Rational Numbers Review Packet Name:________________________
Date:____________
Class:________ Addition Rules:
If●the numbers have the same sign: Add the absolute values and keep the same sign.
If the
● numbers have different signs: Subtract the absolute values and keep the sign of the number with the bigger
absolute value.
Example: Add: ­9 + 13
Same sign? Subtract the absolute values.
Choose the sign.
No
13 ­ 9 = 4 |13| > |­9| , so answer is 4. Example: Add: ­7 + ­4
Same sign? Add the absolute values.
Choose the sign.
Add each expression
Same Sign?
(yes/no)
Yes
7 + 4 = 11 Both numbers are negative, so the answer is ­11 Add or Subtract Absolute values
Sum
− 16 + 9
no
16 - 9 = 7
-7
− 23 + (− 14)
yes
23 + 14
-37
57 + (− 90)
− 19 + (− 6)
− 123 + 132
76 + 34
subtraction problem
● as an addition problem. (Add the opposite)
s for addition.
●
Example: Subtract: ­9 ­ 13
Rewrite as addition, (add ­13).
Same sign? Add the absolute values.
Choose the sign.
­9 + (­13) Yes
9 + 13 = 22 Same sign, so keep that sign. The answer is ­22. Example: Subtract: ­7 ­ (­4) Rewrite as addition, (add 4)
Same sign? Subtract the absolute values.
­7 + 4
No
7 ­ 4 = 3 e as addition
Date:____________
Choose the sign.
|­7| > |4|, so the answer is ­3. Same
Sign?
Add or Subtract Absolute
values
Class:________ Sum
− 16 + (− 9)
Yes
16 + 9 = 25
-25
− 41 − (− 14)
45 − (− 29)
− 33 − (− 86)
− 35 − 35
7 − 19
− 16 − 9
positive.
negative.
lues
Rational Numbers Review Packet Name:________________________
●
●
●
Example: Divide: ­39 ÷ 13
Divide absolute values
.
Same sign? Different signs, so the quotient is negative.
Example: Multiply: ­7 ∙ (­4) Multiply absolute values.
Same sign? Same sign, so the product is positive.
Same Sign?
39 ÷ 13 = 3 No
­39 ÷ 13 = ­3 7 ∙ 4 = 28
Yes
­7 ∙ (­4) = 28 Product or Quotient
(16)( 9) = 144 No
-144
(− 48) ÷ (− 3)
7(− 12)
− 135 ÷ 9
(− 13)(− 13)
324
−18
− 16 • 9
Rational Numbers Review Packet Name:________________________
Date:____________
Class:________ Example: 8 to a decimal Convert 15
Divide the numerator by the denominator
8 ÷ 15 8 =0.5333... 15
Convert each fraction to a decimal by dividing the numerator by the denominator. Fraction 2
9
Decimal 88
94
29
50
6
32
●
●
●
Example: Convert 0.624 to a fraction Write the digits as the numerator
Write place value as the denominator
Simplify
624 1000 624 ÷ 4 = 154 ÷ 2 = 77 1000 ÷ 4 = 250 ÷ 2 = 125 77 0.624 = 125
Convert each decimal to a fraction. Decimal Fraction 0.34 0.442 1.55 Rational Numbers Review Packet Name:________________________
0.008 Date:____________
Class:________ ●
●
●
●
Example 1: Convert 0.3444… to a fraction. Set the decimal equal to x. ­­­­­­­­> x = 0.3444... Multiply x by 10
­­­­­­­­­­> 10x = 3.444… (x & 10x do not have same decimal pattern) Multiply x by 100
­­­­­­­­­­> 100x = 34.444… (10x & 100x have same decimal pattern) Subtract: 100x ­ 10x ­­­­­­­­­­­­­­­> 100x = 34.444.... 10x = 3.444… 90x = 31
Solve and simplify
­­­­­­­­­­­­­­­> x = 31/90 0.3444… = 31/90
Example 2: Convert 0.2323… to a fraction. Set the decimal equal to x. ­­­­­­­­> x = 0.2323... Multiply x by 100
­­­­­­­­­­> 100x = 23.2323… (x & 100x have same decimal pattern) Subtract: 100x ­ x
­­­­­­­­­­­­­­­> 100x = 23.2323.... x = 0.2323… 99x = 23
Solve and simplify
­­­­­­­­­­­­­­­> x = 23/99 0.2323… = 23/99
Convert each decimal to a fraction. 24.
0.444...
25.
0.0222...
26.
0.7171...
●
●
Example: Rational Numbers Review Packet Name:________________________
Date:____________
Class:________ √81 Find the square root of 81.
What number times itself = 81
9 • 9 = 81 √81 = 9 Find the Square Root
What number times itself equals the radicand
solution
27.
√49
7 • 7 = 49 √49 = 7 28.
√289
29.
√361
30.
√100
31.
√64
32.
√
100
121 √36 = 6 − √36 = − 6 ●
●
Example: Find the two square roots of 25.
Positive and Negative square root
± √25 5 • 5 = 25 & − 5 •− 5 = 25 5 & ­5 Find the two square roots Positive Negative ± √16 ± √36 ± √225 Perfect Squares:​ These are numbers whose square roots are real numbers. Example: 100 is a perfect square because √100 = 10 1.44 is a perfect square because √1.44 = 1.2 9 is a perfect square because √
9
25
= 35 The square root of a non­perfect square is an irrational number. This means it is a decimal with no repeating pattern and it never ends. (Just like ) Rational Numbers Review Packet Name:________________________
Date:____________
Class:________ ●
●
●
Example: Find the square root of 78. 1. Find the two perfect squares,
78 is between 64 and 81. so, √78 is between √64 and √81 78 is closer to 81 so, √78 is closer to √81 than √64 78 is really close to 81, since √81 = 9, √78 ≈ 8.8 . 2. Determine which one it is closest to
3. Educated Guess
Square Between which two Root perfect squares 36.
√50
49 & 64 37.
√180
196 & 225 38.
√18
39.
Closer to which Educated Calculator perfect square Guess Check 49 7.1 Was your estimate close? (Y/N) √50 = 7.07106 Yes √59
40.
√260
41.
√8