g for f = 5, g = 7
26
17 7
28
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1-4
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Order from least to greatest: , –1, 0.5, – 0.2, 23
18
– 1, – 0.2, , 0.5,18
23
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
(For help, go to Skills Handbook p. 775.)
Write an integer for each situation.
1. lose $7 2. find $9
3. 8 steps forward 4. 3 yards gained
5. 5 floors down
Check Skills You’ll Need
1-4
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Solutions
1. lose $7 2. find $9
–7 9
3. 8 steps forward 4. 3 yards gained
8 3
5. 5 floors down
–5
1-4
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Write a number to represent the temperature shown by the thermometer.
The thermometer shows 2 degrees Celsius below zero, or –2°C.
Quick Check
1-4
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Graph 2, –2, and –3 on a number line. Order the
numbers from least to greatest.
The numbers from least to greatest are –3, –2, and 2.
1-4
Quick Check
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Use a number line to find |–5| and |5|.
|–5| = 5 |5| = 5
1-4
Quick Check
Integers and Absolute ValueIntegers and Absolute ValuePRE-ALGEBRA LESSON 1-4PRE-ALGEBRA LESSON 1-4
Write an integer to represent each situation.
1. A debt of $50
2. A dive of 23 feet below the surface
Simplify.
3. | –12 | 4. | 8 |
12
–50
–23
8
1-4
1-5
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
List each set of fractions in order from greatest to least.
a. , , b. , , c. , , 56
910
35
16
23
27
14
13
15
27
13
14
15
27
23
16
, , , , 9 10
56
35
, ,
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
(For help, go to Lesson 1-4.)
Compare. Use >, <, or = to complete each statement.
1. –6 –3 2. 2 –15
3. –5 | 5 | 4. | 10 | | –10 |
5. | 9 | | –2 | 6. | –8 | | 0 |
Check Skills You’ll Need
1-5
PRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
Solutions
1. –6 < –3 2. 2 > –15
3. –5 < | 5 | 4. | 10 | = | –10 |
5. | 9 | > | –2 | 6. | –8 | > | 0 |
1-5
Adding IntegersAdding Integers
(–7) + 3 Model the sum.
– 4 Group and remove zero pairs. There are four negative tiles left.
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
Use tiles to find (–7) + 3.
(–7) + 3 = – 4
Quick Check
1-5
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
From the surface, a diver goes down 20 feet and then comes back up 4 feet. Find –20 + 4 to find where the diver is.
The diver is 16 feet below the surface.
–20 + 4 = –16
Start at 0. To represent –20, move left 20 units. To add positive 4, move right 4 units to –16.
1-5
Quick Check
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
Find each sum.
b. 13 + (–17)
a. –20 + (–15)
Since –17 has the greater absolute value, the sum is negative.
13 + (–17) = – 4
Since both integers are negative, the sum is negative.
–20 + (–15) = –35
Find the difference of the absolute values.|–17| – |13| = 17 – 13
= 4 Simplify.
1-5
Quick Check
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
A player scores 22 points. He then gets a penalty of 30
points. What is the player’s score after the penalty?
Write an expression.22 + (–30)
Find the difference of the absolute values.|–30| – |22| = 30 – 22
Since –30 has the greater absolute value, the sum is negative.
22 + (–30) = – 8
The player’s score is – 8.
= 8 Simplify.
1-5
Quick Check
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
Find –7 + (– 4) + 13 + (–5).
Add from left to right.–7 + (– 4) + 13 + (–5)
–7 + (– 4) + 13 + (–5) = –3
–3 |5| – |2| = 3. Since –5 has the greater absolute value, the sum is negative.
The sum of the two negative integers is negative.
–11 + 13 + (–5)
|13| – |11| = 2. Since 13 has the greater absolute value, the sum is positive.
2 + (–5)
1-5
Quick Check
Find each sum.
1. –37 + (–5) 2. 14 + (–4)
3. –100 + 5 + (–3) 4. Evaluate 33 + t for t = –11.
Adding IntegersAdding IntegersPRE-ALGEBRA LESSON 1-5PRE-ALGEBRA LESSON 1-5
–98
–42 10
22
1-5
1-6
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
Find all possible number pairs for which the sum of two wholenumbers is 63 and the difference between the numbers is lessthan 10.
31 and 32; 30 and 33; 29 and 34; 28 and 35; 27 and 36
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
(For help, go to Lesson 1-5.)
Find each sum.
1. 8 + (–9) 2. –11 + (–18) 3. –4 + (–6)
4. 14 + (–3) 5. 6 + (–6) 6. –13 + (–10)
Check Skills You’ll Need
1-6
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
Solutions
1. 8 + (–9) 4. 14 + (–3)
| –9 | – | 8 | = 9 – 8 | 14 | – | –3 | = 14 – 3
= 1 = 11
8 + (–9) = –1 14 + (–3) = 11
2. –11 + (–18) 5. 6 + (–6)
–11 + (–18) = –29 | –6 | – | 6 | = 6 – 6
= 0
6 + (–6) = 0
3. –4 + (–6) 6. –13 + (–10)
–4 + (–6) = –10 –13 + (–10) = –23
1-6
Start with 7 negative tiles.
Take away 5 negative tiles. There are 2 negative tiles left.
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
Find –7 – (–5).
–7 – (–5) = –2
Quick Check
1-6
Start with 2 positive tiles.
There are not enough positive tiles to take away 8. Add 6 zero pairs.
Take away 8 positive tiles. There are 6 negative tiles left.
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
Find 2 – 8.
2 – 8 = –6
1-6
Quick Check
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
An airplane left Houston, Texas, where the
temperature was 42°F. When the airplane landed in Anchorage,
Alaska, the temperature was 50°F lower. What was the
temperature in Anchorage?
The temperature in Anchorage was –8°F.
Write an expression.42 – 50
To subtract 50, add its opposite.42 – 50 = 42 + (–50)
= –8 Simplify.
1-6
Quick Check
Find each difference.
1. –24 – (–5) 2. 19 – (–4) 3. –33 – 11
4. 14 – 46 5. –200 – 50 – (–10)
Subtracting IntegersSubtracting IntegersPRE-ALGEBRA LESSON 1-6PRE-ALGEBRA LESSON 1-6
–44–19 23
–32 –240
1-6
1-7
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Find the difference between and . 312
18
324
18
=
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
(For help, go to Skills Handbook.)
Find each difference.
1. –3 – 4 2. –7 – 4
3. –11 – 4 4. –15 – 4
Check Skills You’ll Need
1-7
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Solutions
1. –3 – 4 2. –7 – 4
–3 – 4 = –3 + (–4) –7 – 4 = –7 + (–4)
= –7 = –11
3. –11 – 4 4. –15 – 4
–11 – 4 = –11 + (–4) –15 – 4 = –15 + (–4)
= –15 = –19
1-7
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Use inductive reasoning. Make a conjecture about the next figure in the pattern. Then draw the figure.
Observation: The circles are rotating counterclockwise within the square.
Conjecture: The next figure will have a shaded circle at the top right.
Quick Check
1-7
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Write a rule for each number pattern.
a. 0, – 4, – 8, –12, . . .
b. 4, – 4, 4, – 4, . . .
c. 1, 2, 4, 8, 10, . . .
Start with 0 and subtract 4 repeatedly.
Alternate 4 and its opposite.
Start with 1. Alternate multiplying by 2 and adding 2.
1-7
Quick Check
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Write a rule for the number pattern 110, 100, 90, 80, . . .
Find the next two numbers in the pattern.
The rule is Start with 110 and subtract 10 repeatedly.The next two numbers in the pattern are 80 – 10 = 70 and 70 – 10 = 60.
The next numbers are found by subtracting 10. – 10 – 10 – 10
The first number is 110. 110, 100, 90, 80
1-7
Quick Check
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
A child grows an inch a year for three years in a
row. Is it a reasonable conjecture that this child will grow
an inch in the year 2015?
No; children grow at an uneven rate, and eventually they stop growing.
1-7
Quick Check
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Is each conjecture correct or incorrect? If it is incorrect, give a counterexample.
a. Every triangle has three sides of equal length.
b. The opposite of a number is negative.
The conjecture is incorrect. The figure below is a triangle, but it does not have three equal sides.
The conjecture is incorrect. The opposite of –2 is 2.
1-7
(continued)
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
c. The next figure in the pattern below has 16 dots.
The conjecture is correct. The diagram belowshows the next figure in the pattern.
1-7
Quick Check
Inductive ReasoningInductive ReasoningPRE-ALGEBRA LESSON 1-7PRE-ALGEBRA LESSON 1-7
Find the next three numbers in each pattern.
1. 1, –1, 2, –2, 3, . . . 2. 1, 3, 7, 15, 31, . . .
3. –11, –8, –5, –2, . . .
1, 4, 7
–3, 4, –4 63, 127, 255
1-7
1-8
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
Describe the pattern in this sequence of numbers and find the nexttwo numbers. 5, 8, 4, 9, 3, . . .
description: + 3, – 4, + 5, – 6; next two numbers: 10, 2
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
(For help, go to Lesson 1-7.)
Write a rule for each pattern. Find the next three numbers.
1. 8, 11, 14, 17, . . . 2. 1, 5, 4, 8, 7, . . .
3. 3, 5, 10, 12, 24, . . . 4. 1, 4, 7, 10, . . .
Check Skills You’ll Need
1-8
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
Solutions
1. 8 11 14 17 20 23 26
+3 +3 +3 +3 +3 +3Start with 8 and add 3 repeatedly.
2. 1 5 4 8 7 11 10 14
+4 –1 +4 –1 +4 –1 +4Start with 1. Alternate adding 4 and subtracting 1.
3. 3 5 10 12 24 26 52 54
+2 2 +2 2 +2 2 +2Start with 3. Alternate adding 2 and multiplying by 2.
4. 1 4 7 10 13 16 19
+3 +3 +3 +3 +3 +3Start with 1 and add 3 repeatedly.
1-8
Each student on a committee of five students
shakes hands with every other committee member. How
many handshakes will there be in all?
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
The pattern is to add the number of new handshakes to the number of handshakes already made.
4 the number of handshakes by 1 student
4 + 3 = 7 the number of handshakes by 2 students
1-8
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
(continued)
There will be 10 handshakes in all.
Make a table to extend the pattern to 5 students.
Student
Number of originalhandshakes
Total number ofhandshakes
1
4
4
2
3
4 + 3
3
2
7 + 2
4
1
9 + 1
5
0
10 + 0= 7 = 9 = 10 = 10
Quick Check
1-8
Problem Solving Strategy: Look for a Pattern Problem Solving Strategy: Look for a Pattern PRE-ALGEBRA LESSON 1-8PRE-ALGEBRA LESSON 1-8
Solve using any strategy.
1. You have a penny, a nickel, a dime, and a quarter. You give away three coins. How many different amounts of money can you give away? Name the values.
4; 16¢, 31¢, 36¢, 40¢
1-8
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
For 3 weeks, Jessica worked 2 hours per day, 4 days per week babysitting. If she earned $3.50 per hour, how much did she earn in all?
$84.00
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
(For help, go to Skills Handbook p. 759.)
Simplify each expression.
1. 5 4 2. 3 8 3. 5 5
4. 14 2 5. 6 5 6. 20 7
Check Skills You’ll Need
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
Solutions
1. 5 2. 3 3. 5 4 8 5 20 24 25
4. 14 5. 6 6. 20 2 5 7 28 30 140
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
A diver is descending from the surface of the water
at a rate of 5 ft/s. Write an expression with repeated
addition to show how far the diver is from the surface of
the water after four seconds.
4 (–5) = (–5) + (–5) + (–5) + (–5) = –20
The diver is 20 feet below the surface of the water.
Use a number line to show repeated addition.
Quick Check
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
a. –2(7)
Use a pattern to find each product.
2(7) = 14 Start with products you know.
1(7) = 7
0(7) = 0
–1(7) = –7 Continue the pattern.
–2(7) = –14
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
b. –2(–7)
(continued)
2(–7) = –14 Start with products you know.
1(–7) = –7
0(–7) = 0
–1(–7) = 7 Continue the pattern.
–2(–7) = 14
1-9
Quick Check
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
Multiply 6(–2)(–3).
6(–2)(–3) = (–12)(–3) Multiply from left to right. The product of a positive integer and a negative integer is negative.
= 36 Multiply. The product of two negative integers is positive.
1-9
Quick Check
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
Use the table to find the average of the differences in the values of a Canadian dollar and a U.S. dollar for 1994–1997.
Write an expression for the average.
–27 + (–27) + (–26) + (–28)4
1-9
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
(continued)
The quotient of a negative integer and a positive integer is negative.
= –27
For 1994–1997, the average difference was –27¢.
Use the order of operations. The fraction bar acts as a grouping symbol.
–1084=
1-9
Quick Check
Find each product or quotient.
1. –7(–3) 2. –36 ÷ (–9)
3. –12 • 2 4. 7(–3)
5. –6 • (–2) • (–1)
Multiplying and Dividing IntegersMultiplying and Dividing IntegersPRE-ALGEBRA LESSON 1-9PRE-ALGEBRA LESSON 1-9
–24
21 4
–21
–12
1-9
1-10
The Coordinate PlaneThe Coordinate PlanePRE-ALGEBRA LESSON 1-10PRE-ALGEBRA LESSON 1-10
Order from greatest to least: –1, 3, 0, – 2, – 4
3, 0, – 1, – 2, – 4
The Coordinate PlaneThe Coordinate PlanePRE-ALGEBRA LESSON 1-10PRE-ALGEBRA LESSON 1-10
(For help, go to Lesson 1-4.)
Graph numbers on a number line.
1. –2, 1, –5 2. 0, 2, –4
3. –3, 3, –2 4. –1, –5, –8
Check Skills You’ll Need
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The Coordinate PlaneThe Coordinate PlanePRE-ALGEBRA LESSON 1-10PRE-ALGEBRA LESSON 1-10
Solutions
1. –2, 1, –5 2. 0, 2, –4
3. –3, 3, –2 4. –1, –5, –8
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The Coordinate PlaneThe Coordinate PlanePRE-ALGEBRA LESSON 1-10PRE-ALGEBRA LESSON 1-10
Write the coordinates of point G. In which quadrant
is point G located?
Point G is located 2 units to the left of the y-axis.
So the x-coordinate is –2.
The point is 3 units below the x-axis.
So the y-coordinate is –3.
The coordinates of point G are (–2, –3). Point G is located in Quadrant III. Quick Check
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The Coordinate PlaneThe Coordinate PlanePRE-ALGEBRA LESSON 1-10PRE-ALGEBRA LESSON 1-10
Graph point M(–3, 3).
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Quick Check
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