8th grade-Unit 4 Review
Solving Word Problems-page 142-147-Be able to write an equation for a word
problem and solve.
Example: The sum of a certain number and 15 is 41. What is the number?
n + 15 = 41
check your work
n + 15 – 15 = 41 – 15
26 + 15 = 41
n = 26
41 = 41
Example: The sum of twice a number and 8 is 44. What is the number?
2n + 8 = 44
check your work
2n + 8 – 8 = 44 – 8
2 (18) + 8 = 44
2n = 36
36 + 8 = 44
2n/2 = 36/2
44 = 44
n = 18
Example: Seven times a certain number is 266. What is the number?
7n = 266
check your work
7n/7= 266/7
7(28) = 266
n = 38
266 = 266
Example: Separate the number 78 into three parts so that the second part is
twice the first part and the third part is 6 more than the first part.
x + 2x + x + 6 = 78
check your work
4x + 6 = 78
18 + 2(18) + 18 + 6 = 78
4x + 6 – 6 = 78 – 6
18 + 36 + 18 + 6 = 78
4x = 72
78 = 78
4x/4 = 72/4
x = 18
Formulas, Table, and Graphs- page 147-150
Be able to complete a table and graph for the given formula. Refer to page 149
for an example.
Positive and Negative Numbers-page 151Adding signed numbers-page 155-156.
Know the rules for adding signed numbers using a number line
To add a positive number using the number line, move from the first number to
the right as many units as the second number is.
To add a negative number using the number line, move from the first number to
the left as many units as the second number.
When a number is added to its inverse, the result is zero.
See examples on page 155.
Adding signed numbers without using a number line-page 157-158.
Follow these three rules:
1. When the addends have the same, add and give the sum the same sign as
the addends.
Example: 12 + 8 = 20
(-5) + (-17) = -22
(-4) + (-9) + (-7) = 20
2. When the addends have different signs, ignore the signs and subtract the
number having the smaller absolute value from the number having the
larger absolute value. Put the sign of the number having the larger
absolute value in front of the sum.
Example: (+8) + (-5) = +3
(-8) + (+4) = -4
3. When a problem contains several addends having different signs, add up
the positive numbers and add up the negative numbers. Ignore the signs
and subtract the sum having the smaller absolute value from the sum
having the larger absolute value. Put the sign of the number having the
larger absolute value in front of the sum.
Example: (+8) + (-5) + (+4) + (+5) + (-6) =
1. Add the positive numbers.
8 + 4 + 5 = +17
2. Add the negative numbers.
-5 + -6 = -11
3. Subtract 11 from 17 because 11 has a smaller absolute value
than 17.
17 (-11) = +6
4. Give the answer the sign of the larger absolute value which is 17.
Subtracting signed numbers using a number line-page 159
To subtract a positive number using the number line, move from the first
number to the left as many units as are in the second number.
To subtract a negative number using the number line, move from the first
number to the right as many units as the second number is.
See page 159 for an example.
Subtracting signed numbers without using a number line-page 160-161.
To subtract a signed number, change the sign of the subtrahend and add.
Example: (-12) – (+6)
(18) – (-9)
(25) – (+6)
(-12) + (-6)
18 + (9)
25 + (-6)
-18
27
19
Multiplying Signed Numbers page 162-163
When the two factors have the same sign, the product is positive.
Example: (-5) x (-6) = 30
5 x 6 = 30
When the two factors have opposite signs, the product is negative.
Example: (-5) x (6) = -30
(5) x (-6) = -30
Finding the Product of more than two factors
Multiply two of the factors together and then multiply the product by another
factor.
Example: (-4) (+6) (-3) (-4) =
1. Multiply -4 by +6.
-24 (-3) (-4) =
2. Multiply -24 by -3.
+72 (-4) =
3. Multiply 72 by -4.
-288
When zero is one of the factors in a multiplication problem, the product is zero.
Example: (+8) (-4) (0) (+5) (-6) = 0
Dividing signed numbers page 164-165
When the dividend and the divisor have the same signs, the quotient is positive.
Example: -25/ -5 = 5
When the dividend and the divisor have opposite signs, the quotient is negative.
Example: -25/ 5 = -5