Broward College MAT 0018 Final Exam Study Guide PDF

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The objective of this final exam study guide is to prepare yourself for the upcoming final exam for Developmental Mathematics II. Take your time when you read each question and what you need to do in order to solve various problems that you have learned during the duration of taking Developmental Ma...

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College/University: Broward College

MAT 0018 - Developmental Mathematics I MAT 0018 Final Exam Study Guide

Writer: ”Lew” Sterling Jr.

1. Write out the number 63, 203 in words. First off, one common idea is separate every part of the number then express them. 63, 203

= 60, 000 + 3, 000 + 200 + 00 + 3 = 60, 000 + 3, 000 + 200 + +3

Secondly, just express the numbers into words. 60, 000 3, 000 63, 000

sixty thousand three thousand sixty-three thousand

200 3 203

two hundred three two hundred three

63, 203

sixty-three thousand two hundred three 2. Write out the following number: three hundred twenty thousand forty-one

First off, it would be best to express all parts then, write the words as numbers then simplify. three hundred twenty thousand forty-one three hundred twenty thousand forty-one Sum

320, 000 41 320,041 3. Add the following: 8, 257 + 392 + 459

First off, it would be best to add everything and if any place value is more than 10, then add 1 into the next place value. 121 8257 392 + 459 9108 4. Subtract the following: 71, 034 − 19, 867

First off, it would be best that you can subtract 1 from the top number in its respectable column while crossing out the original number that you’re borrowing from and subtracting 1 from that number then write the new number above you’re crossed out. Secondly, simplify.

6 10 12 13 10 ✁7 1✁ . ✁0 ✁3 4✁ -1 9 . 8 6 7 5 1 . 4 7 3 5. Add the following: 4 2 + 5 9 One common way to add fractions like this one is to find a common denominator then simplifying. 4 5

+ 92

4·9 5·9

= =

36 45

+

2·5 9·5

10 + 45

=

36+10 45

=

46 45

45 + = 45

=1+ = 1

1 45 1 45

1 45

The reason there are 2 boxed answers in red instead of one is because there are ways to write the final answer, as either its mixed fraction answer or its mixed number answer. 6. Add the following: 6

1 3 +2 4 7

One common way to adding mixed numbers is to add the whole numbers together then add the fractions together then combine and simplify. 6 17 + 2 43

= (6 + 2) + ( 17 + 43 ) 1·4 = (8) + ( 7·4 +

3·7 ) 4·7

4 + 21 ) = 8 + ( 28 28

) = 8 + ( 4+21 28 5 ) = 8 + ( 28

=8+

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5 28

= 8

5 28

7. Subtract the following: 6 1 − 7 3

One common way to subtracting fractions like this one is to find a common denominator then simplifying. 6 7

−

1 3

=

6·3 7·3

=

18 21

=

−

1·7 3·7

− 217

18−7 21

=

11 21

8. Subtract the following: 9

1 1 −4 3 12

One common way to subtracting mixed numbers is to subtract the whole numbers first then add the subtracted fractions then combine and simplify. 1 − 41 9 12 3

1 = (9 − 4) + ( 12 − 31) 1·1 − = (5) + ( 12·1 1 − = (5) + ( 12

1·4 ) 3·4 4 12 )

1 = (5 − 1) + (1 + 12 − 1 = (4) + ( 12 12 + 12 −

4 ) 12

4 ) 12

4 = (4) + ( 12+1 12 − 12 ) 4 = (4) + ( 13 12 − 12 ) −4 = (4) + ( 1312 ) 9 = (4) + ( 12 )

= (4) + ( 43 )

9. Solve the following: 1 x + 4 = −21 5

Page 3

= 4

3 4

The first step is to make the variable be by itself on one side by adding/subtracting any non-variabled terms (aka ”constants”) to the other side the solving for x. 1 x 5 1 x 5

+ 4 = −21

+ 4 − 4 = −21 − 4 1 x 5

= −25

5 · 15 x = 5 (−25) x = −125 10. Convert the following decimal to a percent: 0.03

When it comes to converting decimals to percents, the best technique is to multiply the given decimal by 100 since ”percent” means ”per 100”. 0.03

= 0.03 · 100% = 0.3 · 10% = 3 · 1% = 3%

11. Convert the following decimal to a percent: 0.49

When it comes to converting decimals to percents, the best technique is to multiply the given decimal by 100 since ”percent” means ”per 100”. 0.49

= 0.49 · 100% = 4.9 · 10% = 49 · 1% = 49%

12. Convert the following decimal to a percent: 8.71

When it comes to converting decimals to percents, the best technique is to multiply the given decimal by 100 since ”percent” means ”per 100”. 8.71

= 8.71 · 100% = 87.1 · 10% = 871 · 1% = 871%

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13. Simplify the following: |23| − |−51|

When it comes to simplifying absolute values, just always remember that |−x| = |x| = x. |23| − |−51| = (23) − (51) = 23 − 51 = −28 14. Simplify the following: |−34| + |18|

When it comes to simplifying absolute values, just always remember that |−x| = |x| = x. |−34| + |18| = (34) + (18) = 34 + 18 = 52 15. Simplify the following: 56 ÷ 8 · 22 + 19

When it comes to the Order of Operations, remember PEMDAS, which be expressed as PE(MD)(AS) since M and D, multiplication and division, are done together as one step like A and D, addition and subtraction. 56 ÷ 8 · 22 + 19

= 56 ÷ 8 · (22 ) + 19 = 56 ÷ 8 · (4) + 19

= 56 ÷ 8 · 4 + 19 = (56 ÷ 8) · 4 + 19 = (7) · 4 + 19

= 7 · 4 + 19 = (7 · 4) + 19 = (28) + 19 = 28 + 19 = (28 + 19) = 47

16. What is 132 less than 61? First off, when you are being asked what is a number less than another number, you are actually subtracting the second number from the first number. For example, if you are asked ”what is 2 less less 1”, then you are being asked ”what is 1 − 2”. So, the same concept here. Secondly, when you are subtracting a larger number from a smaller number, then you have to switch the order of the numbers then remember to add the minus sign at the end.

Page 5

0 13 ✁1 3✁ ✁2 - 6 1 7 1 .. . - 7 1 17. What is −57 decreased by −21? When a number is being decreased by another number, then that means that you are subtracting the first number from the second number. In this case, since the second number is a negative number, remember to make it positive since −(−a) = a. −57 − (−21)

= −57 + 21 = −(57 − 21) = −(36) = −36

18. Using the following formula, find W is P = 42 and L = 13: P = 2L + 2W

When given a formula along with the substitutions, then all you have to do is plug and play then simplify and solve for the remaining variable. P = 2L + 2W P = 42

L = 13 (42) = 2(13) + 2W 42 = 26 + 2W 42 − 26 = 26 + 2W − 26 16 = 2W 16 2W 2 = 2 8=W W=8 19. Simplify the following: 4 11 8 33

When you are dividing a fraction by another fraction, you always have to remember than the top and bottom terms will be divided by the middle terms, which mean be expressed by the following: a c a d a·d ad a b . Afterwards, just simplify. c = b ÷ d = b · c = b·c = bc d

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4 11 8 33

4 11

= =

4 11

=

8 33

÷

33 8

·

4·33 11·8 1

✟ ✯3 33 ✁✕✟ = 4· 2 ✟ ✯✁8✕1 11· ✟ =

1·3 1·2

=

3 2

20. Simplify the following: −12 + 2 (−7) 14 − 27

When it comes to the Order of Operations, remember PEMDAS, which be expressed as PE(MD)(AS) since M and D, multiplication and division, are done together as one step like A and D, addition and subtraction. −12+2(−7) 14−27

=

−12−14 14−27

=

−12−14 14−27

=

−(12+14) −(27−14)

=

−(26) −(13)

= =

−26 −13 26 13

= 2

21. Simplify the following:   11 − 5 12 − 23

When it comes to the Order of Operations, remember PEMDAS, which be expressed as PE(MD)(AS) since M and D, multiplication and division, are done together as one step like A and D, addition and subtraction.

Page 7

  11 − 5 12 − 23

  = 11 − 5 12 − 23 = 11 − 5 (12 − (2 · 2 · 2)) = 11 − 5 (12 − (8)) = 11 − 5 (12 − 8) = 11 − 5 (4) = 11 − 20 = −(20 − 11) = −(9) = −9

22. Convert the following percent to a decimal: 85%

When it comes to converting a percent to a decimal, the best tip is to divide the percentage by 100. 85% = 85 ÷ 100 = 8.5 ÷ 10 = .85 ÷ 1 = 0.85 23. Convert the following percent to a decimal: 2%

When it comes to converting a percent to a decimal, the best tip is to divide the percentage by 100. 2% = 2 ÷ 100 = .2 ÷ 10 = .02 ÷ 1 = 0.02 24. Convert the following percent to a decimal: 9.17%

When it comes to converting a percent to a decimal, the best tip is to divide the percentage by 100. 9.17% = 9.17 ÷ 100 = .917 ÷ 10 = .0917 ÷ 1 = .0917 25. Write the following decimal as a fraction in lowest terms: 0.72

When it comes to converting a decimal to a fraction, the best tip is to place the decimal as the numerator with 100 being its denominator then simplifying.

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0.72

= =

72 100

72÷4 100÷4

=

18 25

26. Write the following decimal as a fraction in lowest terms: 0.05

When it comes to converting a decimal to a fraction, the best tip is to place the decimal as the numerator with 100 being its denominator then simplifying. 0.05

= =

5 100

5÷5 100÷5

=

1 20

27. Write the following decimal as a fraction in lowest terms: 0.39

When it comes to converting a decimal to a fraction, the best tip is to place the decimal as the numerator with 100 being its denominator then simplifying. 0.39

=

39 100

28. Write the following fraction as a decimal: 3 10

There are two ways to convert a fraction to a decimal; one can be making the given fraction into a fraction of 100 with another method being to turn the fraction into an equation then simplifying as a fraction. Method 1 3 10

= =

Method 2 x 3 10 = 100

3·10 10·10 30 100

= 0.3

3(100) = 10(x) 300 = 10x 300 10x 10 = 10 30 = x 30 100

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= 0.3

29. Write the following fraction as a decimal: 41 50

There are two ways to convert a fraction to a decimal; one can be making the given fraction into a fraction of 100 with another method being to turn the fraction into an equation then simplifying as a fraction. Method 1 41 50

=

41·2 50·2

=

82 100

Method 2 41 = x 50 100 41(100) = 50(x) 4100 = 50x 4100 50x 50 = 50 82 = x

= 0.82

82 100

= 0.82

30. Write the following fraction as a decimal: 4 5

There are two ways to convert a fraction to a decimal; one can be making the given fraction into a fraction of 100 with another method being to turn the fraction into an equation then simplifying as a fraction. Method 1 4 5

=

4·20 5·20

=

80 100

Method 2 4 x 5 = 100 = 0.8

4(100) = 5(x) 400 = 5x 400 = 5x 5 5 80 = x 80 100

= 0.8

31. Write the following fraction as a decimal: 29 100

There are two ways to convert a fraction to a decimal; one can be making the given fraction into a fraction of 100 with another method being to turn the fraction into an equation then simplifying as a fraction.

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Method 1 29 100

Method 2 x 29 100 = 100

= 0.29

29(100) = 100(x) 2900 = 100x 2900 100x 100 = 100 29 = x 29 100

= 0.29

32. Given that 1 ft2 = 144 in2 , convert 15 ft2 into in2 . One common method is to create proportions like Method 2 of the previous (and recent) ”writing a fraction as a decimal” problems. 1 ft2 144 in2 1 144

= =

15 ft2 x in2 15 x

1(x) = 15(144) x = 2160 1 ft2 144 in2

=

15 ft2

2160 in2

33. Given that 1 liter = 1.06 quarts, convert 23 liters into quarts. One common method is to create proportions like Method 2 of the ”writing a fraction as a decimal” problems. 1 liter 1.06 quarts

=

23 liters x quarts

1 1.06

=

23 x

1(x) = 1.06(23) x = 24.38 1 liter 1.06 quarts

=

23 liters

24.38 quarts

34. Given that 1 pound = 16 ounces, convert 48 ounces into pounds. One common method is to create proportions like Method 2 of the ”writing a fraction as a decimal” problems.

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1 pound 16 ounces

=

x pounds 48 ounces

1 16

=

x 48

1(48) = 16(x) 48 = 16x 48 16x 16 = 16 3=x x=3 1 pound 16 ounces

35. If

1 8

=

3 pounds 48 ounces

of the 232 students at a party like chocolate ice cream, how many students like chocolate ice cream?

When you are given a fraction of a certain number, then you are being asked to multiply the fraction by the number. For example, if you are asked for either ” 12 of 2” or ” 12 of the 2 [of something]”, then that means 21 · 2. 1 8

· 232

1 8

·

232 1

1 8÷8

·

232÷8 1

= =

=

1 1

=

·

29 1

1·29 1·1

=

29 1

= 29 students

36. Round 837, 594 to the nearest ten. When it comes to rounding to the nearest ten, look at the number in the tens place, then look at the number to the right of the tens place, which is the ones place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the tens place down by leaving it the number in the tens place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the tens place up by 1. 837, 594 837, 594 837, 590 837, 590 37. Round 837, 594 to the nearest thousand. When it comes to rounding to the nearest thousand, look at the number in the thousands place, then look at the number to the right of the thousands place, which is the hundreds place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the thousands place down by leaving it the number

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in the thousands place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the thousands place up by 1. 837, 594 837, 594 838, 000 838, 000 38. Round 837, 594 to the nearest hundred thousand. When it comes to rounding to the nearest hundred thousand, look at the number in the hundred thousands place, then look at the number to the right of the hundred thousands place, which is the ten thousands place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the hundred thousands place down by leaving it the number in the ten thousands place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the hundred thousands place up by 1. 837, 594 837, 594 800, 000 800, 000 39. Round 2, 571.8925 to the nearest tenth. When it comes to rounding to the nearest tenth, look at the number in the tenths place, then look at the number to the right of the tenths place, which is the hundredths place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the tenths place down by leaving it the number in the tenths place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the tenths place up by 1. 2, 571.8925 2, 571.8925 2, 571.9000 2, 571.9 40. Round 2, 571.8925 to the nearest thousandth. When it comes to rounding to the nearest thousandth, look at the number in the thousandths place, then look at the number to the right of the thousandths place, which is the ten thousandths place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the thousandths place down by leaving it the number in the thousandths place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the ten thousandths place up by 1. 2, 571.8925 2, 571.8925 2, 571.8930 2, 571.893 41. Round 2, 571.8925 to the nearest hundredth.

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When it comes to rounding to the nearest hundredth, look at the number in the hundredths place, then look at the number to the right of the hundredths place, which is the thousandths place. If the number to its right is 0, 1, 2, 3, or 4, then round the number in the hundredths place down by leaving it the number in the hundredths place the same. If the number to its right is 5, 6, 7, 8, or 9, then round the number in the hundredths place up by 1. 2, 571.8925 2, 571.8925 2, 571.8900 2, 571.89 42. Eighteen more than two times a number is the same as eight times the number. Find the number. The best tip is to first let x, or n depending on which variable you prefer, be the unknown number. Next, if you are given something like ”eighteen more than a number”, then that means a number plus 18, which can be written as x + 18. When given something like ”two times a number” or even ”twice a number”, then that means 2 times a number, which can be written as 2 · x = 2x. Whenever you see the word ”is”, then that is basically the equal sign. Eighteen more than two times a number is the same as eight times the number. same as} eight times a number . Eighteen more than two times{za number} is | the {z | {z } | {z } | {z } | = 2x + 8x 18 | {z } 2x+18

18 + 2x = 8x 18 + 2x − 18 = 8x − 18 2x = 8x − 18 2x − 8x = 8x − 18 − 8x −6x = −18 −6x −18 −6 = −6 x=3 43. Find the area of a rectangle with length of 9 inches and width of 7 inches. When it comes to finding the area of a rectangle, then you just have to remember its formula, which is the area being equivalent to its length times its width, which can be expressed as the following: A = lw

A

= lw = (l)(w) = (9 in)(7 in) = (9 · 7)(in · in) = (63)(in2 ) = 63 in2

44. Find the area of a triangle with base of 11 yards and height of 4 inches.

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When it comes to finding the area of a triangle, then you just have to remember its formula, which is the area being equivalent to ”its height times its base while its fully divided by 2” or even ”a half times the quantity of its height times its base”, which can be expressed as the following: A=

Method 1 A

=

1 1 hb = (hb) = hb 2 2 2 Method 2 A

hb 2

=

1 2

(hb) = 12 hb

=

(4 yd)(11 yd) 2

= 21 (4 yd)(11 yd)

=

(4·11)(yd·yd) 2

= 21 (4 · 11)(yd · yd)

(44)(yd2 ) 2

= 21 (44)(yd2 )

=

=

44yd2 2

= 22(yd2 )

= 22 yd2

= 22 yd2

45. Add the following: 3.914 + 8.73

First off, it would be best to add everything and if any place value is more than 10, then add 1 into the next place value. Even though this has decimals and not just whole numbers, this is the same concept as Problem #3. 11 3.914 + 8.730 12.644 46. Subtract the following: 31.415 − 42.85

First off, it would be best that you can subtract 1 from the top number in its respectable column while crossing out the original number that you’re borrowing from and subtracting 1 from that number then write the new number above you’re crossed out. Secondly, simplify. Even though this has decimals and not just whole numbers, this is the same concep...