Basic Equations

Question 0

How to solve…

4 + 5 x 6 =

Answer 0

= 4 + (5 x 6)

= 4 + 30

= 34

Question 1

Order of Operations

Answer 1

(1) Substitute for letters
(2) Do work in parentheses first then tops and bottoms of fractions
(3) Do exponents
(4) Do multiplications and divisions from left to right
(5) Addition & subtraction from left to right.

Question 2

How to solve…

( 4 + 5 ) 6 =

Answer 2

= ( 9 ) 6

= 54

Question 3

How to solve…

1000 ÷ 2 x 4

Answer 3

= ( 1000 ÷ 2 ) x 4

= 500 x 4

= 2000

Question 4

How to solve…

1000 ÷ ( 2 x 4 )

Answer 4

= 1000 ÷ (8)

= 125

Question 5

How to solve…

4[ 3 + 2( 5 - 1 ) ]

Answer 5

= 4[ 3 + 2( 4 ) ]

= 4[ 3 + 8 ]

= 4[ 11 ]

= 44

Question 6

How to solve…

3⁴ - 1¹⁰ / 4 - 10 x 2

Answer 6

= 81 - 1 / 4 - 20

= 80 / -16

= -5

Question 7

How to solve…

x = -3

7 - 5x - x²

Answer 7

= 7 - 5(-3) - (-3)²

= 7 - (-15) - 9

= 7 + 15 - 9

= 13

Question 8

How to solve…

x = -3, y = -4

xy² - (xy)² =

Answer 8

= (-3)(-4)² - ( -3 x -4 )²

= (-3)(16) - (12)²

= -48 - 144

= -192

Question 9

How to solve…

Jim received 83 and 92 on two tests. What grade must the third test be in order to have a average of 90?

Answer 9

Solution 1:
3(90) = 270
270 - 83 - 92 = 95

Solution 2:
83 + 7 = 90
92 - 2 = 90
90 + 7 - 2 = 95

Question 10

How to solve…

Which is bigger?

243 x 78 -or- 244 x 77

Answer 10

243 x 78 = (77 + 1)243 -or- 77(243) + 243

244 x 77 = 77(243 + 1) -or- 77(243) + 77

Top equation is the larger

Question 11

How to solve….

Which is bigger?

94 x 357 x 10 x 9 x 8 x 7 / 7 x 3 x 2

-or-

7 x 4 x 3 x 2 x 357 x 94 / 9 x 8 x 7

Answer 11

Get rid of the common numbers!

10 x 9 x 8 / 3 x 2 vs. 4 x 3 x 2 / 9 x 8

The first is the larger

Question 12

How to solve…

Which is larger?

x - 1 -or- x + 1

Answer 12

Subtract x!

-1 vs. +1

Question 13

How to solve…

Which is larger?

x -or- 1/x

Answer 13

Substitute x with 1, 3, and 1/2

1 vs. 1

3 vs. 1/3

.25 vs. 4

Not enough information

Question 14

How to solve…

Which is larger?

(-3)⁸ -or- -3⁸

Answer 14

With the parenthesis, you are multiplying (-3) by itself eight times making it a positive number.

Without the parenthesis, you are multiplying 3 by itself eight time then subtracting it thus making it negative.

Question 15

How to solve….

Which is smaller?

(4.2)² -or- √4.1

Answer 15

√4.1

(4.2)² will be bigger than 4 where √4.1 will be smaller

Question 17

How to solve….

Which is bigger?

1/6 or 1/0.06

Answer 17

1/0.06

Question 18

How to solve….

Which is bigger?

1/3 1/6
—- -or- —-
1/6 1/3

Answer 18

1/6

The top is bigger. In the other, the bottom is bigger

Question 19

How to solve….

Which is bigger?

(-1/2)⁵ -or- (-1/2)⁶

Answer 19

(-1/2)⁶

(-1/2)⁵ < 0

(-1/2)⁶ > 0

Question 20

How to solve…

8% of what is 32?

Answer 20

32 ÷ 0.08

= 400

Question 21

How to solve…

What is 12% of 1.3?

Answer 21

0.12 x 1.3

= 0.156

Question 22

How to solve…

9 is what percent of 8?

Answer 22

9 ÷ 8

= 1.125

= 112.5%

Question 23

How to solve…

In ten years, the population increases form 20,000 to 23,000. Find the actual increase and the percentage increase.

Answer 23

Actual Increase
23,000 - 20,000 = 3,000

Percentage Increase
3,000 ÷ 20,000 = .15 -or- 15%

Question 24

How to solve…

The cost of a $2000 TV is decreased by 30%. If there is a 7% sales tax, how much did you pay?

Answer 24

$2000 x .70 = $1400

$1400 x 1.07 = $1498

Question 25

How to solve…

30% of 20% of a number is the same as 40% of what percentage of the same number?

Answer 25

30 x 20 = 600

600 ÷ 40 = 15

= 15%

Question 26

How to solve…

The reciprocal of 2 - 3/4 is…

Answer 26

8/4 - 3/4 = 5/4

Flip this to get 4/5

Question 27

How to solve…

Which discount is larger: a 65% discount or a discount of 50% followed by an additional 20% discount?

Answer 27

$100 x 0.5 = $50
$50 x .8 = $40

$100 x .35 = $35

The 65% discount is the largest discount

Question 28

How to solve

Which is larger: 2/3 of 37.5% or 33.3% of 3/4?

Answer 28

2/3 x 375/1000.....Reduce!
    = 2/3 x 75/200
    = 2/3 x 15/40
    = 2/3 x 3/8
    = 2/1 x 1/8
    = 1/1 x 1/4
    = 1/4

1/3 x 3/4
= 1/1 x 1/4
= 1/4

They are the same!

Question 29

How to solve….

Which is larger: 2.5 or the largest value of x/y when 8≤x≤10 and 4≤y≤6 ?

Answer 29

Take the largest possible number for x and the smallest possible for y.

So 10/4 = 2.5

The amounts are the same