8 7 1 Division is the inverse of multiplication Examine the product below 2 10

8 7 1 division is the inverse of multiplication

This preview shows page 9 - 11 out of 55 pages.

To undo this addition, we use the inverse of addition, which is subtraction. 8 - 7 = 1 Division is the inverse of multiplication: Examine the product below: 2 · 10 = 20 To undo this multiplication, we use the inverse of multiplication, which is division. 20 10 = 2 Note: This process only works for nonzero real numbers. This process fails for multiplication and division if the number zero is introduced. Multiplication is the inverse of division: Examine the quotient below: 8 4 = 2 To undo this division, we use the inverse of division, which is multiplication. 2 · 4 = 8 Note: This process only works for nonzero real numbers. This process fails for multiplication and division if the number zero is introduced. Copyright © 2020 MindEdge Inc. All rights reserved. Duplication prohibited.
Jars. In the expression above, the variable j appears twice. When the same variables, with the same exponents on those variables, appear in an expression more than once, they are considered "like terms." "Like terms" in an expression should be combined, whenever possible, in order to simplify the expressions - a process referred to as combining like terms. Simplifying an expression by combining like terms can be helpful for a number of reasons, including solving equations. To understand how we can combine these terms, or why we even want to combine these terms, let's assign meaning to this variable. Let's say the variable j represents jars . Replacing j with jars , the expression reads as follows: In this example, we have one jar, plus two jars, which equals three jars: As shown above, combining like terms leaves us with a shorter, more desirable expression: " 3 j ." This process of combining like terms can be completed with any "like" variable, even when there are other variables involved in an expression. We can add a "cookie" to our jar example: In the example above, we only combine the like terms. The presence of "cookie" does not prevent us from combining the "jars," but also does not get combined with "jars" because it's a different variable. 3.04.1 Identifying Like Terms Identifying Like Terms To combine like terms, we first need to identify which terms qualify as "like terms." As a reminder, a term is comprised of a constant multiplied by variable(s) and their exponent(s). When identifying whether two terms are like terms, we only need to examine the variable(s) and their exponent(s); we can ignore the coefficient in the term. Like Terms The following pairs of terms are like terms: j + 2 j ( jar ) + 2 ( jar ) one jar+two jars = three jars ( jar ) + 2 ( jar ) = 3 ( jar ) j + 2 j = 3 j one jar+one cookie + two jars = three jars + one cookie ( jar ) + ( cookie ) + 2 ( jar ) = 3 ( jar ) + ( cookie ) j + c + 2 j = 3 j + c For terms to be like terms, they need to have the same variable(s) with the same exponent(s) . Like Terms a and 2 a -4 and 7 3 D 2 ; and 6 D 2 The terms a and 2 a are like terms because they share the same variable: a . After ignoring any coefficients in the terms a and 2 a , we are left with the same variable: a . There is no exponent written next to either variable, so the exponent is the same for both terms. The terms -4 and 7 are like terms because they are both constants, and therefore they both lack a variable. This lack of a variable constitutes an identical variable.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture