HW # 23- Rational Numbers worksheet Study for QUIZ 2-1 to 2-6 (review last night’s HW) Warm up

Week 6, Day Three

Is the statement below true or false? Explain how you arrived at your conclusion.

My number and your number are both divisibleby 8. Therefore, the sum of our numbers will be divisible by 4.

Warm Up Response1. If my number is divisible by 8, then 8 is a factor

of my number.

2. Since 4 is a factor of 8, my number would also be divisible by 4.

3. The same would be true for your number.

4. Therefore, even if I add the numbers together, 4 would remain a factor of the sum.

EX: 16 + 32 = 48 which is divisible by 4 (and 8)

Homework Check You should have checked your answers online last night.

PLEASE be sure that you do this. If you did not get a majority of the problems correct, fill out a Hall Pass in your Panther Planner and come see me! There is a quiz on Day Four!

Goals for Today

• Mystery Numbers

• Solving Equations (both single and multi-step)

Mystery Numbers

Each group has a different statement. Decide if the statement is TRUE or FALSE.

Prove your answer.Be sure to use complete sentences and math vocabulary.

2-7 Lesson Quiz

Solve.1. x – 23.3 = 17.8 2. j + = –14

3. 9y = 4. 115

y =

x = 41.1

j = –15 5 12

3

4

3

5

d4 = 2 3

8

2

3

12d = 9

5. 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?

5 hours

2 5

Include an explanation of why you did what you did for #4.

2-7 EXTRA PRACTICE EXAMPLES

m + 4.6 = 9m + 4.6 = 9

Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition.

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

8.2p = –32.8

–4p =

Since p is multiplied by 8.2, divide both sides by 8.2.

–32.8 8.2

8.2p 8.2

=

Additional Examples 1B: Solving Equations with Decimals

Solve.

Additional Examples 1C: Solving Equations with Decimals

x = 18

Since x is divided by 1.2, multiply both sides by 1.2.

= 15x 1.2

x 1.2 = 1.2 • 15 1.2 •

Solve.

m + 9.1 = 3

m + 9.1 = 3

Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition.

Check It Out! Example 1

–6.1 m =

–9.1 = –9.1

Solve.

A.

B. 5.5b = 75.9

75.9 5.55.5 5.5=b

13.8b =

Since b is multiplied by 5.5, divide both sides by 5.5.

= 90

Check It Out! Example 1C

y = 405

Since y is divided by 4.5, multiply both sides by 4.5.

y 4.5

y 4.5 = 4.5 • 904.5 •

Solve.

C.

Additional Example 2A: Solving Equations with Fractions

= – 3 7

n + 2 7

n + – = – –3 7

2 7

27

2

7

n = – 5 7

Solve.

2 7Since is added to n, subtract

from both sides.2 7

1

6= 2

3y –

Additional Example 2B: Solving Equations with Fractions

Find a common denominator, 6.=y 4 6

1 6

+

=y – 2 3

1

6

Solve.

Since is subtracted from y, add

to both sides.

1 61

6

+ 1 6 + 1

6

=y 5 6

5 6 =

5 8x

6 5••

6 5

5

6= 5

8x

Multiply by the reciprocal. Simplify.

Additional Example 2C: Solving Equations with Fractions

x =3 4

3

4

Solve.

Since x is multiplied by ,

divide both sides by .5 6

5 65

6÷ = ÷ 5

8x 5

65 6

1

11

1

1

1

1 9

= – 5 9

n +

Check It Out! Example 2A

n = – 2 3

Simplify.

Solve.

n + – = – –5 9

1 9

19

1

9

n = – 6 9

1 9Since is added to n, subtract

from both sides.1 9

Check It Out! Example 2B

y = 1 1 4

Solve.

Simplify.

=y – 1

2

3 4

Find a common denominator, 4.=y 3 4

2 4

+

=y – 3 4

1

2

Since is subtracted from y, add

to both sides.

1 21

2

+ 1 2 + 1

2

=y 5 4

Check It Out! Example 2C

Solve.

3 8 =

3 4x

8 3••

8 3

3

8= 3

4x

Multiply by the reciprocal. Simplify.

x = 2

2

1

Since x is multiplied by ,

divide both sides by .3 8

3 83

8÷ = ÷ 3

4x 3

83 8

1

1

1

11

1

Write an equation:

Capacity of minivan’s tank

2/3 Capacity of car’s tank• =

Check It Out! Example 3

g 242 3

Rick’s car holds the amount of gasoline as his

wife’s van. If the car’s gas tank can hold 24

gallons of gasoline, how much gasoline can the tank in the minivan hold?

2 3

• =