Algebraic Mbush

Question 1

Addition of Signed Numbers

Procedure for Adding Two or More Numbers with the Same Signs

Answer 1

• Add the absolute values of the numbers.
• If all the numbers are positive, then the sum is positive. A positive sign is not needed as a
prefix.
• If all the numbers are negative, prefix a negative sign to the sum.

Question 2

Procedure for Adding Combinations of Two or More Positive and Negative Numbers

Answer 2

• Add all the positive numbers.
• Add all the negative numbers.
• Add their sums, following the procedure for adding signed numbers.

Question 3

6–6 Subtraction of Signed Numbers

Procedure for Subtracting Signed Numbers

Answer 3

• Change the sign of the number being subtracted (subtrahend) to the opposite sign.
• Add the resulting signed numbers.

NOTE: When the sign of the subtrahend is changed, the problem becomes one in addition.
Therefore, subtracting a negative number is the same as adding a positive number. Subtracting
a positive number is the same as adding a negative number.

Question 4

6–7 Multiplication of Signed Numbers

Procedure for Multiplying Two or More Signed Numbers

Answer 4

• Multiply the absolute values of the numbers.
• If all numbers are positive, the product is positive.
• Count the number of negative signs.
• If there is an odd number of negative signs, the product is negative.
• If there is an even number of negative signs, the product is positive.
It is not necessary to count the number of positive values in an expression consisting of
both positive and negative numbers. Count only the number of negative values to determine the
sign of the product.

Question 5

6–8 Division of Signed Numbers

Procedure for Dividing Signed Numbers

Answer 5

• Divide the absolute values of the numbers.
• Determine the sign of the quotient.
• If both numbers have the same sign (both negative or both positive), the quotient is
positive.
• If the two numbers have unlike signs (one positive and one negative), the quotient is
negative.

NOTE: Recall that zero divided by any number equals zero.

Question 6

Procedure for Multiplying Expressions that Consist of More than One Term

Answer 6

Multiply each term of one expression by each term of the other expression.
• Combine like terms.
Before applying the procedure to algebraic expressions, two examples are given to show
that the procedure is consistent with arithmetic

Question 7

FOIL Method

Answer 7

Find the sum of the products of:
1. the first terms: F
2. the outer terms: O
3. the inner terms: I
4. the last terms: L
Then combine like terms.

Question 8

Procedure for Dividing when the Dividend Consists of More than One Term

Answer 8

• Divide each term of the dividend by the divisor, following the procedure for division of
signed numbers.
• Combine terms.
Before the procedure is applied to algebraic expressions, an example is given to show that
the procedure is consistent with arithmetic.

Question 9

13–6 Powers

Procedure for Raising a Single Term to a Power

Answer 9

• Raise the numerical coefficients to the indicated power following the procedure for powers of
signed numbers.
• Multiply each of the literal factor exponents by the exponent of the power to which it is
raised.
• Combine numerical and literal factors.