2-6 Solving Equations with Rational Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes
2-6 Solving Equations with Rational Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-6 Solving Equations with Rational Numbers
Warm UpAdd or subtract.
+ 15
1
116
1
1. 5 10
2. 5 16
2 – 1
3. 4.8 + 3.6
4. 2.4 – 0.05
8.4
2.35
7 10
3 8
2-6 Solving Equations with Rational Numbers
Coefficient
The numerical factor of a term that contains a variable.
coefficient 3x variable
2-6 Solving Equations with Rational Numbers
MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems…
Sunshine State Standards
2-6 Solving Equations with Rational Numbers
m + 4.6 = 9
m + 4.6 = 9Use the Subtraction Property of Equality. Subtract 4.6 from both sides.
Once you have solved an equation it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation.
Remember!
Additional Examples 1A: Solving Equations with Decimals
Solve.
4.4 m =– 4.6 = – 4.6
2-6 Solving Equations with Rational Numbers
8.2p = –32.8
–4p =
Use the Division Property of Equality. Divide both sides by 8.2.
–32.8 8.2
8.2p 8.2
=
Additional Examples 1B: Solving Equations with Decimals
Solve.
2-6 Solving Equations with Rational Numbers
Additional Examples 1C: Solving Equations with Decimals
x = 18
Use the Multiplication Property of Equality. Multiply both sides by 1.2.
= 15x 1.2
x 1.2
= 1.2 • 15 1.2 •
Solve.
2-6 Solving Equations with Rational Numbers
m + 9.1 = 3
Check It Out: Example 1A and 1B
m + 9.1 = 3
–6.1 m =–9.1 –9.1
Solve each equation.A.
B. – 3.1p = 15.5
15.1 –3.1
–3.1 –3.1
=p
–5p =
2-6 Solving Equations with Rational Numbers
2 7
= –3 7
n +
Additional Example 2A: Solving Equations with Fractions
n – + = – –2 7
3 7
27
27
n = – 5 7
Subtract from both sides.2 7
Solve.
2-6 Solving Equations with Rational Numbers
1 6 = 2
3y –
Additional Example 2B: Solving Equations with Fractions
Find a common denominator, 6.
y = 5 6
=y 4 6
1 6
+
1 6
= 2 3
–1 6
+ 1 6
+y Add to both sides.1 6
Solve.
2-6 Solving Equations with Rational Numbers
5 6 =
5 8x
6 5••
6 5
5 6
= 5 8
x
Simplify.
Additional Example 2C: Solving Equations with Fractions
Multiply by the reciprocal.
x =3 4
3
4
Solve.
5 6
Divide both sides by . 5 6
= 5 8
x ÷ 5 6
5 6÷
2-6 Solving Equations with Rational Numbers
1 3
= 5 8
m –
Check It Out: Example 2A
Solve each equation.
m – + = +1 3
5 8
13
13
m = 23 24
m = + 8 24
15 24
m – = 5 8
13
2-6 Solving Equations with Rational Numbers
3 8 x = 6
19
Check It Out: Example 2BSolve each equation.
= 6 19
3 8
x
÷3 8
3 8
x = 6 19 ÷
3 8
•8 3
3 8
x = 6 19
8 3
•2
1
16 19
x =
2-6 Solving Equations with Rational Numbers
Write an equation:
Total servings
Amount needed for each dessert
Amount of sugar
Additional Example 3: Solving Word Problems Using Equations
=
Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving of the dessert has tablespoon of sugar, how many servings can he make for the party?
2 3
2 3
s2 3
2 3 = 2
2-6 Solving Equations with Rational Numbers
Now solve the equation.Additional Example 3 Continued
Mr. Rios can make 4 servings.
2 3 = 2 s 3
22 3
3 2
2 3
= 2s 2 3
24 6 , or 4 s =
8 3s = 3
2
Multiply both sides by the reciprocal.
Simplify.
2 3
Divide both sides by . 2 3
= 22 3s ÷ 2
32 3÷
2-6 Solving Equations with Rational Numbers
Check It Out: Example 3
Rick’s car holds the amount of gasoline as his
wife’s van. If the car’s gas tank can hold 16
gallons of gasoline, how much gasoline can the tank in the minivan hold?
3 5
21
• =Amount of gas in van
Three-fifths Amount of gas in car
2-6 Solving Equations with Rational Numbers
Check It Out: Example 3 Continued
3 5
=x •
33 2
=x • •5 3
x = 33 • 5 2 • 3
3 5
= 33 2
x ÷ 3 5
3 5÷
1 216
3 5
=x • 33 2
1
11
155 2
, or=
So, the tank in the minivan can hold gallons of gas.
271 2
271 2
2-6 Solving Equations with Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-6 Solving Equations with Rational Numbers
Lesson Quiz: Part I
Solve.
1. x – 23.3 = 17.8
2. j + = –14
3. 9y =
4.
115
y =
x = 41.1
3 5
2 3
3 4
j = –155 12
d4 = 2 3
812
d = 9
2-6 Solving Equations with Rational Numbers
Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard?
Lesson Quiz: Part II
5.
5 hours
2 5
2-6 Solving Equations with Rational Numbers
1. Solve.
a – 36 = 44.9
A. a = 36.7
B. a = 49.2
C. a = 59.9
D. a = 80.9
Lesson Quiz for Student Response Systems
2-6 Solving Equations with Rational Numbers
2. Solve.
c + = –11
A. c = 12 C. c = 11
B. c = –12 D. c = 11
Lesson Quiz for Student Response Systems
11
2011
20
4 5
3 4
3 4
4 5
2-6 Solving Equations with Rational Numbers
3. Solve.
8e =
A. e = 8 C. e =
B. e = 5 D. e =
Lesson Quiz for Student Response Systems
2 3
1 3
1 12
3 20
2 3