Name ______
Color ______
Real Numbers/Square Roots/Exponents Review
Real Numbers, Square Roots, Exponents Review
· Irrational: Numbers that are non-terminating and non-repeating.
· Rational: Numbers that DO terminate OR repeat.
· Integers: Negative and positive whole numbers including zero.
· Whole: Positive numbers and zero that do not have fractions or decimals.
· Natural Numbers: Numbers used to count.
o Also called ______
Real Numbers Diagram
1. Which number on the list is rational?
Why? ______
2. Which number on the list is irrational?
Why? ______
3. Which number is not natural?
0 10 10,000 1,000,000
4. Which number is an integer?
2.5 -.5 -32 Why? ______
5. Which number is not a whole number?
0 2 -10 15 Why? ______
6. Rational ______Irrational ______
Square Roots
List the perfect square roots above each number!
State the square root of each “perfect square.”
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
State the two whole numbers that the given square root falls between.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
Exponents
· Rule 1: When multiplying exponents with the same base ______the exponents.
· Rule 2: When dividing exponents with the same base, ______the exponents.
· Rule 3: When exponents have higher powers, ______the exponents.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
Adding, Subtracting, Multiplying & Dividing Integers
NO CALCULATORS!!!
· Adding Rule:
o Same signs: Keep the sign and add like normal
o Different Signs: Find the difference and take the sign of the “bigger” number
· Subtracting Rule:
o Keep-Change-Change: Change the subtraction sign to addition and change the sign of the next number
o Then follow the rules of addition
· Multiplying/Dividing:
o Same Signs: answer is positive – multiply/divide like normal
o Different Signs: answer is negative – multiply/divide like normal
1) 6 + 9 2) –1 –(–5) 3) 25 ÷ (–5)
4) –3 x 2 5) –9 – (3) 6) 4 + (–7)
7) 32 ÷ (–2) 8) –9 + 9 9) 5 – 1
10) 6 – 6 11) –4 x (–4) 12) 15 + 12
13) (–2)(5)(9) 14) (–3)(4)(–2) 15) (–6)(–1)(–8)
16) 0 – (–8) 17) 20 + (–12) 19) –30/–5
Word Problems with Integers
Write the expression and solve.
1) In Buffalo, New York, the temperature was –14°F in the morning. If the temperature dropped 7°F, what is the temperature now?
2) A submarine was situated 800 feet below sea level. If it rises 250 feet, what is its new position?
3) Maggie owes the candy store $35. Each of 5 friends will help her pay off her debt. How much will each friend pay?
4) Lilly bought 4 pairs of blue jeans at $32 each. How much money did she pay the clerk?
5) In the Sahara Desert one day it was 136°F. In the Gobi Desert a temperature of -50°F was recorded. What is the difference between these two temperatures?
6) A pelican 5 ft above the ocean’s surface dove 13 ft. to catch a fish. Find the depth in the ocean.
7) Bernice recorded the weeks’ low temperatures as –5°, –7°, 10°, 5°, 0°, –9° and –8°. What is the average low temperature for the week?
Order of Operations – PEMDAS
Evaluate each of the following show EVERY step!!!
1. 2.
3. 4.
5. 6.
7. 8.
1