Evaluate variable expressions involving rational numbers

Algebra 2 Tutorial

Evaluate variable expressions involving rational numbers

Intro

Variable expressions involving rational numbers are one of the first lessons in Algebra 2. A rational number is basically a fraction or a decimal, but it can’t repeat forever (infinity). Technically, it’s “any number that can be expressed as the quotient or fraction p/q of two integers.”-mathforum.org. For example, .8, which can be expressed as 4/5 OR the decimal .75, which is the equivalent of 3/4

[pi, or π, is an irrational number because it cannot be expressed as a fraction p/q of two integers. It is not an exact decimal, but it can be shortened to 3.14 versus an unending 3.14159265359….]

A bit more from mathforum.org: Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

As with my tutorial Evaluate variable expressions involving integers, it’s known that
Parentheses equal an asterisk or a multiplication symbol:
9(3)= 27 OR 9 * 3 = 27 OR 9 × 3 = 27
And a negative number times a negative number equals a positive number (or a negative number times a positive number equals a negative number):
-2 * -3 = 6
-3 * 4 = -12

Sample Problem

Question source

Evaluate the expression for m= -1.5

9.8m=

Solution

Evaluate the expression for m= -1.5

9.8m=

Here we plug in -1.5 for m. This can be expressed 2 equal ways:

9.8(-1.5) OR 9.8 * -1.5

9.8
*-1.5
_______
490
98
_______
1470 There are two numbers behind the decimal point (both 8 and 5), so we know to move to places to the left ONE: 147.0 TWO: 14.70.

We multiplied one positive number (the multiplicand) by a negative number (the multiplier), resulting in a negative answer (answer or product, in multiplication)

ANSWER: -14.70

———————————–

Another problem:

Evaluate the expression for r=3. Simplify your answer.

r/3=

Fill in the 3 for “r”:
(3)/3
Which is the same as
3/3
Simplify:
3/3=1



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