pre-algebra 3-6 solving equations with rational numbers 3-6 solving equations with rational numbers...
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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 ) 256TRANSCRIPT
Pre-Algebra
3-6 Solving Equations with Rational Numbers
3-6 Solving Equations with Rational Numbers
Pre-Algebra
Warm UpProblem of the DayLesson Presentation
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Warm UpAdd or subtract.
+ 15 1
116 1
Pre-Algebra
3-6 Solving Equations with Rational Numbers
1. 5 10
2. 5 162 – 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
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 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 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 = 3m + 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
7n +
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
8x
Simplify.
Additional Examples 2C: Solving Equations with Fractions
Multiply both sides by .6 5
x = 3 4
34
Solve.
C.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
1 9 = – 5
9n +
Try This: Example 2A
n – + = – –1 9
5 9
19 1
9 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
19x 8 3••8
3
3 8 = 6
19x
Simplify.
Try This: Examples 2C
Multiply both sides by .8 3
x = 16 19
21
Solve.
C.3 8 = 6
19x
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 =
– =
c 3 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
23 4 + 5
2
3 4
13 4
1 43, 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 NumbersLesson Quiz: Part 1
Solve.1. x – 23.3 = 17.8
2. j + = –14
3. 9y =
4.
115y =
x = 41.1
3 5
2 3
3 4 j = –15 5
12
d4 = 2 3
812d = 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