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33 Cards in this Set
- Front
- Back
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Integers
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Whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.
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The further a number is to the right on a number line, the ________the value.
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Greater
28>12 -4>-12 -12<12 |
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Irrational numbers
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Numbers that cannot be expressed as a fraction.
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Real numbers
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Includes all rational and irrational numbers. Includes any number that can be made into a fraction.
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Rational numbers
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Any number that can be expressed as a fraction. Includes decimals that terminate or repeat.
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Factors
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An integer that divides evenly into the number with no remainders.
5 is a factor of 50 because 50/5=10 |
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Prime Numbers
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A number that has only 1 and itself as a factor.
2,3,5,7,11,13,17,19 |
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Greatest Common Factor of two numbers
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The largest factor that they both share.
GCF of 24 and 18 Factors of 24= 1,2,3,4,6,8,12,24 Factors of 18= 1,2,3,6,9,18 6 is the greatest common factor. |
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Prime Factorization
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You need to make a factor tree. What are the factors of a number.
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Divisibility
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Another way to state factors of a number.
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Divisibility trick of 2
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Only even numbers are divisibly by 2.
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Divisibility trick of 3
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If the sum of the digits of a number is divisible by 3, the number is also divisible by 3.
4158=Add the digits together. 18/3=6. So that number is div. by 3 |
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Divisibility trick of 4
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If the last 2 digits of a number are divisible by 4, the whole number is divisible by 4.
23,924 is divisible by 4 since 24/4=6 |
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Divisibility trick of 5
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Any number that ends in 0 or 5 is divisible by 5
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Divisibility trick of 6
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Any number that is divisible by both 2 and 3 will by divisible by 6
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Divisibility trick of 8
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If the last 3 digits are divisible by 8, then the whole number will be. 984,840 is div. by 8 sincde 840 is divisibly by 8.
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Divisibility trick of 9
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If the sum of the digits of a number is divisible by 9, then the whole number will be.
4,158=4+1+5+8=18, 18/9=2 |
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Divisibility trick of 10
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Any number that ends in 0 is divisible by 10.
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Multiple
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Equal to that number times an interger. All even numbers are multiples of 2
2,4,6,8,10,12,14... |
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Least common multiple
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The smallest non-zero multiple that the numbers share. To find, list multiples of each number.
8 and 6 8=8,16,24, 6=6,12,18,24 If the 2 numbers do not share any factors, then their product is the lcm |
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Averages
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Add the numbers, then divide by the amount of digits.
3,4,8= 3+4+8/3=5 |
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Adding 2 negative #s
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Adding as usual but place the negative sign in front of the sum.
-23+-74= -97 |
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Adding a positive and a negative number
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Subtract the smaller number from the larger one and then assign the sign of the greater #.
-48+32= 48-32=16= -16 |
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Subtraction of a positive # such as 25-75
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Same as 25+-75= 75-25=50. 75 is greater, so it will by -50.
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Subtraction of a negative number
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Equivalent to adding a positive number.
32- -45=32+45=77 -15- -40=-15+40=25 |
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Absolute Value
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A number that is its distance from zero. Always expressed in positive terms.
l42l=42 l-13l= 13 |
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Powers or exponents
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Represents how many times a number is multiplied by itself.
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Multiplying exponents
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When the bases are the same, you can add the exponents.
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Dividing exponents
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When the bases are the same, you can subtract the exponents.
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Negative Exponents
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Indicates that the expression is a fraction with 1 as the numerator and the base raised to the power as a denominator.
2 to the -5th power= 1/2x2x2x2x2=1/32 |
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Square Roots
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A number times itself
Square root of 81=9 |
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Third Root
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A number times itself 3 times.
Third root of 64 is 4 since 4x4x4=64 |
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Fractional Exponents
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The denominator is the root and the numerator is any exponential power.
84 to the 1/4th power=Fourth power of 81=3 2 to the 4/2 power=Square root of 2 to the 4th power=Square root of 16=4 |
