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Linglestown Middle School

SUMMER REVIEW PACKET

OF PREALGEBRA SKILLS

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FOR ALL STUDENTS TAKING

ALGEBRA 1

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Dear Student and Parent,

The math department at Linglestown Middle School wants you to be a successful student in the math courses that we offer. We also want you to be able to score proficient or advanced on the PSSA tests. This summer packet was put together for you to help reach this success.

This packet is a review of the skills that you should know prior to taking the Algebra 1 course that you have signed up for. I have included a diagnostic test with the answers (located at the back of your packet) for your child to take to see what they may need additional reinforcement on. Please take some time to look over the packet, do all problems, and get on the website for additional help, if needed. On the last page of the packet, I have included additional websites that may be of help to you, if you need it.

When you return in August, your teacher will give you the opportunity to ask questions. Math Help will also be available the first week if you request additional help. At the end of the first or second week of school, you will be given a quiz on the prerequisite material that is in this packet to see if you are ready for Algebra 1. The results of that quiz will be given to you and to your parents.

We hope that you have an enjoyable summer and return to school ready to be successful in Algebra 1.

See you in August!

The LMS Math Department

I. Reduce the following fractions and give your answer as a decimal.

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

II. Rewrite the following as a decimal.

75%= 35%= 99%= 15%= 100%=

[pic] [pic] [pic] [pic] [pic]

200%= 50% = 67% = 5% = 25%=

II. Rewrite the following as a decimal (continued).

[pic] [pic] [pic] [pic] [pic]

33%= 1% = 300%= 49%= 8%=

[pic] [pic] [pic] [pic] [pic]

150% = 10% = [pic] [pic] [pic]

III. Find the following products.

9 x 9 = 5 x 8= 4 x 7= 4 x 5= 8 x 5=

9 x 6= 2 x 8= 6 x 0= 9 x 7= 3 x 9=

8 x 4 = 0 x 9= 3 x 7= 1 x 9= 7 x 8=

7 x 1= 9 x 5= 8 x 3= 3 x 6= 9 x 2=

2 x 7 = 6 x 8= 7 x 4= 7 x 5= 8 x 9=

6 x 5= 8 x 6= 8 x 7= 4 x 8= 2 x 6=

8 x 1 = 9 x 4= 0 x 8= 7 x 9= 7 x 6=

8 x 8= 7 x 7= 5 x 6= 5 x 7= 4 x 9=

5 x 9 = 7 x 0= 5 x 5= 6 x 6= 6 x 7=

6 x 4= 9 x 3= 6 x 9= 4 x 6= 1 x 6=

IV. Rewrite the following as a fraction in reduced form.

.1 = .7 = 40% = 150% = 2.25 =

.4 = .65 = .74 = 33% = .8 =

.6 = .95 = .3 = .55 = 60% =

67% = 50% = 15% = 75% = 20% =

.35 = 90% = 30% = 10% = .85 =

.54 = 5% = .05 = .2 = .9 =

35% = 1.75 = 65% = 1.5 = 100% =

70% = 80% = .01 = .25 = 1.25 =

V. Reduce the following fractions.

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

[pic] [pic] [pic] [pic] [pic]

ALGEBRA Helpful Hints

If 5x = 10, then divide both sides by 5, and x = 2.

If 10x = 5, then divide both sides by 10, and x = ½.

[pic] [pic] [pic]

Zero divided by any number = zero.

[pic] [pic] [pic] [pic]

Any number divided by zero is called UNDEFINED. If you tried this in your calculator, it would say “error”.

[pic] [pic] [pic]

A negative fraction can be expressed three different ways:

[pic] or [pic] or [pic]

An improper fraction is when the numerator is greater than the denominator. We transform this into a mixed number by dividing.

[pic] [pic] = [pic]

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[pic][pic] [pic]

[pic] [pic] [pic] [pic]

REMEMBER- show all steps of work and circle your final answer.

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Exercises: Find the perimeter and area for each figure.

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5. a rectangle with length 6ft and width 4ft 6. a rectangle with length 12 cm and width 9 cm

7. a square with length 3m 8. a square with length 15 in

9. a rectangle with width 8 ½ in and length 11 in 10. a rectangular room with width 12 ¼ ft and length 14 ½ ft

11. The Granville Parks and Recreation Department uses an empty city lot for a community vegetable garden.

Each participant is allotted a space of 18 feet by 90 feet for a garden. What is the perimeter and area of each plot?

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4. the radius is 1.5 km 5. the diameter is 1 yd 6. the diameter is 5 ¼ ft

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11. the diameter is 4 yds 12. the radius is 1 m 13. the radius is 1.5 ft

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Perimeter and Area of Triangles

The PERIMETER of a triangle is the sum of the lengths of its sides. In less precise terms, this is sometimes stated as "the distance around the triangle." If the three sides are labeled a, b, and c, the perimeter P can be found by the following formula:

P = a + b + c

The area of a triangle is the space bounded (enclosed) by its sides. The formula for the area can be found by using a triangle which is part of a rectangle. In figure, triangle ABC is one-half of the rectangle. Since the area of the rectangle is b times h (that is, bh), the area of the triangle is given by the following formula:

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This formula is valid for every triangle, including those with no two sides perpendicular.

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Exercises: find the perimeter and area of each figure.

1. 2. 3.

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1. P(quarter) 2. P(dime) 3. P(nickel or dollar)

4. P(quarter or nickel) 5. P(value less than $1.00) 6. P(value greater than $0.10)

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7. P (Sum less than 7) 8. P(sum less than 8) 9. P(sum greater than 12)

10. P(sum greater than 1) 11. P(sum is between 5 and 10) 12. P(sum is between 2 and 9)

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13. P(triangle) 14. P(pentagon) 15. P(not a triangle)

16. P(not a quadrilateral) 17. P(more than three sides) 18. P(more than one right angle)

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19. the letter a 20. the letter t 21. a vowel

22. a consonant 23. an uppercase letter 24. a lowercase letter

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-----------------------

12m

5m

b

h

h

13m

9ft

9ft

5ft

12ft

10in

3in

6in

7.2in

15.

15.

14.

14.

13.

13.

12.

12.

18.

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17.

17.

16.

16.

21.

21.

20.

20.

19.

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26.

27.

28.

[pic]

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It is NOT = -1/-3 because a negative divided by a negative would be positive.

CAUTION:

All addition and subtraction need to be done before multiplication and division-

3 – 2 + 1 = 3 – 3 3 – 2 + 1 = 1 + 1 = 2

10 / 2 x 5 = 10 /10 10 / 2 x 5 = 5 x 5 = 25

Be sure to show all steps of work!

Show the substitution as in #3

CIRCLE YOUR FINAL ANSWER.

2 + (3)2

2 + 9

11

DID YOU SHOW ALL YOUR WORK?

*SEE NEXT PAGE FOR EXERCISES*

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To add or subtract fractions with unlike denominators, first find the least common denominator(LCD). Rewrite each fraction with the LCD, and then add or subtract. Simplify if necessary.

This means show all work and REDUCE. Circle your answer.

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4.0

5.0

6.0

10.

9.0

8.0

7.0

12.

11.

15.

16.

13.0

14.

19.

20.

17.0

18.

The reciprocal of [pic] is [pic]

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e.

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f.

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This is called a COMPLEX FRACTION.

it means we have one fraction(division problem made from two fractions)

27. 0

28.

Remember: [pic] is a mixed number. As an improper fraction it is [pic]

Ex.

33.

32.

31.

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Use improper fraction form to make multiplying and dividing mixed numbers easier.

More Practice with Rational Numbers- Show the substitution all work and circle the final answer.

1.

9.

8.

7.

6.

5.

4.

3.

2.

11.

10.

5.

5.

4.

4.

3.

3.

2.

2.

1.

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