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Page 129 #24-57 ANSWERS
Student Learning Goal Chart
Lesson Reflections
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
Pre-Algebra Learning Goal
Students will understand rational and real numbers.
Students will understand rational and real numbers by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
• Learn to add and subtract decimals and rational numbers with like denominators (3.2)
• Learn to add and subtract fractions with unlike denominators (3.5)
• Learn to multiply fractions, decimals, and mixed numbers (3.3)
• Learn to divide fractions and decimals (3.4)
• Learn to solve equations with rational numbers (3.6)
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Today’s Learning Goal Assignment
Learn to solve equations with rational numbers.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Pre-Algebra HW
Page 138#14-26 all
Pre-Algebra
3-6 Solving Equations with Rational Numbers3-6 Solving Equations with Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Warm UpMultiply.
+ 15
1
116
1
Pre-Algebra
3-6 Solving Equations with Rational Numbers
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
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Problem of the Day
A computer word is made of strings of 0’s and 1’s. How many different words can be formed using 8 characters? (An example is 01010101.)256
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Today’s Learning Goal Assignment
Learn to solve equations with rational numbers.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
m + 4.6 = 9
m + 4.6 = 9
Subtract 4.6 from both sides.
Once you have solved and 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 Example 1A: Solving Equations with Decimals.
Solve.
4.4 m =– 4.6 = – 4.6
A.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
8.2p = –32.8
–4p =
Divide both sides by 8.2–32.8 8.2
8.2p 8.2
=
Additional Examples 1B: Solving Equations with Decimals
Solve.B.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
= 15
Additional Examples 1C: Solving Equations with Decimals
Solve.
x = 18
Multiply both sides by 1.2
x 1.2x
1.2= 1.2 • 15 1.2 •
C.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
m + 9.1 = 3
m + 9.1 = 3
Subtract 9.1 from both sides.
Try This: Example 1A & 1B
–6.1 m =
–9.1 = –9.1
Solve.A.
B. 5.5b = 75.975.9 5.5
5.5 5.5 =b
13.8b =
Divide both sides by 5.5
Pre-Algebra
3-6 Solving Equations with Rational Numbers
= 90
Try This: Examples 1C
y = 405
Multiply both sides by 4.5
y 4.5
y 4.5
= 4.5 • 904.5 •
Solve.
C.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
2 7
= – 3 7
n +
Additional Examples 2A: Solving Equations with Fractions
n – + = – –2 7
3 7
27
27
n = – 5 7
Subtract from both sides.2 7
Solve.
A.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
1 6 = 2
3y –
Additional Examples 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.
B.
Simplify.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
5 6 =
5 8x
6 5••
6 5
5 6
= 5 8
x
Simplify.
Additional Examples 2C: Solving Equations with Fractions
Multiply both sides by .6 5
x =3 4
3
4
Solve.
C.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
1 9
= – 5 9
n +
Try This: Example 2A
n – + = – –1 9
5 9
19
19
n = – 2 3
Subtract from both sides.1 9
Simplify – .6 9
Solve.A.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
1 2 = 3
4y –
Try This: Example 2B
Find a common denominator; 4.
y = 1 1 4
=y 3 4
2 4
+
1 2
= 3 4
–1 2
+ 1 2
+y Add to both sides.1 2
Solve.B.
Simplify.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
3 8
= 6 19
x 8 3
••8 3
3 8
= 6 19
x
Simplify.
Try This: Examples 2C
Multiply both sides by .8 3
x =16 19
2
1
Solve.
C.
3 8
= 6 19
x
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Write an equation:
Original amount of milk
Milk for casserole
Milk for cereal
Convert fractions:
Additional Examples 3: Solving Word Problems Using Equations
5 2
2(2)+1 2 =1
22 =
– =
c3 4
5 2
Mr. Rios wants to prepare a casserole that requires 2 cups of milk. If he makes the casserole, he will have only cup of milk left for his breakfast cereal. How much milk does Mr. Rios have?
1 2 3
4
– =
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Now solve the equation.
Additional Examples 3 Continued
5 2– =c
Mr. Rios has 3 cups of milk.1 4
5 2 =c – +
5 2
3 4 +
5 2
3 4
13 4
1 4
3, or c =
3 4c = +
10 4
Add to both sides.5 2
Find a common denominator, 4.
Simplify.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Write an equation:
Van’s gas tank
Ratio of car’s tank to van’s tank
Capacity of car’s tank• =
Convert decimal to a fraction:
Try This: Examples 3
g31 2
2 3
Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 15.5 gallons of gasoline, how much gasoline can the tank in the minivan hold?
2 3
15.5 = 15 = = 1 22
15(2)+1 31 2
• =
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Simplify.
31 2
2 3
=g •
Now solve the equation.
Try This: Examples 3 Continued
The van’s gas tank holds 23 gallons of gasoline.1 4
31 2
2 3
=g •3 2• •
3 2
g = 93 4
1 4g = 23
Multiply both sides by .3 2
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Lesson Quiz: Part 1
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
d5 = 2 3
812
d = 9
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Tamara had 6 bags of mulch for her garden. Each bag contained 8 lb of mulch. What was the total weight of the mulch?
Lesson Quiz: Part 2
5.
50 lb
1 3
Pre-Algebra
3-6 Solving Equations with Rational Numbers
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