Name _________________________
SLHS Summer Assignment for Algebra 1 (No Calculator)
Use the instructional links to help you solve each problem. We encourage you to complete this assignment
prior to the first day of class- it will help prepare you to be successful in Algebra 1!
Topic 1 – Number Sense (Adding, Subtracting, Multiplying, and Dividing Integers)
A. Adding and Subtracting
https://www.khanacademy.org/math/arithmetic/addition-subtraction/basic_addition/v/basic-addition
https://www.khanacademy.org/math/arithmetic/addition-subtraction/basic_addition/v/basic-subtraction
https://www.khanacademy.org/math/arithmetic/addition-subtraction/two_dig_add_sub/v/subtraction-2
When adding or subtracting numbers, think of a number line! When adding, move to the right, and
when subtracting, move to the left.
1. −15 + 4 =
2. 10 − 5 =
3. 4 − 8 =
4. −7 − 3 =
5. 1 − 0 =
6. −10 + 13 =
7. −11 + (−2) =
8. −2 − (−4) =
9. 3 + (−5) =
B. Multiplying and Dividing
https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/multiplication-intro
https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/more-on-the-concept-of-multiplication
https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/the-idea-of-division
Remember:
(−) ∙ (−) = +
(+) ∙ (+) = +
(−) ∙ (+) = −
(+) ∙ (−) = −
Example:
Example:
Example:
Example:
−5 ∙ −2 = 10
3∙2=6
−4 ∙ 1 = −4
7 ∙ −1 = −7
When multiplying or dividing, it’s extremely important to know the multiplication table up to 12!
Bottom line: memorize it! It will make your life easier 
56
=
10. −12 ∙ 3 =
11. 72 ÷ 9 =
12.
13. 3 ∙ 11 =
14. −7 ∙ −4 =
15. 12 ÷ 6 =
−8
Topic 2 – Fractions (Adding, Subtracting, Multiplying, Dividing)
A. Adding and Subtracting
https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/adding-fractions-with-likedenominators
https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/subtracting--fractions
https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/v/adding-and-subtracting-fractions
When adding or subtracting fractions, they must have common denominators!
16.
4
+ =
19.
4
+ =
3
7
1
17.
1
− =
8
20.
5
− =
23.
5
+ =
3
22. 4 +
7
9
2
=
2
2
2
3
18.
1
21.
1
24.
2
4
4
3
+
3
+ =
10
10
4
3
5
10
6
2
6
− =
5
=
B. Multiplying and Dividing
https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-a-fraction-by-a-fraction
https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-byfractions
When multiplying fractions, multiply straight across. Always reduce fractions in the final answer.
Example:
1 3
∙ =
2 5
1∙3
2∙5
=
3
10
When dividing fractions, keep the first fraction the same, change the sign to multiplication, and take
the reciprocal of the second. Then multiply. In other words: keep, change, flip!
2
Example:
3
𝟏𝟏
2 𝟒𝟒
÷ = ∙ =
𝟒𝟒
3 𝟏𝟏
8
3
25.
2 3
28.
10 6
29.
31.
2
32.
∙ =
5 1
3
5
∙ =
2
3
÷ =
1
26.
1 7
∙ =
5 4
4 3
− ∙ =
9 7
2
5
÷
4
−10
=
27.
12 −2
30.
2
33.
2
9
∙
3
=
2
÷ =
4
3
− ÷
2
10
7
=
Topic 3 – Order of Operations
https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/introduction-to-order-of-operations
Remember the acronym PEMDAS when simplifying expressions or solving equations because it tells
the order in which to simplify.
P (Parentheses)
E (Exponents)
M D (Multiplication/Division-whichever comes first)
A S (Adding/Subtraction—whichever comes first)
Simplify.
34. 3(2 + 4)
35. 9 − 32 ÷ 4
36. 40 ÷ 4 − (5 − 3)
37. (5 + 16) ÷ 7 − 2
38. 4 − 32 − 1
39. 4 + (−3)2 − 1
Topic 4 – Solving Equations
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/adding-and-subtracting-thesame-thing-from-both-sides
When solving equations, you need to isolate the variable by performing the inverse operation. The
nice thing about solving equations is you can always check your answer by evaluating the equation
with your answer.
Example 1: 𝑥𝑥 + 7 = 4
−7
−7
𝑥𝑥 = −3
Example 2: 7𝑥𝑥 = 14
÷7
Example 3:
𝑥𝑥
6
÷7
𝑥𝑥 = 2
𝑥𝑥
=4
6∙6 = 4∙6
𝑥𝑥 = 24
Inverse operation of addition is subtraction
Subtract 7 from both sides
You solved for 𝑥𝑥!
Inverse operation of multiplication is division
Divide both sides by 7
You solved for 𝑥𝑥!
Inverse operation of division is multiplication
Multiply both sides by 6
You solved for 𝑥𝑥!
Solve for the indicated variable.
40. 𝑥𝑥 + 6 = 10
43.
𝑥𝑥
5
=3
46. 32 = −4𝑥𝑥
41. −4 + 𝑘𝑘 = 9
42. 10𝑡𝑡 = 60
44. 𝑦𝑦 − 18 = 2
45. −12 = 4𝑝𝑝
47. 𝑤𝑤 + 17 = 27
48.
𝑥𝑥
−7
= 11