Ch.1: Language of Algebra
Consider the expression:
(|-23+9|div7)/(5+(-3))
Which operation should be done first?
23+9, because it is in the absolute value
Which quadrant contains order pairs that have this characteristic:
(x, y), such that x < 0 and y > 0.
Quadrant II
Fill in the blanks:
A rational number is any number that can be turned into a ______ of ________.
fraction, integers
True or false:
1/a^n = a^(1/n)
False
A student is presented the expression:
(9+10div5)/(6times 2)
The first step in the student's work is:
(19div5)/(12)
What error did the student make?
They violated the orders of operations. They added first in the numerator, when they should have divided first.
Fill in the blank:
The set of integers is ℤ ={ ____________ }
{... -2, -1, 0, 1, 2 ... }
What comes after the equality sign:
a/b div c/d =
(atimesd)/(btimes c)
Find the closest integer to the following cubed root:
root(3)(310)
root(3)(300)approx7
Evaluate the expression:
(|-23+9|div7)/(5+(-3))
1
Fill in the blank: When adding a positive and negative number together, the sign of the sum is determined by which additive has the greater ________.
Hint: Consider the example 5 + (-9).
Possible Answer: Absolute Value, Distance away from 0, Magnitude
If a number is part of the Natural Numbers, you know it's going to be Rational as well. This means that the Rational Numbers contain the Natural Numbers.
Besides the natural numbers, what other sets does the Rational Numbers contain?
Wholes and Integers.
We must "align" the exponents when perform certain operations on numbers written in scientific notation. What are those two operations?
Adding and Subtracting.
Besides the Substitution Property of Equality, what are the other 7 properties that we learned in Chapter 1?
Commutative Property of Addition, Commutative Property of Multiplication, Associative Property of Addition, Associative Property of Multiplication, Additive Identity Property, Multiplicative Identity Property, and Multiplicative Property of Zero.
Evaluate the following expression:
|8+ (-17)| + 9 div (-3)
6
Evaluate the following expression:
-6/17 + (6 8/9)(-9/17)
-4
Simplify the following expression:
(8a^-4b^-2)/(4a^9b^-7)(5a^2b^5)
10a^-11b^10