Warm Up Identify the property represented. 1. 4 + (9 + 3) = (4 + 9) + 3
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Transcript of Warm Up Identify the property represented. 1. 4 + (9 + 3) = (4 + 9) + 3
![Page 1: Warm Up Identify the property represented. 1. 4 + (9 + 3) = (4 + 9) + 3](https://reader035.fdocuments.us/reader035/viewer/2022070402/568137c7550346895d9f65e3/html5/thumbnails/1.jpg)
Using Properties with Rational Numbers
Warm Up
Identify the property represented.
1. 4 + (9 + 3) = (4 + 9) + 3
2. 10(5 - 6) = 10 . 5 - 10 . 6
3. 17 . 1 = 17
Associative Property
Distributive Property
Identity Property
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Using Properties with Rational Numbers
Problem of the DayFran made 18 three-point shots and 12 one-point shots. She had a total of 102 points for the basketball season. How many two-point shots did Fran make for the season?18 two-point shots
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Using Properties with Rational Numbers
Learn to use properties of rational numbers to write equivalent expressions and equations.
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Using Properties with Rational Numbers
You can use the Distributive Property to calculate Orlando’s total earnings two different ways.
The Distributive Property can be used to help you perform calculations more easily by writing equivalent expressions.
Orlando works part-time at amoving company to earn money for a car. He earns $12.75 per hour.
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Using Properties with Rational Numbers
The Distributive Property states:a(b + c) = ab + aca(b - c) = ab - ac
Remember
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Using Properties with Rational Numbers
Additional Example 1: Writing Equivalent Expressions
An art teacher pays $13.89 for one box of watercolor brushes. She buys 6 boxes in March and 5 boxes in April. Use the Distributive Property to write equivalent expressions showing two ways to calculate the total cost of the watercolor boxes.
Write an expression to show how much the teacher pays for a box and how many boxes purchased. Then use the Distributive Property to write an equivalent expression
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Using Properties with Rational Numbers
Method 1$13.89(6 + 5) $13.89(11)$152.79
Method 2$13.89(6) + $13.89(5)$83.34 + $69.45 $152.79
Both methods result in a calculation of $152.79 for the amount of money spent of watercolor brushes.
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Using Properties with Rational Numbers
Check It Out : Example 1
Jamie earns $8.75 per hour. Last week she worked 15 hours and next week she will work 20 hours. Use the Distributive Property to write equivalent expressions showing two ways to calculate how much money she earned.
Write an expression to show how much Jamie earns and the number of hours she works. Then use the Distributive Property to write an equivalent expression.
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Using Properties with Rational Numbers
Method 1$8.75(15 + 20) $8.75(35)$306.25
Method 2$8.75(15) + $8.75(20)$131.25 + $175 $306.25
Both methods result in a calculation of $306.25 for Jamie’s salary.
Continued: Check It Out Example 1
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Using Properties with Rational Numbers
Additional Example 2 : Writing Equivalent Expressions
34
x + 7 = 56
Write an equivalent equation for that does
not contain fractions. Then solve the equation.
34
X + 7 = 56
The LCM of denominators is 12.
34
x+ 7 = 56
12 12 Multiply both sides by 12.
31 4
x + 12 (7) = 51 6
3 12 12 2 Simplify.
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Using Properties with Rational Numbers
Additional Example 2 : Continued
9x + 84 = 10 9x + 84 = 10 is an equivalent expression
9x + 84 = 10-84 -84
9x = -74
Subtract 84 from both sides.
Divide both side by 99 9
x = -829
An equivalent equation is 9x + 84 = 10 and the
solution is x = -829
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Using Properties with Rational Numbers
Write an equivalent equation for
that does not contain fractions. Then solve
the equation.
Check It Out: Example 2
12
X + 9 = 46
12
X + 9 = 46
The LCM of denominators is 6
12
x+ 9 = 46
6 6 Multiply both sides by 6.
11 2
x + 6 (9) = 41 6
3 6 6 1 Simplify.
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Using Properties with Rational Numbers
3x + 54 = 4 3x + 54 = 4 is an equivalent expression
3x + 54 = 4
-54 -54
3x = -50
3 3
Subtract 54 from both sides.
Divide both side by 3
x = -1623
An equivalent equation is 3x + 34 = 4 and the
solution is x = -1623
Continued: Check It Out Example 2
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Using Properties with Rational Numbers
0.75 can also be
written as
Helpful Hint
75100
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Using Properties with Rational Numbers
The soccer team uses a 36.75-liter container to take water to games. The team manager fills 0.75 liter bottles from this. He has used 22.5 liters. How many more 0.75 liter bottles can he fill before he runs out of water? Write and solve an equivalent equation without decimals.
Additional Example 3: Construction Application
Write an equation to represent the situation.0.75x + 22.5 = 36.75
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Using Properties with Rational Numbers
Write an equivalent equation without decimals.
100(0.75x + 22.5) = (36.75)100
The equation has decimals to the hundredths, so multiply both sides by 100.
Use the Distributive Property
100(0.75x + 100(22.5) = (36.75)100
75x + 2,250 = 3,675
Simplify to get an equivalent equation without decimals
Continued: Example 3
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Using Properties with Rational Numbers
75x + 2,250 = 3,675
-2250 -2250
75x = 1,425
75 75
x = 19
The number of 0.75 liter bottles that he can fill before he runs out of water is 19.
Continued: Example 3
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Using Properties with Rational Numbers
Check It Out: Example 3…If the soccer team uses a 42.5-liter container, about how many 0.75 liter bottles can the manager fill before he runs out of water?
Write an equation to represent the situation.0.75x + 22.5 = 42.5
Write an equivalent equation without decimals.
100(0.75x + 22.5) = (42.5)100
The equation has decimals to the hundredths, so multiply both sides by 100.
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Using Properties with Rational Numbers
Use the Distributive Property
100(0.75x + 100(22.5) = (42.5)100
75x + 2,250 = 4,250
Simplify to get an equivalent equation without decimals
Continued: Check It Out Example 3
75x + 2,250 = 4,250
-2250 -2250
75x = 200075 75
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Using Properties with Rational Numbers
Continued: Check It Out Example 3
The number of 0.75 liter bottles that he can fill before he runs out of water is 19.
x ≈ 26.6
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Using Properties with Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
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Using Properties with Rational Numbers
Lesson Quiz
1. Jai earns $9.75 per hour. Jai works 3 hours one day and then works 7 hours the next day. Use the Distributive Property to write equivalent expressions showing two ways to calculate Jai’s total earnings.
9.75(3) + 9.75(7);9.75(3 + 7); $97.50
Write an equivalent equation that does not contain fractions. Then solve the equation.
45
x + 4 = 12
2. 8x + 40 = 5; x = -438
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Using Properties with Rational Numbers
Lesson Quiz
23
x - 4 = 14
3. 8x - 48 = 3; x = 638
4. Joy has $67.85. She buys several pairs of earrings at $9.98 per pair and has $17.95 left. How many pairs of earrings did she buy? Write and solve an equivalent equation without decimals.
9.98x + 17.95 = 67.85; 998x + 1795 = 6785; x = 5;Joy bought 5 pairs of earrings.
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Using Properties with Rational Numbers
1. Write an equivalent equation that does not contain fractions.
A. 2x + 6 = 4
B. 2x + 36 = 4
C. 3x + 6 = 4
D. 3x + 36 = 4
Lesson Quiz for Student Response Systems
13
x + 6 = 46
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Using Properties with Rational Numbers
2. Write an equivalent equation that does not contain fractions.
A. 8 = 2x + 16
B. 8 = 2x + 2
C. 7 = 2x + 2
D. 7 = 2x + 16
Lesson Quiz for Student Response Systems
78
= 14
x + 2
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Using Properties with Rational Numbers
3. Solve the equation
A. x = -4
B. x = -5
C. x = 3
D. x = 5
Lesson Quiz for Student Response Systems
68
= 14
x + 2