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88 Cards in this Set
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- Back
- 3rd side (hint)
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multiple
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The product of a specified number and some integer. For example, 3, 12 and 90 are all multiples of 3. 4 is not a multiple of 3 because there is no integer that can be multiplied by 3 and yield 4
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1
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An integer is divisible by 2 if...
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...if its last digit is divisible by 2
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2
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An integer is divisible by 3 if...
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...if its digits sum to a multiple of 3 6,930 is a multiple of 3 because 6+9+3+0=18 which is a multiple of 3
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3
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An integer is divisible by 4 if...
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...if its last two digits are a multiple of 4 4,716/4 = 1179
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4
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An integer is divisible by 5 if...
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...if its last digit is 0 or 5
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5
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An integer is divisible by 6 if...
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...if it divisible by 2 and 3
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6
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An integer is divisible by 9 if...
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...if its digits sum to a multiple of 9 6,930...6+9+3+0=18, which is a multiple of 9
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7
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factors (aka divisors)
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The factors of an integer are the positive integers by which it is evenly divisible. 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36
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8
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5% as a decimal and fraction
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0.05 and 1/20
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9
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12.5% as a decimal and fraction
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0.125 and 1/8
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10
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20% as a decimal and fraction
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0.2 and 1/5
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11
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33 1/3% as a decimal and fraction
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.3333 and 1/3
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12
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10% as a decimal and fraction
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.1 and 1/10
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13
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16 2/3 % as a decimal and fraction
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0.16666 and 1/6
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14
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percent formula
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PART/WHOLE x 100 = PERCENT
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15
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percent increase (or decrease)
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amount of increase/original whole X 100
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16
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to multiple powers with the same base...
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add the exponents and keep the base 7^3 x 7^5 = 7^8
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17
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to divide powers with the same base...
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subtract the exponents and keep the base the same 4^5/4^2 = 4^3
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18
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to multiple powers (or raise a power to a power)
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multiply the exponents 7^2(^3) = 7^6
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19
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a negative number raised to an even power...
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...yields a positive result (-1)^2 = 1
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20
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a negative number raised to an odd power...
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...yields a negative result (-1)^57 = -1
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21
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raising a fraction between zero and 1 to a power...
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...yields a smaller result (1/2)^2 = 1/4
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22
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what happens when an exponent is negative?
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Take the reciprocal of the base and change the sign of the exponent (2)^-2 = 1^2/2^2 = 1/4
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23
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Express 9^1/2 as a radical
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= the square root of 9 = 3
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24
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Express 8^1/3 as a radical
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= the cube root of 8 = 2
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25
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to simplify a radical...
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factor out the perfect squares and move them to the front of the radical sign. For example, the square root of 50 = 5 square root 2
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26
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when can radicals be added and subtracted?
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only when the number under the radical is the same! 6radical7 + 2radical7 = 8radical7
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27
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to multiply radicals...
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...multiply the numbers under the signs and then put a single radical sign over them the new number
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28
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to divide radicals...
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...divide the two numbers in question and then put them under a single radical
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29
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if multiplying or dividing an inequality by a negative number...
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REVERSE the inequality sign -3x < 6 = x > 2
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30
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supplementary angles
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two angles are supplementary if their measures sum to 180
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31
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complementary angles
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two angles are complementary if their measures sum to 90
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32
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adjacent angles
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angles that are adjacent (next to each other) are supplementary because they lie along a straight line
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33
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vertical angles
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two angles that are not adjacent to each other are opposite, or vertical, and are equal in measure
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34
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perimeter of a triangle
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the sum of the lengths of all three sides
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35
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area of a triangle
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area of a triangle = 1/2(base)(height)
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36
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isosceles triangles
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an isosceles triangle has two equal sides and the angles opposite these sides are equal as well
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37
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equilateral triangle
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all three sides of an equilateral triangle are equal and the interior angles equal 60
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38
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right triangles
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triangles with one interior angle of 90. The hypotenuse lies opposite the right angle. The other two sides are legs. leg^2 + leg^2 = hypotenuse^2
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39
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pythagorean triplets (2)
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3:4:5 (leg:3 leg:4 hypotenuse:5) and 5:12:13
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40
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isosceles right triangles
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angles = 45, 45, and 90 the ratio of sides is always 1:1:root2
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41
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30-60-90 right triangles
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the ratio of sides is always 1:root3:2 paired as follows...the side opposite the 30 degree angle is 1, etc.
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42
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define: quadrilateral
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a four sided polygon where the four interior angles add up to 36, regardless of the quadrilateral's shape
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43
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define: parallelogram
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a parallelogram has two pairs of equal sides. Opposite angles are equal. Consecutive angles add up to 180
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44
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define: rectangle
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a quadrilateral with four right angles. Opposite sides are equal.
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45
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perimeter of a rectangle
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perimeter = 2(length + width)
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46
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area of a rectangle
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area = length x width
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47
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area of a square
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area = (side)(side)
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48
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area of a parallelogram
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area = base x height, but the height is NOT the length of the side. You must draw a line from the one base to the other to form a right angle - that line = the height.
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49
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volume of a rectangular solid
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volume rectangle = length x width x height
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50
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volume of a cube
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volume of a cube = (edge)^3
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51
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define: diameter of a circle
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diameter: a line segment that connects two points on the circumference of a circle and passes through the center
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52
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define: radius of a circle
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radius: 1/2 of a circle's diameter, it's a line segment that connects the center with a point on the circle
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53
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define: central angle of a circle
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central angle: an angle formed by two radii
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54
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define: circumference
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circumference: the distance around a circle = (2)(pi)(r)
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55
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define: arc length
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arcs are the portion of a circle cut off by a particular central angle. The degree measure of an arc is equal to the central angle that cuts it off arc length = n/360 x (2)(pi)(r)
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56
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area of a circle
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area of a circle = (pi)(r^2)
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57
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area of a sector
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area of a sector: a slice of pie, n/360(pi)(r^2)
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58
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define: cylinder and give the formula for volume
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cylinder: a solid whose horizontal cross section is a circle. The volume of a cylinder = (pi)(r^2)(h)
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59
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distance formula, used to define the distance between two points:
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distance formula = square root of (x1-x2)^2+(y1-y2)^2
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60
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define: slope
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change in y/change in x
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61
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what is the equation for a straight line?
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y = mx + b where, m = slope and b = y-intercept
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62
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which is bigger: 8/3 or the square root of 7?
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to figure this out, square both sides. They compare 64/9 to 7 (or 63/9)...64/9 (or 8/3) is a little bigger
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63
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fractions get smaller as...
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...their denominator gets bigger
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64
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when a positive fraction is less than 1 squared the result is...
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...less than the original fraction
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65
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the smaller the negative number...
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...the larger its square
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66
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which are even:
a. odd +/- odd b. even +/- even c. odd +/- even d. odd x odd e. even x even f. even x odd |
a, b, e, and f are even c and d are odd
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67
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how do you find the least common multiple?
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to find the least common multiple, check out the multiples of the larger number until you find one that's also a multiple of the smaller. LCM of 12 and 15 is 60
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68
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how do you find the greatest common factor
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the find the greatest common factor, break down both numbers into their prime factorization and take all the prime factors they have in common. the GCM of 36 and 48 is 12
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69
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how do you find the prime factorization of an integer?
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to find the prime factorization of an integer, just keep breaking it up into factors until all factors are prime. 72 - 3 x 3 x 2 x 2 x 2
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70
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cross multiply: x/y = a/b
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bx = ya
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71
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how do you add or subtract fractions?
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to add or subtract fractions, first find a common denominator, then add or subtract the numerators
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72
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how do you multiply fractions?
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to multiply fractions, multiply the numerators and multiply the denominators
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73
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how do you divide fractions?
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to divide fractions, invert the second one and multiply
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74
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how do you compare fractions?
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one way to compare fractions is to re-express them with a common denominator. Another way to compare fractions is to convert them both to decimals
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75
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how do you compare decimal fractions?
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the simplest way to compare decimal fractions is to add zeros after the last digit to the right of the decimal point in each decimal fraction until all the decimal fractions you're comparing have the same number of digits
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76
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how do you convert decimals into fractions?
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to convert a decimal to a fraction, set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point. Then simplify the fraction.
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77
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how do you express a % as a fraction in lowest terms?
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a percent is a fraction with an implied denominator of 100. set % over 100 and simplify
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78
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express 1/10, 1/5, 1/4, 1/3, 2/3, and 1/8 as percentages
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1/10 = .10 = 10% 1/5 = .2 = 20% 1/4 = .25 = 25% 1/3 = .333 = 33 1/3% 2/3 = .666 = 66 2/3% 1/8 = .125 = 12 1/2%
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79
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how do you find an average?
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to find the average of a set of numbers, add them up and divide by the number of numbers
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80
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how do you use the average to find the sum? example: the average of 10 numbers is 50. What is the sum of the 10 numbers?
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sum = average x number of terms if the average of 10 numbers is 50, then they add up to 10 x 50, or 500
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81
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how do you use the average to find the missing number? example: the average of 4 numbers is 7. If 3 of the numbers are 3, 5, and 8, what is the fourth number?
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to find a missing number when you're given the average, use the sum. if the average of 4 numbers is 7, then the sum of those 4 numbers is 4 x 7 or 28. Three of the numbers (3, 5, & 8) add up to 16 of that 28, which leaves 12 for the fourth number
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82
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how do you determine the average of consecutive numbers? example: what is the average of all the integers from 13 through 77 inclusive
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to find the average of evenly spaced numbers, just average the smallest and largest. the average of all the intefers from 13 through 77 is 13 + 77 / 2 = 90/2 = 45
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83
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how do you find the median of a group of numbers?
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the median is the middle value in a group of numbers. If there's an even number of values, the median is halfway between the two middle values. median of 12, 15, 23, 40, and 40 is 23 b/c its the middle value. median of 12, 15, 23, and 40 is 19 b/c its halfway b/w the two middle values of 15 and 23
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84
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how do you determine the mode of a group of numbers?
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the mode is the number that appears the most often. If two numbers appear equally often, they are both the modes. the mode of 12, 15, 23, 40, and 40 is 40 b/c it appears more often.
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85
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how do you use a ratio to find a number? example: in a group of 18 people, the ratio of men to women is 1:2. How many women are there?
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if the parts add up to the whole, a part-to-part ratio can be turned into 2 part-to-whole ratios by putting each number in the original ratio over the sum of the numbers. if the ratio of men to women is 1 to 2, then the men-to-people ratio is 1/ 1+ 2 = 1/3. And the women-to-peeps ratio is 2/1+2 = 2/3. 2/3 of the 18 are women, or 12.
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86
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what is the distance, rate, time equation in terms of distance?
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distance = rate x time.
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87
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what is the average rate equation?
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Average A per B = total A / total B Average speed = total distance/total time
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88
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