Basic Equations Flashcards
How to solve…
4 + 5 x 6 =
= 4 + (5 x 6)
= 4 + 30
= 34
Order of Operations
(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.
How to solve…
( 4 + 5 ) 6 =
= ( 9 ) 6
= 54
How to solve…
1000 ÷ 2 x 4
= ( 1000 ÷ 2 ) x 4
= 500 x 4
= 2000
How to solve…
1000 ÷ ( 2 x 4 )
= 1000 ÷ (8)
= 125
How to solve…
4[ 3 + 2( 5 - 1 ) ]
= 4[ 3 + 2( 4 ) ]
= 4[ 3 + 8 ]
= 4[ 11 ]
= 44
How to solve…
3⁴ - 1¹⁰ / 4 - 10 x 2
= 81 - 1 / 4 - 20
= 80 / -16
= -5
How to solve…
x = -3
7 - 5x - x²
= 7 - 5(-3) - (-3)²
= 7 - (-15) - 9
= 7 + 15 - 9
= 13
How to solve…
x = -3, y = -4
xy² - (xy)² =
= (-3)(-4)² - ( -3 x -4 )²
= (-3)(16) - (12)²
= -48 - 144
= -192
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?
Solution 1:
3(90) = 270
270 - 83 - 92 = 95
Solution 2:
83 + 7 = 90
92 - 2 = 90
90 + 7 - 2 = 95
How to solve…
Which is bigger?
243 x 78 -or- 244 x 77
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
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
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
How to solve…
Which is larger?
x - 1 -or- x + 1
Subtract x!
-1 vs. +1
How to solve…
Which is larger?
x -or- 1/x
Substitute x with 1, 3, and 1/2
1 vs. 1
3 vs. 1/3
.25 vs. 4
Not enough information
How to solve…
Which is larger?
(-3)⁸ -or- -3⁸
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.
How to solve….
Which is smaller?
(4.2)² -or- √4.1
√4.1
(4.2)² will be bigger than 4 where √4.1 will be smaller
How to solve….
Which is bigger?
1/6 or 1/0.06
1/0.06
How to solve….
Which is bigger?
1/3 1/6
—- -or- —-
1/6 1/3
1/6
The top is bigger. In the other, the bottom is bigger
How to solve….
Which is bigger?
(-1/2)⁵ -or- (-1/2)⁶
(-1/2)⁶
(-1/2)⁵ < 0
(-1/2)⁶ > 0
How to solve…
8% of what is 32?
32 ÷ 0.08
= 400
How to solve…
What is 12% of 1.3?
0.12 x 1.3
= 0.156
How to solve…
9 is what percent of 8?
9 ÷ 8
= 1.125 = 112.5%
How to solve…
In ten years, the population increases form 20,000 to 23,000. Find the actual increase and the percentage increase.
Actual Increase
23,000 - 20,000 = 3,000
Percentage Increase
3,000 ÷ 20,000 = .15 -or- 15%
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?
$2000 x .70 = $1400
$1400 x 1.07 = $1498
How to solve…
30% of 20% of a number is the same as 40% of what percentage of the same number?
30 x 20 = 600
600 ÷ 40 = 15
= 15%
How to solve…
The reciprocal of 2 - 3/4 is…
8/4 - 3/4 = 5/4
Flip this to get 4/5
How to solve…
Which discount is larger: a 65% discount or a discount of 50% followed by an additional 20% discount?
$100 x 0.5 = $50
$50 x .8 = $40
$100 x .35 = $35
The 65% discount is the largest discount
How to solve
Which is larger: 2/3 of 37.5% or 33.3% of 3/4?
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!
How to solve….
Which is larger: 2.5 or the largest value of x/y when 8≤x≤10 and 4≤y≤6 ?
Take the largest possible number for x and the smallest possible for y.
So 10/4 = 2.5
The amounts are the same
