The document provides a math practice for a 3rd period exam covering various topics: I) Converting between decimal and binary numbers II) Converting between binary and decimal numbers III) Writing missing numbers in a number line IV) Ordering numbers on a number line The practice also includes: V) Determining if algebraic expressions are correct VI) Writing algebraic expressions from word problems VII) Solving word problems using algebraic equations VIII) Writing equations from word problems It also covers distributing the distributive property, combining like terms, and solving equations using integers rules.

1. COLEGIO SAN PATRICIO
Math Practice for 3rd Period Exam
School Year 2010 – 2011
Binary System
I. Convert each decimal number to the binary number it represents.
48 = 110000 104 = 1101000
II. Convert each binary number to the decimal number it represents.
1110010 = 114 10101 = 21

2. The Number Line
III. Write the missing numbers.
IV. Order the next numbers in the number line.
0 0.50 1 1½ 1.25 2
Verbal Phrases and Algebraic Expressions.
V. Answer the next problems.
Is it correct?
1. 2x + 6 = 12 CORRECT Two times a number, plus six is
twelve.
2. (5) (6) − x = 25 INCORRECT Five times the difference of six
5(6−x)=25 and a number is twenty five.
3. 8(4 + 9) = 104 CORRECT Eight times the sum of four and
nine is one hundred four.

3. VI. Write each as an algebraic expression.
1. The difference of 10 and 5 10−5
2. The quotient of 14 and 7 14÷7
3. u decreased by 17 u − 17
4. The product of x and 7 7x
5. Twice q 2q
Problem Solving Using Algebraic Equations.
VII. Solve.
1. If 2/3 of the pizza is left, what part will you and your two friends get?
A: for each. (You divide 2/3 by the 3 friends)
2. My brother will be forty years old in four years (I wrote forty instead of
four). Let b be the age of my brother now:
A: b) b+4 = 40, then you need to solve the equation. Do as follows:
Checking Process
b + 4 = 40 b + 4 = 40
b = 40 – 4 36 + 4 = 40
b = 36 40 = 40

4. 3. Donna got 84 in a quiz, which includes 5-point bonus. Let x be the
grade she would have had without the bonus.
A: c) x + 5 = 84, then you need to solve the equation. Do as follows:
Checking Process
x + 5 = 84 x+ 5 = 84
x = 84 – 5 79 + 5 = 84
x = 79 84 = 84
VIII. Write an equation.
1. I have to check 90 exams. I have checked 35. How many exams am I
missing?
A: Possible equation: x + 35 = 90 I am missing 55 exams
x = 90 – 35
x = 55
Checking Process:
x + 35 = 90
55 + 35 = 90
90 90
4. One trip is ¾ kms. If we decide to take 6 trips, how many kilometers
are we going to travel?
A: 4 ½ kms. (You multiply ¾ by the 6 trips)
Distributive Property.
1. Apply the Distributive Property.
1. −6(a+8) 2. 6(−5n+7) 3. (1+9x)(-4x) 4. 7m(m-9)
-6a – 48 - 30n + 42 -4x – 36x² 7m² - 63m

5. Combining Like Terms
2. Simplify the expression. (Order it, then combine like terms, and
simplify).
1.
-5c + 3c + 9 – 2
-2c + 7 (this is the answer)
2.
-4u² - u² + 10+8
-5u²+18 (this is the answer)
3.
7x + (8 – 4x)
7x + 8 – 4x
7x – 4x + 8
3x+8 (this is the answer)
Equations
3. Find the value of the variable.
1. 2. 3. 4.
40 - 30 = 10x a = 33/3 n=0+5 p = 20 + 20
10 = 10x a = 11 n=5 p = 40
10/10 = x
1=x
x=1
Checking Process Checking Process Checking Process Checking Process
40 = 10x + 30 3a = 33 -5 + n = 0 p – 20 = 20
40 = 10 (1) + 30 3(11) = 33 -5 + (5) = 0 40 – 20 = 20
40 = 10 + 30 33 = 33 -5 + 5 = 0 20 = 20
40 = 40 0=0
1. 20 5. 7. 8.
x/2 = 20 – 10 k = 10 (2) 2x – 4 = 6 x = 60/3
x/2 = 10 k = 20 2x = 6 + 4 x =20
x= 10(2) 2x = 10
x = 20 x= 10/2
x= 5

6. Checking Process Checking Process Checking Process Checking Process
x/2 + 10 = 20 k/2 = 10 3x – x - 4 = 6 3x =60
20/2 = 10 20/2 = 10 3(5) – 5 – 4 = 6 3(20) = 60
10 = 10 10 = 10 15 – 5 – 4 = 6 60 = 60
10 – 4 = 6
6=6
4. Solve using the integers rules.
1. 7- (+8) – 5 2. 45 (-5) + |6| 3. 4 + (-5) 4. 5 – (-5+8)
7–8–5 -225 + 6 4–5 5+5–8
-1 – 5 - 219 -1 10 – 8
-6 +2