Decoding and Translating Flashcards
This deck allows for mastery of translating word phrases into number sentence components. It is essential to handling SAT word problems quickly and accurately.
Decode this:
x - 11 | = 7
The absolute value of x minus 11 is equal to 7.
Logically, this means either…
- x* - 11 = 7 or
- x* - 11 = -7
So, x = 18 or
x = 4
“…the first 15 square values…”
1, 4, 9, 16, 25, 36, 49, 64, 81,100,121,144,169,196, 225
Knowing your squares is a time saver. These represent the first 15 negative values squared as well.
the product of the first three odd prime numbers
3 x 5 x 7
105
the sum of a number and 11
n + 11
the sum of a number and minus 7
n + (-7) or n - 7
number increased by 100
n + 100
number is increased by 25%
n + (n x .25) or
n + n / 4 or
n x (5/4) or
5n / 4
2 greater than a number
n + 2
“Greater than” in this context means “more than”. Do not confuse it with “Is greater than” which means “>”.
number is decreased by 14
n - 14
5 less than a number
n - 5
Decode:
…absolute value of a number…
|a | = a
if a is greater than or equal to zero.
|a| = -a
if a is less than zero.
…the absolute value of the sum of a and b…
|a + b|
…the sum of the absolute values of a and b…
|a| + |b|
Note: “…the product of the absolute value of a and b…” won’t be asked on the SAT. The result is identical to the “the product of the absolute values of a and b”.
“…the sum of the first 8 prime numbers divided by the absolute value of the difference between the 5th and the 6th square values…”
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19
77 / |25 - 36| = 7
(a + b)(a - b)
(a + b)(a - b) = a2 - b2
a2 - b2
a2 - b2 = (a + b)(a - b)
(a + b)2
a2+ 2ab + b2
(a - b)2
a2- 2ab + b2
…what is n in terms of w and c…
n = some combination of w and c
To “solve or express in terms” means to isolate one variable on one side of the equation, leaving the other variables on the other side of the equation.
…the two mixtures combine to make a solution…
m1 + m2
…gained 60 milligrams…
Changing words into algebraic expressions is necessary to solve word problems.
What are some of the words you can name that mean the subtraction operation?
Here are some words that translate into subtraction:
- remove
- deduct
- depriciate
- shorten
- drop
- lose
- lower
- left
- difference
- decreased by
- fewer
- less than
- smaller than
- take away
Changing words into algebraic expressions is necessary to solve word problems.
What are some of the words you can name that mean multiplication operation?
Here are some words that translate into multiplication:
- double
- twice
- triple
- quadruple
- times
- squared
- cubed
- factor
- product
- multiple of
Changing words into algebraic expressions is necessary to solve word problems.
What are some of the words you can name that mean division operation?
Here are some words that translate into division:
- ratio
- average
- split
- half
- per
- quotient
- third
- fourth
- part of