Pre-Algebra Test 3 Review

Give a two-letter word, as well as a four-letter word, that is often written in an example of transitive property.

IF & THEN

Why is the expression, 10(26)(3)(1/2), being solved as (26)(1/2)(3)(10) an example of the commutative property of multiplication?

The numbers moved around so that the problem could be solved for the same answer but in a different way.

Evaluate 1/3 minus 5/8.

The problem becomes 8/24 minus 15/24, or -7/24.

Why is the equation abc(3) = 3cba an example of the symmetric property?

The right side of the equation is a reversed version of the left side.

Writing 2(-1) = (-1) + (-1) = -2 helps explain what rule about multiplication?

a positive times a negative is a negative

If you want to write the equation, ¾ x = 15, as a proportion, you would need to put with .... a. the 3 b. the 4

a, (put the x with the three)

To solve - 33 - (- x) = 5, you _______ 33 to both sides.

add

When you move a term by adding or subtract, you do so ______ time(s) on each side. What number goes in the blank?

one

13 divided by 0 is...

undefined.

Any number divided by zero is...

undefined.

The equation - 1,231 - (- x) = 534 should be re-written as...

-1,231 + x = 534

Simplify (5 - 20x ) · -2.

-10 + 40x, or 40x - 10

How should -10x + - 8 be written before giving it as a final answer?

-10x - 8, or else - 8 - 10x

Simplify (11 - 2x ) · -1.

-11 + 2x, or 2x - 11

Evaluate 20 - 33.

-13

Evaluate 8(-2).

-16

Simplify (6 - 20x ) · -3.

-18 + 60x, or 60x - 18

Evaluate -10 + (-10).

-20

Evaluate -10 - 10.

-20

Simplify (5 - 10x ) · -4.

-20 + 40x, or 40x - 20

Evaluate -1(3).

-3

What is 4 - 35?

-31

Evaluate -31 + (-9).

-40

Evaluate 25 divided by -5.

-5

Simplify - 5(x + 5) + 1.

-5x - 24, or -24 - 5x

Evaluate -99 divided by 11.

-9

Simplify -1x + y.

-x + y

Simplify -x -(-y).

-x + y

Simplify -x -1(xy).

-x - xy

Simplify -x + (-y).

-x - y

Simplify -1xy + (-1x) - (-xyz).

-xy - x + xyz

Evaluate -10 - (-10).

0

Evaluate -15 - (-15).

0

Evaluate 10 + (-10).

0

Simplify 4(x - 1) + 20.

4x + 16, or 16 + 4x

Evaluate -30 / -6.

5

How many terms are in the expression that follows; ab + xy + 3x + 4y + 9?

5

Suppose you solve an equation with a final answer of 40/8. This is the same as 5(2)(2)(2) over (2)(2)(2). Since there are three 2s in both the numerator and the denominator, the 2s cancel out and the final answer would be...

5

Write 3/10 times (2/21) in a way that looks normal on a sheet of looseleaf. The ten could be changed to a ___ and the two to a ____ .

5, 1

How do you rewrite 5/7 divided by 7 as a multiplication problem?

5/7 times 1/7

What is the simplest way to write -250 -(-530) so that it could be done by even a 4th grader?

530 - 250

How do you rewrite 6/5 divided by 8 as a multiplication problem?

6/5 times 1/8

Evaluate -21 divided by -3.

7

Which choice that follows is an example of the commutative property of multiplication? 7(17)(10) = (7*10)(17) 3xyz = 3xyz 4 + 5 + 6ab = 6ab + 5 + 4 q(0) = 0 1/2 (2) = 1

7(17)(10) = (7*10)(17)

Simplify 3x + 4(x - 10) + 50.

7x + 10, or 10 + 7x

Which equation has a solution of 1/2? 30x = 60 or 7x = 3.5

7x = 3.5

To change 5/9 to a fraction with a denominator of 81, you should multiply the 5 by ____ ?

9

How do you rewrite 9 divided by 2/3 as a multiplication problem?

9 times 3/2

Which equation has a solution of 2? 6x = 3 or 9x = 18

9x = 18

Which choice that follows is an example of the reflexive property? 2abc = abc(2) it + was + great = great + it + was 3.14math = 3.14math

3.14math

Simplify 20x + 10(x + 2) - 21.

30x - 1, or -1 + 30x

Simplify 5x + 3x(9) + 6.

32x + 6, or 6 + 32x

Simplify 35x + 3(x - 8) + 11.

38x - 13, or -13 + 38x

To change 3/11 to a fraction with a denominator of 44, you should multiply the 3 by ____ ?

4

What is the coefficient of 4x?

4

-8(4) is the same as what addition problem that involves the same four negative numbers?

(-8) + (-8) + (-8) + (-8)

Simplify 3(1 - 4x ) - 2.

1 - 12x, or -12x + 1

Write 3/10 times 2/21 in a way that looks normal on a sheet of looseleaf. The three could be changed to a ___ and the 21 to a ____ .

1, 7

What is the solution to -1,231 - (- x) = 534?

1,765

Suppose you solve an equation with a final answer of 3/9. This is the same as 1(3) over (3)(3). Since a 3 is in both the numerator and the denominator, the 3s cancel out and the final answer would be...

1/3

What is the solution to 3/10 times (2/21)?

1/35

What is the coefficient of x/4?

1/4

Evaluate -10(-10).

100

Evaluate 4 - (-10).

14

Evaluate (-3)(-5).

15

What is the simplest way to write 37 -(-172) so that it could be done by even a 4th grader?

172 + 37

What are the coefficients of the following expression; 2x - y + 13xy?

2, -1, and 13

Evaluate 10 - (-10).

20

Evaluate 13 - (- 14).

27

To multiply fractions, do you cross multiply or multiply straight across?

You multiply straight across. You only cross multiply when there is an equal sign between the fractions.

Which choice below shows an example of distributive property? a. 15 divided by ½ is the same as 15 times 2 b. 48(53) is the same as 48 x 50 being added with 48 x 3 c. The reciprocal of ¼ is 4.

B 48(53) is the same as 48 x 50 being added with 48 x 3

28(23) being solved as 28(20) plus 28(3) is an application of which property?

Distributive

HOW do you solve - x = 200?

Divide both sides by -1.

To multiply or divide fractions, you (do ... or do not) need common denominators. Pick the correct word or words from the parenthesis.

Do not

True or False (circle one): To solve - x = 7, you could also divide both sides by -x.

FALSE. Divide both sides by -1.

True or False. The variable x, by itself, is the same thing as 1.

False

True or False: The work shown below (to solve the equation x + 20 = 40) is shown correctly. x + 20 = 40 -20 -20 -20 x = 20

False

True or False (circle one): To solve 5/6x = 25 in Mrs. Satterlee's Pre-Algebra class, you have been expected to show work by dividing both sides by 5/6.

False. Multiply by the reciprocal of 5/6 instead of dividing by 5/6. In other words, multiply both sides by 6/5.

Why is the equation racecar = racecar also an example of the reflexive property?

It is exactly the same on both sides.

Why is the equation racecar = racecar an example of the symmetric property?

It is the same forward and backward.

Why would the following answer be marked wrong? How should it be written? -1x + 2xy

Just write -x + 2xy

True or False (circle one): Before solving an equation, like - 1,231 - (- x) = 534, the equation should be re-written to get rid of the double-signs.

True

True or False (circle one): When solving 11x = 15, a final answer of 15/11 is more precise than 1.36.

True

True or False: Any variable by itself, like x, has a 1 in front of it even if you don't see the one.

True

True or False. Never leave a lonely one all by itself in the denominator.

True. If all you have in the denominator is a 1, then there is no need to write the expression as a fraction.

To add or subtract fractions, you must make sure they have ___________ ______________ and then work with only the ______________ .

common denominators, numerators

What eight-letter word ends in T and is another name for a number?

constant

To give an example of an expression, you need to make sure and NOT write a(n) ???

equal sign

When you multiply or divide when solving an equation, your work does not need to have an __ __ __ __ __ __ __ __ __ __ __ .

equation bar

In the expression 11x + 13 y-squared, the 2 is a(n) _____________ and the 11 & 13 are __________________ .

exponent, coefficients

To solve ¼ x = 24, you should ________ both sides by 4.

multiply

Simplify x - (-xy) + (-y).

x + xy - y

Which of the following is an example of an expression? a + b = c or x + y

x + y

What is the solution to the equation x + 17 = 5 ?

x = -12

What fraction, with an x, has a coefficient of 1/23, but no 1?

x/23

What fraction, with an x, has a coefficient of 1/5 but no 1?

x/5

Zero divided by any number is ...

zero.