Pre-Algebra
A person has a debt of $1024 and is ordered to pay it back in four equal payments. Represent the amount of each payment by a quotient of integers, and find the quotient
-1024/4 = -256 each payment.
Write 0.00026849577 as a fraction
0.00026849577 = 11 digits thus 11 zeros 26,849,577/100,000,000,000
Write 0.0847 as a fraction or a mixed number.
0.0847 Move the decimal all the way to the right 847/1000
Estimate to the nearest hundred-million then add. 1. 760.5 million 2. 658.7 million 3. 623.3 million 4. 533.3 million 5. 474.5 million 6. 460.9 million
1. 800 + 700 + 600 + 500 +500 + 500 = $3600 millions
There are approximately 39.37 inches in 1 meter. How many meters to the nearest tenth of a meter, are there in 2000 inches?
1000/39.37 200,000/3937 Answer before rounding up: 5.08 meters Actually answer: 5.1m
Write each decimal as a fraction or a mixed number. 11. 0.16 12. -12.023
11. 0.16 16 = it moved two decimal places. 16/100 4/25 12. -12.023 -12; .023 = moved two decimal places -12 = 23/1000 -12 (23/1000)
Write 14.2% as a decimal and a fraction. Also 0.5%
14.2 x 0.01 = 0.142 14 . 2 / 100 14.2 divide by 0.2 / 100 divided by 0.2 = 71/ 500 0.01 x 0.5= 0.005 0.5 x 1/100 = 0.5/100 = 0 . 5 divided by 0.5 and 100 divided by 0.5 = 1/200
Write each decimal number in word form. 15. $321.42 17. $91.68
15. Three hundred twenty-one and 42/100 17. Ninety-one and 68/100
Simplify
16 divided by (-2) x 4 16/-2 x 4 -8 x 4= -32
Multiply. 17. 6.5 x 10 19. 8.3 x 0.1 21. (-7.093)(1000) 23. 0.7 x 100 25. (-9.83)(-0.01) 27. 25.23 x 0.001 31. (147.9)(100 35. (937.62)(-0.01) 37. 562.3 x 0.001
17. 6.5 x 10 65 19. 8.3 x 0.1 0.83 21. (-7.093)(1000) -7093 23. 0.7 x 100 70 25. (-9.83)(-0.01) 0.0983 27. 25.23 x 0.001 0.02523 31. (147.9)(100) 14,790 35. (937.62)(-0.01) (-9.3762) 37. 562.3 x 0.001 0.5623
Determine whether two whole numbers each square root is between without using a calculator or table. 17. square root (38) 19. square root (101)
17. square root (38) 6 x 6 = 36 and 7 x 7 = 49 36 - 49 6 and 7 19. square root (101) 10 x 10 = 100 and 11 x 11 = 121 10 and 11
Find the unknown measurements. Refer to the picture on phone.
18(7/8) - 10(3/8) 8 ( 7/8 - 3/8) 8(4/8) 8(1/2) divided by 2 17/2 x 1/2 17/4 4(1/4) 4 (1/4) inches
Find the unknown length. Use photos from phone. 19. 23. 25. 27.
19. 18/z = 40/30 18/z =4/3 18 x 3 = 4z 4z = 54 z=54/4 z = 27/2 z= 13.5 23. 18(1/3)/3(2/3) = y/2 (55/3) / (11/3) = y/2 55/3 x 3/11 = y/2 55/11 =y/2 5/1 = y/2 y=10 25. 60/z = 32/15 60 x 15/ 32z 900/32z z= 28.125 27. x/7 = 15/10(1/2) x/7 = 15/21/2 x/7 = 15/1 x 2/21 x/7 = 5/1 x 2/7 x/7 = 10/7 7x = 70 x=10
29. 2.958/-0.087
2.958/-0.087 2958/-87 A:-34
A student would like to estimate the height of the statue of Liberty in NYC harbor. The length of the Statue of Liberty's right arm is 42 feet. The student's right arm is 2ft long and her height is 5(1/3) feet. Use this information to estimate the height of the Statue of Liberty. How close is your estimate to the statue's actual height of 111 feet, 1 inch from heel to top of head?
2/ 16/3 = 42/ x 2x = 16/3 x 42/1 2x = 16 x 42/3 2x = 16 x 14 2x=224 x=112 feet
Round each decimal to the given place value. 22. 16.34925, nearest thousandth
22. 16.34925 Answer = 16.349
Simplify each expression 23. (3/4)^2 divided by (3/4 - 1/12) 27. ( 3/4 + 1/8)^2 - (1/2 + 1/8) 25. (2/5 - 3/10)^2 21. 2 x (1/4 + 1/5) + 2 19. (7/8 - 1/2) divided 3/11
23. (3/4)^2 divided by (3/4 - 1/12) 9/16 divided (3/4 - 1/12) 9/16 divided 3/3(3/4) - 1/12 9/16 divided 9/12 - 1/12 9/16 divided 8/12 9/16 x 12/8 9 x 3/ 4 x 8 27/32 27. (3/4 + 1/8)^2 - (1/2 + 1/8) (6/8 + 1/8)^2 - (4/8 + 1/8) (7/8)^2 - (5/8) 49/64 - 5/8 49/64 - 40/64 9/64 25. (2/5 - 3/10)^2 (4/10 - 3/10)^2 ( 1/10)^2 1/100 21. 2 x (1/4 + 1/5) + 2 2 x (5/20 + 4/20) + 2 2 x (9/20) + 2 9/10 + 2 = 9/10 + 20/10 29/10 19. (7/8 - 1/2) divided 3/11 (7/8 - 4/8) divided 3/11 (3/8) divided 3/11 3/8 x 11/3 11/8
Find 26/5 using the process of repeated subtraction
26 - 5= 21 - 5 = 16 -5 = 11 - 5 = 6 - 5 = 1 Answer: 5 with a reminder of 1
Solve. Pictures on phone. 31. 37.
31. x/40 = 25/2 2x = 40 x 25 2x = 1000 x = 500 feet 37. a^2 + b^2 = c^2 200^2 + b^2 = 430^2 40,000 + b^2 = 184,900 b^2 = 144,900 b = 381 rounded to the nearest whole foot.
Evaluate each expression if x=-1/3, y=2/5, and z= 5/6 33. x^2 - yz 35. ( 1 + x)(1 + z)
33. (-1/3)^2 - (2/5 x 5/6) 1/9 - 1/3 1/9 - 3/9 -2/9 35. (1 + x)(1 + z ) (1 + -1/3)(1 + 5/6) (3/3 - 1/3)(6/6 + 5/6) (2/3)(11/6) 22/18 11/9
Which number is minuend and which number is subtrahend
48 - 1 48 is minuend and 1 is subtrahend subtract 7 from 70 70 is minuend and 7 is subtrahend
Solve. 53. 1/3 / 3/8 = 2/5 / n
53. 1/3 / 3/8 = 2/5 / n 1/3 x 8/3 = 2/5 x 1/n 8/9 = 2/5n 8 x 5n = 9 x 2 40n = 18 18/40 = n 9/20
Multiply or divide as indicated. Round to the nearest thousandths, if necessary. 111. 54.98 divided by 2.3 97. 8935/175
53.98/2.3 539.8/23 Answer = 23.9043 Rounded answer = 23.904 97. 8935/175 Answer 51.0571 Rounded answer: 51.057
Refer to the photo on iPhone/
54. 10/x =24/2 20 = 24x x= 5/6 (5/6)^2 + 2^2 = c^2 25/36 + 4 = c^2 25/36 + 144/36 = c^2 169/36 = c^2 c = 13/6 y= 2(1/6) in and x = 5/6 in
Perform each indicated operation. if the result is an improper fraction, also write the improper fraction as a mixed number. 57. 3 + 1/2 59. 9 - 5/6
57. 3 + 1/2 6/2 + 1/2 7/2 Mixed number= 3(1/2) 59. 9 - 5/6 (9 x 6/ 1 x 6) - 5/6 54/6 - 5/6 49/6 Mixed number = 8(1/6)
Find the average of each pair of numbers 65. 1/4, 2/14
65. 1/4, 2/14 1/4 + 2/14 28(1/4 +2/14/2) ( 7 + 4)/ 56 11/56 11 x 1/56 11/56
Write using exponential notation.
7 x 7 x 7 x 7 = 7^4 5 x 5 x 5= 5^3 10 x 10= 10^2
Trump World Tower in NYC is 881 feet tall and contain 72 stories. The Empire State Building contains 102 stories. If the Empire State Building has the same number of feet per floor as the Trump World Tower, approximate its height rounded to the nearest floor.
881/72 =x/102 72x = 89,862 x= 1248 feet.
Find each ratio of the corresponding sides of the given similar triangles. use phone for photos.
9. 12/6, 14/7, 22/11 The ratio is 2/1 11. 9/6, 12/8, 10.5/7 3/2, 3/2, 3/2 The ratio is 3/2
Perform the indicated operations. 96. 23(7/8) - 24(7/10) 111. 2x/3 + x/4: Simplify
96. 23 - 24 ( 7/8 - 7/10) -1 (7/8 - 7/10) -1 (7/8 - 7/10) -1(35/40 - 28/40) 35/40 - 68/40 -33/40 111. 4(2x/3) + 3(x/4) 8x/12 + 3x/12 11x/12
For the first quarter of 2013, Wal-Mart, Inc. posted a loss of $33 million in membership and other income. If this trend was consistent for each month of the quarter, how much would you expect this loss to have been for each month?
A full quarter has 4 quarters and theirs 12 months in a year, so 12/4 = 3. Now divide 33 million by 3, so each month Walmart is expected to lose 11 million dollars.
What is a proportion? Give an example.
A proportion is a statement that two ratios or rates are equal. For example, 5/6 = 10/12
What is a similar triangle? Also how does it differ from a congruent triangle?
A similar triangle is when a triangle has the same shape, but not the same size. The difference between a congruent triangle and a similar triangle is that a congruent triangle has the same size, but similar triangles. Also similar triangles have corresponding angles and corresponding sides are in proportion, for example 1/2 = 2/4.
What is a unit rate or unit price? Give an example.
A unit rate or unit price is a rate with a denominator of 1. Example: 55 mph = 55 miles/1 hour Write as a unit rate: $31, 500 every 7 months 31,500 dollars/ 7 months 4, 500 dollars/1 month $4,500 dollars a month.
What is a variable term? Give an example.
A variable term is a term that contains a variable For example, 3x + 4y, 3x, 3, 4, 3 are the variable terms.
What is a vertices? Give an example.
A vertex is each angular point of a figure.
What is the formula for perimeter and area of a square?
Area for a square= s^2 Perimeter for a square= 4s
Find the grade point average. Round to the nearest hundredth. Grade: B, C, A, C Credit Hours: 3, 3, 4, 4
Formula for average: sum of all numbers/total numbers. 3 + 3 + 4 + 4 14/9+6+16+8 14/39 39/14 = 2.79
What is a Algebraic expression or expression for short? Give an example.
It is a combination of variables and numbers. For example, 3 + x , 12 + y, and 4 x w - 1
What is the addition property of 0?
It is basically a property that states any number added by zero is that number
What is evaluating the expression? Given an example.
It is when you replaced the variable of an expression with a number and then you solved it. For example, 5x + 3, x = 2 5(2) + 3 13
What is mode? Also give an example.
Mode is the number that repeats the most in a series of numbers. Note their can be more than one mode. Example: 11, 14, 14, 16, 31, 56, 65, 77, 77, 78, 79 The mode is: 14 and 77
What is the multiplication property of equality? Give an example.
allows one to multiply the same quantity to both sides of an equation without changing the solution.
Graph the following fractions on a number line. a. 1/4 b. 4/7 c. 7/3
refer to your phone for the answers. Problems 49, 51, 55
Write this decimal number in words. 13. 2.43
two and forty-three hundredths
A falcon, when diving, can travel five times as fast as a pheasant's top speed. If the total speed for these two birds is 222mph, find the fastest speed of both birds.
x + 5x = 222 6x = 222 x= 37 mph Pheasant = 37mph Falcon = 37 x 5 = 185mph
Coca-Cola was recently named the Most Valuable Global Brand. It has a recognize value worth $43 billion more than Disney's. If the total value of these global brans is $101 billion, find the value of each of the brands.
x + x + 43 = 101 2x + 43 = 101 2x = 58 x=29 Disney= $29 billion dollars Coca-Cola= $72 billion dollars
z/5.2 = 0.08/6, find z and round to the nearest hundredth.
z/5.2 = 0.08/6 6z = 5.2 x 0.08 6z = 0.416 z = 0.06933 - round up z= 0.07
What is the percent equation? Give an example.
Percent equation is a formula: Percent x base = amount. For example, 15% of 60 15% x 60 = 0.15 x 60 = 9
Find the height of the tree. Round the height to one decimal place. Refer to the iPhone for the image.
https://goo.gl/images/bfg7fK Hypotenuse = 32ft Leg A = 20ft 20^2 + b^2 = 32^2 400 + b^2 = 1024 b^2 =624 b = 25 feet Length of the tree = 25 feet
What is the formula for Pythagorean theorem? Also what is theorem used for?
a^2 + b^2 = c^2 It is used to find missing length/s.
What is the addition property of equality? Give an example.
allows one to add the same quantity to both sides of an equation without changing the solution. For example: x - 2 = -1 x + 2 - 2 = -1 + 2 1=1
What is decimal notation. Give an example.
is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. Example: 9.075 = 9 + 0/10 + 7/100 + 5/1000 9000/1000 + 0/100 + 70/1000 + 5/1000 = 9075/1000
71. 0.0726 /10 x 1000
71. 0.0726/10 x 1000 0.0726/10 .00726 x 1000 7.26
Multiply or Divide. Find an exact answer and an estimated answer. 15. 3(4/5) x 6(2/7) - Note the numbers are mixed numbers: Find the exact answer and an estimated answer 13. 2(1/5) x 3(1/2) - Not the numbers are mixed numbers. Find the exact answer and estimated answer. 19. 3(2/3) x 1(1/2)
15. 19/5 x 44/7 19/5 x 44/7 836/35 Now turn it into a mixed number: 23(31/35) Exact answer= 23(31/35) Estimated answer= 24 3(4/5): 4/5 is more than .5, so the three will round up. Next 6(2/7) will not round up because 2/7 is less than .5, so the 6 will not round up. 4 x 6 13. 2(1/5) x 3(1/2) 11/5 x 7/2 77/10 Now turn it into a mixed number: 7(7/10) Exact answer: 7(7/10) Estimated answer: 8 2(1/5): 1/5 is less than .5, so 2 will not be rounded up. 3(1/2): 1/2 is .5 so the 3 will round up. 2 x 4 = 8 19. 3(2/3) x 1(1/2) 11/3 x 3/2 11/1 x 1/2 11/2: Now turn this into a mixed number 5(1/2)
Solve. 21. What percent of 80 is 88 23. 17 is what percent of 50? 35. What percent of 184 is 64.4
21. X x 80 = 88 80x = 88 x = 1.1 1.1 x 100 Percent = 110% 23. 17 = X x 50 17 = 50x 17/50 = x 0.34 x 100 34% 31. 2.58 = X x 50 2.58 = 50x 2.58/50 = x x = 0.0516 x 100 5.16% 35. X x 184 = 64.4 184x = 64.4 x = 0.35 x 100 x = 35%
Write each decimal number in standard form. Negative seven hundred five and six hundred twenty-five thousandths. Forty-six ten-thousandths
23. -705, 625 25. 0.0046
59. 25/n = 3/7/30
25/n =(3/1)/7/30 25/n = 3/1 x 30/7 25/n = 90/7 25 x 7= 90 x n 175 = 90n 175/90 = n n = 35/18
Add. Find an exact sum and an estimated sum. 29. 10(3/14) + 3(4/7). Note the numbers are mixed numbers. Find the exact and estimated sum. 33. 12(3/14) + 10 + 25(5/12): Note some of this numbers are mixed numbers. 37. 3(5/8) + 2(1/6) + 7(3/4): Note this numbers are mixed numbers
29. 10(3/14) + 3(4/7) 10 + 3 ( 3/14 + 4/7 13 (3/14 + 8/14) 13(11/14) Exact: 13(11/14) Estimated: 14 10(3/14) is less than .5, so it'll not be rounding up. 3(4/7): 4/7 is more than .5, so 3 will be rounding up. 10 + 4 = 14 33. 12(3/14) + 10 + 25(5/12) 12 + 10 + 25 = 47 47( 3/14 + 5/12) 47 [ 6(3/14) + 7(5/12)] 47[18/84 + 35/84 47[ 53/84] 47(53/84) 37. 3(5/8) + 2(1/6) + 7(3/4): 3 + 2 + 7 = 12 12[ 5/8 + 1/6 + 3/4] 12 [ 3(5/8) + 4(1/6) + 6(3/4)] 12[15/24 + 4/24 + 18/24] 12[37/24] 12(37/24) 13(13/24)
In the United States recently, 35.8% of households had no landlines, just cell phones. Write each percent as a decimal and a fraction.
35.8 x 0.01 = 0.358 35.8/100 = ? 35.8 divided by 0.2 / 100 divided by 0.2 179/500
Write each decimal as a fraction or a mixed number. Write your answer in simplest form. 39. 15.802 41. 0.3005
39. 15.802 15(802/1000) 15(401/500) 41. 3005/10000 601/2000
Write each decimal in words. 4. 0.00345 5. 109.23 6. 200.000032
4. Three hundred forty- five hundred -thousandths 5. One hundred nine and twenty -three hundredths 6. Two hundred and thirty - two millionths
Solve each equation. 41. 0.7x + 13.8 = x - 2.16 37. -0.9x + 2.65 = -0.5x + 5.45 39. 4x + 7.6 = 2(3x - 3.2) 35. 1.2 + 0.3x = 0.9
41. 0.7x + 13.8 = x - 2.16 0.3x = 15.96 100(0.3x = 15.96) 30x = 1596 x = 53.2 37. -0.9x + 2.65 = -0.5x + 5.45 0. 9x - 0.5x = 2.65 - 5.45 0.4x = -2.80 100(0.4x = -2.80) 40x = -280 x= -7 39. 4x + 7.6 = 2(3x - 3.2) 4x + 7.6 = 6x - 6.4 2x = 14 x = 7 35. 1.2 + 0.3x = 0.9 10(1.2 + 0.3x = 0.9) 12 + 3x = 9 3x = -3 x = -1
Add or subtract as indicated. 41. 3x/10 + x/6
41. 3x/10 + x/6 3(3x/10) + 5(x/6) 9x/30 + 5x/30 14x/30 14/30 7x/15
Simplify the following. 43. 2 + 1/6 / 1 - 4/3 55. (x/3 + 2)/(5 + 1/3) 53. (3/4 divided 6/5) - (3/4 x 6/5) 49. ( -2/9 - 7/9)^4
43. (2 + 1/6)/ (1 - 4/3) (12/6 + 1/6)/ (3/3 - 4/3) (13/6)/(-1/3) (13/6)(-3/1) - 13/2 55. (x/3 + 2)/(5 + 1/3) (x/3 + 6/3)/(15/3 + 1/3) ( x + 6/3)/(16/3) ( x + 6/3)(3/16) x + 6/16 53. (3/4 divided 6/5) - (3/4 x 6/5) (3/4 x 5/6) - (18/20) (5/8) - (9/10) (25/40) - (36/40) -11/40 49. (-2/9 - 7/9)^4 ( -9/9)^4 1
Subtract. Find an exact difference and an estimated difference. 47. 63(1/6) - 47(5/12): Note this numbers are mixed numbers. 45. 6 - 2(4/9): Note 2(4/9) is a mixed number. 43. 9(1/5) - 8(6/25): Note this numbers are mixed numbers. 41. 10(13/14) - 3(4/7): Note this numbers are mixed numbers.
47. 63(1/6) - 47(5/12) 63 - 47 = 16 16 ( 1/6 - 5/12) 16( 2/12 - 5/12) 15 ( 14/12 - 5/12) 15(9/12) 15(3/4) 45. 6 - 2(4/9) 5(9/9) - 2(4/9) 3(5/9) 43. 9(1/5) - 8(6/25) 1 ( 1/5 - 6/25) 1 ( 5/25 - 6/25) (30/25 - 6/25) 24/25 41. 10(13/14) - 3(4/7) 7(13/14 - 4/7) 7( 13/14 - 4/7) 7(13/14 - 8/14) 7( 5/14) Exact Number: 7(5/14) Estimated number: 7 10(13/14): 13/14 is more than .5, so the 10 will round up. 3(4/7): 5/7 is more than .5, so the 3 will round up. So, 11 - 4 = 7
What must you do when multiplying or dividing a whole number/mixed number? Give an example.
48/1(3/5) 48/1 / 8/5 48/1 x 5/8 30
Solve. 49. -3m - 5m = 4/7 25. -3x= -6/11
49. -3m - 5m = 4/7 -8m = 4/7 m= 4/7 x -1/8 m= -1/14 25. -3x= -6/11 x = -6/11 x - 1/3 x = 2/11
Simplify each complex fraction. 5. (2x/27) / (4/9) 7. (3/4 + 2/5) / (1/2 + 3/5) 9. (3x/4) / (5 - 1/8)
5. LCD: 27 27(2x/27) / 27(4/9) 2x/12 = x/6 7. (3/4 + 2/5) / (1/2 + 3/5) 20(3/4 + 2/5) / 20 (1/2 + 3/5) 15 + 8 / 10 + 12 23/22 9. 8(3x/4) / 8(5 - 1/8) 6x/ 40 - 1 6x/39 2x/13
In 2013, 22 states had mandatory helmeted laws. Find the ratio of states with mandatory helmet laws to states without mandatory helmet laws.
50 - 22 = 28 doesn't require helmets 22/28 = 11/14
Divide. Round the quotient to the nearest thousandth if necessary. 50. -0.0063/0.03 47. 0.2631/3
50. -0.0063/0.03 -0.63/3 -0.21 47. 0.2631/3 0.0877
The gas/oil ratio for a certain chainsaw is 50 to 1. a. How much oil (in gallons) should be mixed with 5 gallons of gasoline? b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces. Round to the nearest whole ounce.
50/1 = 5/x 5=50x 5/50 = x 1/10 = x A. 0.1 gallons 128 x 0.10 B. 12.8 fluid ounces - Round up B. 13 fluid ounces
Perform each indicated operation. 53. 3(1/9) x 2: Note one of this numbers is a mixed number. 67. 6(2/11) + 3 + 4(10/33): Note two of this numbers are mixed numbers. 63. 6(4/7) - 5(11/14): Note this are mixed numbers. 59. 5(2/3) - 3(1/6)
53. 3(1/9 ) x 2 28/9 x 2/1 56/9 6(2/9) 67. 6(2/11) + 3 + 4(10/33) 6 + 3 + 4 ( 2/11 + 10/33) 13( 6/33 + 10/33) 13 (16/33) 63. 6(4/7) - 5(11/14) 6 - 5 1 ( 4/7 - 11/14) 1 ( 8/14 - 11/14) 22/14 - 11/14 11/14 59. 5(2/3) - 3(1/6) 5 - 3 2 (4/6 - 1/6) 2 (3/6) 2(1/2)
Write each fraction or mixed number as a percent 51. 7/10 55. 34/50
7 x 10 / 10 x 10 70/100 remember percent means out of 100 51. percent = 70% 55. 34/50 68/100 remember percent means out of 100 68%
Perform operations a indicated. Simplify your answers. Estimated where noted. 89. 1(5/8) x 3(1/5): Find the exact and estimate answer.
89. 1(5/8) x 3(1/5) 13/8 x 16/5 208/40 26/5 Exact= 5(1/5) Estimate= 6 1(5/8): 5/8 is more than .5, so the 1 will round up. 3(1/5): 1/5 is less than .5, so it does not round up. 2 x 3 = 6
Perform the indicated operation. 95. -5(1/8) - 19(3/4): Note the numbers are mixed numbers. 97. -31(2/15) + 17(3/20): Note the numbers are mixed numbers. 101. 11(7/8) - 13(5/6): Note the numbers are mixed numbers. 55. 1(2/3) divided by 2(1/5): Note this are mixed numbers. 21. 2(2/3) divided by 1/7: Note this are mixed numbers.
95. -5(1/8) - 19(3/4) - 5 - 19 -24 ( -1/8 - 3/4) -24 (-1/8 - 6/8) -24( -7/8) -24(7/8) 97. -31(2/15) + 17(3/20) -31 + 17 -14 ( -2/15 + 3/20) -14( -8/60 + 9/60) -13( -68/60 + 9/60) -13( - 59/60) -13(59/60) 101. 11(7/8) - 13(5/6) 11 - 13 -2( 7/8 - 5/6) -2(21/24 - 20/24) -1(21/24 - 44/24) -1( -23/24) -1(23/24) 55. 1(2/3) divided by 2(1/5) 5/3 x 5/11 25/33 21. 2(2/3) divided by 1/7 2(2/3) x 7/1 8/3 x 7/1 56/3 18(2/3)
What is a perfect square? Also give an example.
A perfect square is square root that is a whole number or a fraction. For examples 1/4 = 1/2 x 1/2, 36= 6 x 6, and 4/25= 2 x 5
What is a ratio? Also give an example. What is one special type of ratio? Also define that special type. Also give an example.
A ratio is the quotient of two quantities. For example: The ratio of 1 to 2 can be written as 1 to 2, or 1/2, or 1:2 A special type of a ratio is a rate. A rate is used to compare different kinds of quantities. For example: A marathon runner can run 3 miles in 33 minutes. So this is a rate because both miles and minutes are different quantities. 3 miles/33mintues = 1mile/11 minutes simplest form.
One bag of pesticide covers 4000 sq feet of garden. Find how many bags of pesticide should be purchased to cover a square garden that is 250 feet on each side.
Area = s^2 A= 250^2 A= 62,500 1/4000 = x/62,500 4000x = 62,500 40x = 625 x = 15.6 x = 16 bags
In 2011, sales of Blue-ray Discs were $2 billion, but DVD sales dropped to $6.8 billion. Find the total spent to buy Blue-ray Discs or DVDs in 2011. Write the total in billions of dollars and also in standard notation.
Blue = $2 billion DVD= 6.8 billion 6.8 + 2 = 8.8 billion Standard notation = 8,800,000,000
Formula for circumference of a circle.
C= (2pi)(r) or C= (pi)(r)
Find the grade point average. Round to the nearest hundredth. Grade: A, A, A, B, C Credit Hours: 3, 3, 4, 3, 1
Formula for average: sum of total/total numbers. 3 + 3 + 4 + 3 + 1/12 + 12 + 16 + 9 + 2 14/51 Grade point average: 3.64
Tomaso is going to fertilize his lawn, a rectangle that measures 77.3 feet by 115.9 feet. Approximate the area of the lawn by rounding each measurement to the nearest ten feet.
Formula: Area= Length x Width Area = 77.3 feet x 115.9 feet Approximate = 80 ft x 120 ft Approximate area = 9600 sq feet
What is a irrational number?
Is a number that if written in decimal notation it'll never end and will not follow a pattern. For example: pi= 3.141592653589793238, and will always keep going with no pattern.
What is a right triangle? Also how do you find the hypotenuse and the two legs of a right triangle?
Is a triangle in which one of the angles is a right angle, or measures 90 degrees. The hypotenuse is opposite to the right angle and the remaining two sides are the legs.
What is a complex fraction? Give an example.
It is a fraction whose numerator or denominator or both numerator and denominator contain fractions. For example:
What is median and how do you find it? Give an example.
Median is the number that's in the middle of a series of numbers. Also numbers must be set from smallest to largest, and if their happens to be a even amount of numbers you must add both numbers and divide by 2. For example: 55, 67, 75, 86, 91, 91 Median = 75 + 86/2 Median = 80.5
55. The playing field for football is a rectangle that is 300 feet long by 160 feet wide. Find the length of a straight-line run that started at one corner and went diagonally to end at the opposite corner. Round to the nearest foot, if necessary.
Notice that it is a rectangle shape and they want to know the length of a diagonally line running from the field, so draw a rectangle and a diagonally line. Notice both halves look like a triangle? Solve now using the Pythagorean theorem. Separate both triangles. 300^2 + 160^2 = c^2 90,000 + 25,600 c^2= 115,600 c= 340 feet long is the diagonally
What is fraction notation? Given an example.
Simply means a number is written in fraction form. Give an example:7 = 7/1 and .5 = 1/2
What is the radical used for?
The radical sign is used to denote positive square root of a nonnegative number.
Formula for mean. (average) Give an example.
Total sum/number of items Example: Find the mean = 4 + 5 +2 + 1 + 7 + 1 + 1 21/7 = 3 is the mean
Write 200.0032 in words
Two hundred and thirty-two ten-thousandths.
When are two triangles congruent? Also what are three ways to tell if an angle is congruent and explain this three methods.
Two triangles are congruent when they have the same shape and same size. Three ways to tell if an angle is congruent is: Angle-Side-Angle (ASA): Basically means if two triangles have two same angels and one same side they are congruent. Side-Side-Side (SSS): If two triangles have all three same sides then they are congruent. Side-Angle-Side (SAS): If two triangles have two similar sides and one same angle then both triangles are congruent.
When writing decimals in words write " ? " for the decimal point. Also given an example?
You use the word "and". For example, write 3.08 in words 3 and 8 hundredths
Find the length of the side not give. Approximate to the nearest thousandth. 41. Leg = 10, Leg = 14 43. leg = 35, leg = 28
a^2 + b^2 = c^2 100 + 196 = c^2 c^2 = 296 c= 17.205 Hypotenuse = 17.205 43. a^2 + b^2 = c^2 35^2 + 28^2 = c^2 1225 + 784 = c^2 2009 = c^2 Hypotenuse = 44.822
What is standard form? For example.
is a way of writing down very large or very small numbers easily. For example: 4 x 10^3 = 4000, 10^5 x 4 = 400,000, and 420.3 million = 420,300,000
What is standard form? Give an example.
standard form is writing numbers in numeric form. For example: Eighty-one thousand, nine hundred. 81,900
Find the unknown number.
x/4(1/2) = 2(1/10) / 8(2/5) x/9/2 = (21/10) / 42/5 (x/1) x (2/9) = (21/10) x 5/42 2x/9 = 105/420 (2x) x 420 = 105 x 9 840x = 945 x= 1.125 x = 1 125/1000 x= 1 (1/8)
Mel Wagstaff is a 6-foot tall park ranger who needs to know the height of a particular tree. He measures the shadow of the tree to be 69 ft long when his own shadow is 9ft long. Find the height of the tree.
x/6 = 69/9 - Note the fraction is set like this because we are told that the tree's shadow is 69 feet and his shadow is 9ft. Thus, 69/9 x/6 = 23/3 - Note all portions are set to the same row being the same units. For example, the man's height is 6 feet and his shadow is 9ft, so x/6 = 69/9 23 x 6 = 3x 3x=138 x=46 feet long is the tree.
The difference between a country's exports and imports is called the country's trade balance. In June 2013, the United States had $191 billion in exports and $225 billion in imports. What was the U.S. trade balance in June 2013?
191 - 225 = - 34 billion dollars. It is negative because The United States is importing more than they are exporting.
Refer to image on IPhone for both problems. 1. Writer a proper or improper fraction to represent the shaded part of each diagram. 2. If it is a mixed number then write a fraction to represent that as well.
23. 1/6 - Proper fraction 25. 5/8 - Proper fraction
Find the LCD of each list of fractions. 55. -1/36, 1/24 63. 4/3, 8/21, 3/56 61. 23/18, 1/21
24: 6 x 4 = 2 x 2 x 2 x 3 36: 6 x6 = 2 x 2 x 3 x 3 LCD: 2 x 2 x 2 x 3 x 3 = 8 x 9 = 72 63. 3: 3 x 1 21: 3 x 7 56: 2 x 2 x 2 x 7 LCD: 2 x 2 x 2 x 3 x 7 = 168 61. 18 = 3 x 3 x 2 21 = 3 x 7 LCD: 3 x 3 x 2 x 7= 126
Determine whether the given replacement values are solutions of the given equation. 77. Is -5/18 a solution to 3x = -5/6 79. Is 2/5 a solution to -1/2z = 1/10
3(-5/18) = -15/18 = -5 x 3/3 x 6 = -5/6 Yes, it's a solution -1/2(2/5) = -2/10 = -1 x 2/ 2 x 5 = -1/5 No, it's not a solution.
Divide. Write all quotients in simplest form. 31. 11y/20 divided by 3/11 35. 1/5x divided by 5/x^2
31. 11 x 11 x Y/ 3 x 20 = 121y/60 35. 1 x (X) x (X)/ 5 x 5 x (X)= (X)/25
45. Thirty-three out of the fifty total states in the Untied States contain federal Indian reservations. What's the fraction? 45a. How many states do not contain federal Indian reservations? 45b. What fraction of the states do not contain federal Indian reservations?
45. 33/50 45a. 50 -33 = 17 states do not have federal Indian reservations. 45b. 17/50
Write the following fractions in simplest form 49. 224a^3b^4c^2/16ab^4c^2 47. 189z/216z 37. 36x^3y^2/24xy 41. 40xy/64xyz
49. 224a^3b^4c^2/16ab^4c^2 224/16 = 16/16 = 14/1, = a^3 - a^1 = a^2, b^4 - b^4 = 0, c^2 - c^2 = 0 = 14a^2 47. 189/216 = 21/24 = 7/8 189/9 = 24, 216/9 = 21/24 = 7/8 37. 36x^3y^2/24xy 36/6 = 6, 24/6 =4, 6/4 = 3/2, x^3 - x^ 1 = x^2, y^2 - y^1 = y = 3x^2y/2 41. 40xy/64xyz 40/64, xy/xyz 5/8, 1/z 5/8z
Find how many yards are in 1 mile (A mile is 5280 feet; a yard is 3 feet.)
5280/3 = 1760 yards
Write the following numbers in prime factorization? 7. 162 15. 828 9. 110
7. 162 = 81 x 2 = 9 x 9 x 2 = 3 x 3 x 3 x 3 x 2= 2 x 3^4 15. 828 = 207 x 4 = 2 x 2 x 3 x 69= 2 x 2 x 3 x 3 x 23 = 2^2 x 3^2 x 23 9. 110 = 55 x 2= 2 x 5 x 11
Multiply. Write the product in simplest form. 7. 18X20 x 36/99 17. 11/20 x 1/7 x 5/22 15. - 17y/20 x 4/5y
7. 18 x 36 x X/99 x 20 = 18 x 36/ 99 x 20= 9 x 2 x 6 x 6/ 11 x 9 x 5 x 4= 2 x 6 x 6/ 11 x 5 x 4 = 6 x 6 / 11 x 5 x 2 = 3 x 2 x 6 / 11 x 5 x 2 = 18x/55 17. 11/20 x 1/7 x 5/22 = 11 x 1 x 5/ 20 x 7 x 22 = 1 x 5 x 11 = 7 x 20 x 22 = 1 x 5 x 11/ 4 x 5 x 7 x 2 x 11 = 1/56 15. -17y/20 x 4/5y = - 17 x Y x 4/ 5 x 20 x Y = - 17 x 2 x 2 x Y/ 5 x 2 x 2 x 5 x Y = - 17/25
Write each mixed number as an improper fraction. 73. 6 (5/8) 79 166 (2/3) 75. 11 (6/7)
73. 6(5/8) = 6 x 8= 48 this is derived from multiplying the whole number 6 by the denominator, 48 + 5 = 53 this is derived from adding 48 and the numerator. Thus, 53/8 79. 116(2/3) = 166 x 3 = 498 this is derived from multiplying the whole number 116 by the denominator, 498 + 2 = 500 this is derived from adding 498 and the numerator. Thus, 500/3 75. 11(6/7) = 11 x 7 = 77 this is derived from multiplying the whole number 11 by the denominator, 77 + 6 = 83 this is derived from adding 77 and the numerator. Thus, 83/7.
Solve: 8/0, 0/8; Explain the answers.
8/0 = Undefined; Because zero can't divide any number 0/8= 0
In the United States 7/50 of college freshmen major in business. A community college in Pennsylvania has a freshmen enrollment of approximately 800 students. How many of those freshmen might we project are majoring business?
800(7/50)= 80(7/5) = 560/5 = 112 freshmen students will be majoring in business
Write each improper fraction as a mixed number or whole number. 81. 17/5 87. 225/15 91. 737/112 83. 37/8
81. 17/5 = 3 x 5 = 15 this is derived from multiplying the denominator and finding the nearest possible multiple that's closet to the numerator. 15 + 2 = 17, this is found by adding the difference between the whole number we just got and the numerator, so = 3(2/5) 87. 225/15 = 15 it's a whole number no more steps are needed. 91. 737/112 = 112 x 6 = 672 this is derived from multiplying the denominator and finding the nearest possible multiple that's closet to the numerator. 672 + 65 = 737, this is found by adding the difference between the whole number we just got and the numerator, so 6(65/112).
How do you find if a board such as a seesaw is balance? Also give an example where finding the distance will balance a board.
A board will balance if the following is true. First weight/ second distance = second weight/first distance. For example, First weight = 40 pounds, First distance is 7 feet (note this is the distance from where the object is to the middle of the board), second weight = 60 pounds, and second distance is x. 40/x = 60/7 60x = 280 6x = 28 x= 28/6 x= 14/3 - note this is a improper fraction, so turn it to a mixed number. x= 4(2/3) ft
What is a constant term, or simply a constant? Give an example.
A constant term or a constant is an addend that is only a number. Example, x + 10, x + 3, both 3 and 10 are the constant terms or the constant.
What is a improper fraction? Give an example.
A improper fraction is a fraction whose numerator is greater than its denominator or equal to. Thus, improper fractions are always 1 or more. For example, 3/2, 5/4, 10/9.
What is a integer?
A integer is a whole number that can be both positive and negative, so fractions and decimal answers can not be an integer
What is like and unlike fractions? Give an example.
A like fraction is two fractions that have the same denominator. For example: 2/3 and 1/3, 2/5 and 3/5 A unlike fraction is two fractions that have different denominators. For example: 1/5 and 1/4 , 1/3 and 1/2
What is a mixed number? Give an example.
A mixed number is whole number and a fraction. Mixed numbers are greater than one. 7/3= 2(1/3)
Translate each phrase to an expression. Simplify if possible.
A number decreased by -18: x - (-18) Subtract: -8 from -12: -12 - (-8) = -4
What is a prime number? Given an example.
A prime factor is a natural number greater than 1 whose only factors are 1 and itself. For example: 2/1 = 2, 3 /1 = 3, 5/1 = 5, 7/1 = 7, and etc.
What is a set? Give an example. Also what do the three dots mean in the end?
A set is a series of numbers enclosed by braces. For example, { 0, 1, 2, 3...} The three dots mean that the list of numbers continues in the same manner indefinitely.
What the difference between a integer and a whole number?
A whole number can not be negative.
In 2008, there were 33,319 analog (nondigital) U.S. movie screens. In 2012, this number of screens dropped to 6387. A. Find the change in the number of U.S. analog movie screens from 2008 to 2012. B. Find the average change per year in the number of analog movie screens over this period.
A. 33,319 - 6387 = -26,932, it is negative because those numbers is a loss. B. 26,932 divided by the number of years that has passed, so 26,932/4, the average change is 6733 a year.
A number rounded to the nearest hundred is 8600 A. determine the smallest number possible number B. Determine the largest possible number You must explain.
A. 8550 - it is 8550 because 5 is the smallest number that can round the 5 in the hundred place to a place 6. B. 8649 - is the largest possible number because the 4 will not round the 6 up and the 9 is the highest single digit number
What is the associative property of multiplication and addition? Give an example.
It is a property that states when adding or multiplying you can change the grouping because it doesn't affect the end result. For example: 5 + (3) +2 +(1)= 11 and 5 + (1) + 2 + (3)= 1 5 x 1 x (2) x 3 = 30 and 3 x 5 x 1 x (2) = 30
A building contractor is bidding on a contract to install gutters on seven homes in a retirement community, all in the shape shown. To estimate the cost of materials, she needs to know the total perimeter of all seven homes. Find the total perimeter
Refer to the image on my notes: First in order to find the remaining lengths you must subtract vertically, so 60 - 40 = 20. Next horizontally 30 - 12 = 18, now solve. Since we are finding perimeter we must add up all the sides 60 + 40 +30 + 12 + 18 + 20= 180 feet, but this only one home so we times the answer by 7. 180 x 7= 1260 feet
Round the following problems and explain what did you do
Round 59 to the nearest hundred: 59 is closer to 100 than 0 so it's 100. Round 29 to the nearest hundred: 29 is closer to zero than 100, so it's 0 Round 21, 094 to the nearest thousand: Since the one is in the thousand place you must then take a look at the next number which is a 0. Which cannot round the 1. Thus, 21,000 is to the nearest thousand. Round 328,495 to the nearest hundred: 4 is the number in the hundredth place, so you then look at the next number and it's a 9, which will round up the 4 and will also turn both the 9 and the 5 into zeros. Thus, 328,500 Round 39,994 to the nearest ten: 9 is the number in the tenth place, so then you take a look at the next number, which is a 4 and thus, will not round up the 9. so it'll be 39,990
Is there a commutative property of subtraction? Why or why not?
There's no such thing as commutative property of subtraction because it'll change the answer. For example: 5 - 3 = 2 thus 3 - 5 = -2 Different answers
If A is a negative number, then -A is a positive number. State whether this statement is true or false.
To better imagine this assign a number to the variable, so A= -2 If A is a negative number = -2, then -A is a positive number -(-2) = 2, true.
As of 2013, the United States has had 44 different presidents. A total of seven U.S. presidents were born in the state of Ohio, second only to the state of Virginia in producing U.S. presidents. What fraction of U.S. presidents were born in Ohio?
Total = 44 presidents Ohio = 7 7/44
What is a proper fraction? Give an example.
a proper fraction is a fraction whose numerator is less than its denominator. For example, 1/2, 5/7, and 9/10
Florida has 28 fewer electoral votes for president than California. If the total number of electoral votes for these two states is 82, find the number for each state.
x + x - 28 = 82 2x - 28 = 82 2x = 110 x= 55 California = 55 electoral votes Florida= 55 - 28 = 27 electoral votes
Divide a number by -33
x/-33
Subtract and simplify 17. 1/y - 4/y 21. 20/21 - 10/21 - 17/21 33. 9/12 - 7/12 - 10/12
17. -3/y 21. -7/21 = -1/3 33. -8/12 = -2/3
A railroad inspector must inspect 19/20 of a mile of railroad track. If she has already inspected 5/20 of a mile, how much more does she need to inspect.
19/20 - 5/20 = 14/20 = 7/10mi is needed
Is the expression true or false?
2(xy) = 2x times 2y False: 2xy = 2x times 2y is false because 2x times 2y can't multiply because they are not like terms.
What is the common denominator? Give an example.
Common denominator is when two fractions share the same denominator and when adding or subtracting two or more fractions all fractions must have a common denominator. For example: 1/5 + 2/5 + 2/5 = 5/5 =1 and 3/5 - 2/5 = 1/5
What is the commutative property of addition ? Give an example.
Commutative property is the movement of numbers that are being added. Example: 4 + 5 commutative property: 5 + 4
What is a composite number? Given an example.
Composite number is a natural number greater than 1 that is not prime. For example, 4/2 = 2, 6/2 = 3, 8/2 = 4, 10/5 = 2, and etc. The composite numbers are 4, 6, 8, 10, and etc
The expression 16t^2 gives the distance in feet that an object falls after t seconds. Complete the table by evaluating 16t^2 for each given value of t.
T= 1, 2, 3 , 4 Expression: 16t^2 16(1)^2= 16 feet 16(2)^2= 16(4)= 64 feet 16(3)^2= !6(9)= 144 feet 16(4)^2= 16(16)=256 feet
What is the additive inverse? Given an example.
Additive inverse is the opposite of a number and it is when you're adding. For example, 3 + (-3) = 0
What is a open line segment and how does it differ from a close line segment both visually and meaning wise?
An open line segment excludes both end points or only includes one of the endpoints. Unlike the close line segment the open line segment will have a circle on top of both or just one endpoint. http://mathworld.wolfram.com/images/eps-gif/Interval_1000.gif
What is a factor? Give an example.
Are numbers that when multiplied gives you a product. For example, 3 x 5 = 15, so the factors are 3 and 15. Can also mean any number that divides a number evenly with no remainders. Example: 12/4 = 3, 4 is the factor.
What is quotient? Give an example
Basically means division. For example: Find the quotient of 20 and 4 = 5
The deepest spot in the Atlantic Ocean is the Puerto Rico Trench, which has an elevation of 8605 meters below sea level. The bottom of the Atlantic's Cayman Trench has an elevation 1070 meters above the level of the Puerto Rico Trench. Use a negative number to represent the depth of the Cayman Trench.
(-8605) + 1070 = -7535 meters is the depth of the Cayman Trench.
Simplify: (7 + 2^4)^5 - (3^5 - 2^4)^2
(7 + 2^4)^5 - (3^5 - 2^4)^2 ( 7 + 16)^5 - (243 - 16)^2 (23)^5 - (227)^2 6,436,343 - 51,529 = 6,384,814
Write each whole number in expand form:
1. 209 2.3470 3.66,049 Expand form: 200 + 9 3000 + 400 + 70 60,000 + 6,000 + 40 + 9
Represent each quantity by an integer
1. A worker in a silver mine in Nevada works 1235 feet underground. Answer: -1235; it is negative because it's underground. 3. The peak of Mount Elbert in Colorado is 14, 433 feet about sea level 13. For the first half of 2013, digital track sales declined 2 percent when compared to the first half of 2012.
Evaluate:
1. x^3 - y^2; x = 21 y = -19 ( 21)^3 - (-19)^2= 9261 - 361 = 8900 2. 10 - x^2, x= -3 10 - (-3)^2 10 - 9 = 1 3. -z^2, Z= -4 -(-4)^2 -16 4. x^2, x=-3 (-3)^2 9 5. x^2 - y, x= -2, y= 4 (-2)^2 - 4= 4 - 4 = 0
33. Of the 131 students at a small private school, 42 are freshmen. What fraction of the students are freshmen? 33a. How many students are not freshmen? 33b. What fraction of the students are not freshmen?
33. 42/131 33a. 131 - 42 = 89 students are not freshmen 33b. 89/131
Add or subtract as indicated. 41. 5/11 + y/3 63. 3x/8 + 2x/7 - 5/14 49. 2a/3 + 6a/13 45. x/2 + x/4 + 2x/16 61. -9/12 + 17/24 - 1/6
41. 5/11 + y/3 = 3 x 5 / 11 x 3 + 11 x y / 3 x 11 = 15/33 + 11y/33 = 15 + 11y/33 63. 3x/8 + 2x/7 - 5/14 = 3X x 7/ 8 x 7 + 2X x 8/ 7 x 8 - 5 x 4 / 14 x 4 = 21x/56 + 16x /56 - 20/56 = 37x - 20 /56 45. 8 x X/2 x 8 + 4 x X/4 x 4 + 2x/16 = 8x + 4x + 2x/16 = 14x/16 = 7x/8 61. -9 x 2/ 12 x 2 + 17/24 - 1 x 4/6 x 4 = -18/24 + 17/24 - 4/24 = -5/24
Simplify. 42/25 x 125/36 divided 7/6 113. The National Park Service is charged with maintaining 27,000 historic structures. Monuments and statues make up 63/200 of these historic structures. How many monuments and statues is the National Park Service charged with maintaining.
42/25 x 125/36 divided 7/6 42 x 125/25 x 36 = 6 x 7 x 25 x 5/ 6 x 6 x 25 = 5 x 7/6 =35/6 divided by 7/6 = 35 x 6 / 6 x 7 = 35/7 = 5 113. 27,000(63/200) = 270(63/2) = 270 x 63 = 17,010/2 = 8505 monuments and statues is National Park Service are charged with maintaining
Ari Trainor is in the requisitions department of Central Electric Lighting Company. Light poles along a highway are played 492 feet apart. The first light pole is at the beginning of a 1-mile strip. Find how many poles he should order for the 1-mile strip of highway. (A mile is 5280 feet)
5280/492 = 10.73, so it is 10 but since their is a light pole in the beginning 10 + 1 = 11 light poles
Find one number that when rounded to the nearest hundred is 5700. Explain
5724; since 7 is in the hundredth place you look to the number to the right and since the number is a 2 it can't round up the seven. Thus, turning everything after the 7 into zeros
Perform each indicated operation 61. 21X^2/10Y divided by 14X/25Y 55. -19/63y x 9y^2 69. (1/2 x 2/3) divided by 5/6 43. -5/28 x 35/25
61. 21 x (X) x (X) x 25 x Y/ 10Y x 14 x (X) = 21 x (X) x 25/10 x 14 = 5 x 5 x 3 x 7 x (X)/ 2 x 5 x 2 x 7= 5 x 3 x (X)/2 x 2 = 15x/4 55. -19 x 9 x Y x Y / 63 x Y = -19 x 9 x Y/ 9 x 7 = -19y/7 69. (2/6)/(5/6) = 2 x 6 / 5 x 6 = 2/5 43. -5 x 35/ 28 x 25 = -5 x 5 x 7/ 5 x 5 x 7 x 4 = -1/4
Write each fraction as an equivalent fraction with the given dominator. 75. 5/9 = ?/36a 73. 2y/3 = ?/12 71. 14x/17 = ?/68
9 x 4a = 36a 5 x 4a = 20a equivalent fraction = 20a/36a 3 x 4 = 12 2y x 4 = 8y equivalent fraction = 8y/12 71. 17 x 4 = 68 14X x 4 = 56X Equivalent fraction = 56x/68
Evaluate
9^2 = 9 x 9= 81 10^3= 10 x 10 x 10 = 1,000 5^3= 5 x 5 x 5= 125 5 x 6^2 = 5 x 6 x 6 = 180
What is an addend? Give an example.
A addend is number or variable that is being addend. Example: x + 3; both are addends.
What is a linear equation in one variable or first-degree equations in one variable? Give an example.
First of all the word linear and first degree is called that because the exponent on each x is one. For example: 5x - 2 = 7x, both x's have a exponent of one, and so no variable is less than one. It is an equation in one variable because it only contains one variable, x.
What is the formula for area of a rectangle ?
Formula: A= Length x Width
Mentally draw and shade a part of a diagram to represent each fraction. 27. 1/5 29. 6/7 31. 4/4
If visualized properly you should get: 27. any of the same five shapes and only 1 of them shaped 29. any of the same seven shapes and only six shaded in 31. any of the same four shapes and al 4 shaded.
What is a line segment?
Is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoint
What is equivalent fractions? Give an example.
It is a fraction that represents the same portion of a whole (use the attached photo for better understanding) or the same point on a number line . Example: 1/2, 2/4, and 4/8 are all equivalent fractions according to the image, and 2/4 and 1/2 are equivalent fractions, also 4/12 and 1/3 are equivalent.
What is the numerical coefficient? Give an example.
It is the number factor of a variable term. Example: 3x, x, and -6y; 3, 1, and 6 are all the numerical coefficient.
Will the difference ever be negative? Given an example.
No, the difference will always be a positive number. Example: Find the difference in temperature between the two months with the lowest temperatures. January is the lowest month with a temperature of - 8, and followed with December with a temperature of - 4. Therefore, there's a 4 degree difference.
Formula of the perimeter of a rectangle and area
P= 2(L + W) A= L X W
Formula of the perimeter of a polygon
P= A+ B + C
Formula of the perimeter of a square
P=4(s)
Formula of the perimeter of a triangle and area
Perimeter of a triangle formula: p= a + b + c Area of a triangle: a= 1/2(b)(h) ;;
What is prime factorization? Given an example.
Prime factorization is when a composite number is written as a product of prime numbers. For example, prime factorization of 12 = 2 x 2 x 3, prime factorization of 18 = 3 x 3 x 2, and prime factorization of 20 = 5 x 2 x 2.
What is the product? Also give an example
Product is the result you get when multiplying two factors. For Example, 3 x 5 = 15, so 15 is the product.
What is the number of distance from zero in a number line?
The absolute value
What is the absolute value and what is the symbol for it?Give an example.
The absolute value is the units from zero on the number line and the symbol for it is | |. For example: |-3| = 3, so it is 3 units away from zero
What is a term? Give an example.
The addend of an algebraic expression is called the terms of the expression. For example, x + 2, 3x + 2y + (-3), first one has two terms and the 2nd expression has three terms.
Write each phrase as an algebraic expression. Let x be the unknown number.
Three times the difference of a number and 11 3(x - 11)
What is the dividend? Give an example.
The dividend is the number being divided. For example 35/5 35 is the dividend
What is the multiplication property of 0? Give an example
The product of 0 and any number is 0 For example: 0 x 1203 = 0
What is the multiplication property of 1? Give an example
The product of 1 and any number is that same number. For example: 1 x 2314 = 2314
How is the retail price found? What is the formula they use? Give an example.
The retail price is found using the formula P= C + M P= the retail price, C = is the wholesale cost,(wholesale cost is the amount the manufactory is selling the manufactured itemed to a retailer) and M= The amount of the markup ( markup is the added cost to the wholesale to make profit.) The retail price of a computer system is $999 after a markup of $450. What is the wholesale cost of the computer system? P= C + M 999= c + 450 c= $549 is the wholesale cost.
How's a house selling price found? Also what is the formula? Give an example.
To find a house's selling price you use the formula P = A + C; P = The house selling price, A is the amount the seller received, and C= The commission the real estate agent received. A house sold for $230,000. The owner's real estate agent receive a commission of $13, 800. How much did the seller receive? $230,000 = A + 13, 800 A = $216,200 is the amount the seller made.
What is a polygon?
a plane figure with at least three straight sides.
