Bel Air Middle School Summer Math Packet - SharpSchool

Bel Air Middle School Summer Math Packet

for students entering

Integrated Math 7

or

7th Grade Algebra I

As you prepare to start 7th grade and begin Integrated Math 7 or Algebra I, it is important that you are confident in the math skills taught to you during previous courses. This math packet is designed to help you review the prerequisite skills that will

help you to be successful in 7th grade. This packet is optional, but we highly recommend that you complete it before starting 7th grade in September. Note: A copy of this document will be available on the Bel Air Middle School website.

Downloading the digital version will enable you to click on the links to go directly to the video helps provided. Have a wonderful summer! The BAMS Math Department

Order of Operations

When several operations are indicated in a numerical expression, proceed in the following order: 1. Work within the parentheses or other grouping symbols 2. Expand each power and/or simplify any square roots 3. Multiply and divide (from left to right) 4. Add or subtract (from left to right).

For additional help: ?

1. 14 7 + 32

2. 42 2(-12 + 9)

3. 49 + 5

4. 18 ? 30 ? 5

5. 48 ? (5 + 7) ? 9

6. 43 ? 5(2) + 13

Operations with Fractions

? When adding or subtracting fractions, be sure to use a common denominator. ? When multiplying fractions, multiply the numerators (straight across) and multiply the

denominators (straight across). Then simplify the fractions. ? When multiplying mixed numbers, change the mixed numbers into improper fractions. Then

proceed as you would with simple fractions. ? When dividing fractions, change the divisor to its reciprocal and multiply.

For additional help: ? Adding and subtracting fractions and mixed numbers: ? Multiplying and dividing fractions and mixed numbers:

1.

5- 3

7 21

2.

31-15

3

9

3.

31+55

8

6

4.

53-24

5

7

5.

41+21+55

3

9

6

6.

71-23+41

3

4

6

7.

23

35

8.

3215

36

9.

13 1 (1 1 )

2 15

10. 1 ? 5

39

11. 2 3 ? 5 1

7

5

12. 4 2 ? 1 5

3

9

1

Operations with Decimals

? When adding or subtracting decimals, be sure to line up the decimals. Annex zeroes as needed to make the numbers line up.

? When multiplying decimals, multiply as though the numbers do not have decimals. Then count the digits that come after the decimals in the factors. Place your decimal in your product so that the same number of digits follow the decimal.

For additional help: ?

1. 10.5 ? 3.78

2. 13.2 + .007

3. 1.75 ? 0.04

4. (4.5)(3.8)

5. (2.45)(1.2)

6. 3(1.74)

7. 32.7 ? 0.12

8. 5.6 ? 3

9. 1.92 ? 1.2

10. 1,302/21

11. 96.15/0.05

12. 7/9

Converting between Decimals, Fractions and Percents

For additional help:

?

2

Using Percents

When determining the percent of a number, first convert the percent into a decimal by dividing by 100 (move the decimal in the percent two places to the left). Then multiply the decimal by the number.

? 45% of 240 = 45% x 240 = 0.45 x 240 = 108

To determine a price with sales tax, calculate the sales tax by converting the percent of the tax to a decimal and multiplying it by the price. Then add the tax to the price.

? Tax of 6% on $15. Tax is .06 x 15 = $0.90. Total price with tax is 15.00 + 0.90 = $15.90.

To determine a price with a discount, calculate the discount by converting the percent of the discount to a decimal and multiplying it by the price. Then subtract the discount from the price.

? Discount of 15% on $39. Discount is .15 x 39 = $5.85. Total price after discount is 39 ? 5.85 = $33.15.

For additional help: ? ?

Find the percent of each number:

1. 30% of 450

2. 7% of 42

3. 10% of 321

4. 0.5% of 54

5. 165% of 32

6. 25% of 64

3

7. Susie has just bought a pair of jeans for $45.00, a sweater for $24.00, and a jacket for $85.00. The sales tax is 5%. What is her total bill?

8. Jack bought a set of golf clubs for $250.00 and received a discount of 20%. How much was the discount?

9. A construction manager calculates it will cost $2,890 for materials for her next project. She must add in 10% for scrap and extras. What will be the total cost?

10. The regular price for a video game system is $164.50 but is on sale for 30% off. What is the amount of the discount? What is the sale price?

11. Cindy earns a 15% commission on all sales. On Saturday, she sold $980 worth of merchandise. What was the amount of commission she earned on Saturday?

12. The band had a fundraiser and sold $25,000 worth of candy. They received 40% of this amount for themselves. How much did they receive?

Operations with Integers

Adding and Subtracting: 1st: Rewrite all subtraction as addition by adding the opposite: 2 ? 5 = 2 + (-5) Then... ? If the integers have the same signs, add their absolute values. The sum will have the same sign of the addends. Example: -2 + -5 = -7 (Both addends have a negative sign, so the sum is negative.) ? If the integers have different signs, subtract their absolute values. The sum has the sign of the addend with the greater absolute value. Example: 2 + -5 = -3 (Since the addends have different signs, subtract 5 ? 2. The difference is 3. -5 has a greater absolute value than 2, so the sum must be negative.)

Multiplying and Dividing: ? The product or quotient of two integers having the same sign is positive. (-2 ? -5 = 10) ? The product or quotient of two integers having different signs is negative. (-2 ? 5 = -10)

For additional help: ?

Evaluate each expression.

1. -7 + -5

2. -17 + 45

3. 53 + -102

4. -8 ? (-5)

5. 12 ? 18

6. -7 ? 12

4

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download