Ron Paul Curriculum 7th Grade Mathematics Solution Set #2 Note: I revised the problem sets after I had made the videos. For Problem Sets 1-40, there are gaps in the numbering of the problems (see below) but the problems I solve during the review will have the same number as they do in the problem sets. Write the following numbers using digits: 1. Twenty thousand, nine hundred fifteen

20,915

2. Four hundred seventy-six trillion, seventeen billion, five hundred twelve million, four hundred fifty-two thousand, seven hundred eighty-two 476,017,512,452,782 4. Twenty-nine million, eight hundred thirty-five thousand, seven hundred twentyfive. 29,835,725 Answer the following questions: 5. Which digit is in the hundreds' place in 4,222? 2 9. Which digit is in the ones' place in 560,373,290?

0

10. Which value does the digit '4' have in 150,249,786? 40,000 Write the following Arabic numerals as Roman numerals: 11. 56

LVI

12. 783

DCCLXXXIII

13. 1972

MCMLXXII

Write the following Roman numerals as Arabic numerals: 16. LXXII

72

17. DCLXXXVIII 20. MCMXLV

688 1945

Ron Paul Curriculum 7th Grade Mathematics Solution Set #3 Solve the following problems: 1. 5 × (−6) = ‒30 2. −12 + (−3) = ‒15 3. 15 − (−4) = 19 4. 24 ÷ (−3) = ‒8 5. −7 × (−7) = 49 6. −25 − (−20) = ‒5 7. |−5| × 5 = 25 8. |−5| × (−5) = ‒25 9. |−5| − |−3| = 2 10. |−5| + |−3| = 8 11. |−10| ÷ 2 = 5 18. |−4| + (−6) = ‒2 20. ‒|‒5| × 4 = ‒20

Ron Paul Curriculum 7th Grade Mathematics Solution Set #4 Rewrite the following numbers as fractions to show they are rational: 1. 6

6/1

2. 0

0/1

3. 0.572

572/1000

4. −17.1

‒171/10

5. 4

1 2

9/2

6. What is a rational number? Any number that can be expressed as a ratio (or fraction) of two integers. 7. What is the difference between a rate and a ratio? A rate has units. A ratio is unitless. 8. What is the difference between a measure and a count? A measure is usually not an integer and probably has units. A count is a unitless positive integer. 9. What is the difference between an integer, a natural number, and a rational number? An integer is any whole number, including negatives and zero. A natural number is a positive integer. A rational number is any ratio of two integers. 10. Is 1/3 a rational number? What is the decimal form of 1/3? What does this mean about whether decimals that do not terminate (end) can be rational numbers? Yes, it is a ratio, so it is a rational number. The decimal form is 0.3333333... It is rational but it does not terminate, so not all rational numbers terminate. We will study this in much more detail in later classes.

Ron Paul Curriculum 7th Grade Mathematics Solution Set #5 Write the following numbers using digits: 1. Fifty-two thousand, four hundred five. 52,405 2. Seventeen million, seven hundred ninety-two. 17,000,792 3. Four hundred twenty-one thousand, sixty-three. 421,063 4. One hundred one trillion, ten billion, one hundred million, one hundred eleven thousand, eleven. 101,010,100,111,011 5. Twenty six billion, forty million, fifty-four thousand, eighty. 26,040,054,080 Answer the following questions: 6. What value does the digit ‘6’ have in 165,928? 60,000 7. Which digit is in the millions place in 541,236,699,203? 6 8. Which digit is in the hundreds place in 694,305? 9. What value does the digit ‘3’ have in 232,496,555?

3 30,000,000

10. Which digit is in the hundred thousands place in 123,456,789? Write the following Arabic numerals as Roman Numerals: 11. 74

LXXIV

12. 98

XCVIII

13. 642

DCXLII

14. 1563

MDLXIII

15. 1241

MCCXLI

Write the following Roman Numerals as Arabic numerals: 16. XVII

17

4

17. CLXVI

166

18. MDCCCLXXVIII

1878

19. LXXXVIII

88

20. CCCXXXIII

333

Solve the following problems: 21. −13 + 10 = ‒3 22. −18 ÷ 6 = ‒3 23. −18 ÷ (−6) = 3 24. −8 × (−9) = 72 25. −12 + (−4) = ‒16 26. |5| × 5 = 25 27. |−5| × (−5) = ‒25 28. ‒|‒3| + 2 = ‒1 Rewrite the following numbers to show they are rational: 29. 0

0/1

30. 23.6

236/10

31. .002

2/1000

32. 1.45

145/100

33. 1

1 2

3/2

Ron Paul Curriculum 7th Grade Mathematics Solution Set #6 Rewrite the following numbers in scientific notation: 1. Twenty thousand

2.0×104

2. 0.003

3.0×10-3

3. 150.02

1.5002×102

9. Fifty billion

5.0×1010

1 10,000

1.0×10-4

10.

Write the following numbers in decimal notation: 11. 1.45×105

145,000

12. 7.67×10-5

0.0000767

13. 5.5×10-4

0.00055

Use your scientific calculator to solve the following problems: 14. 5 × 1.45×105 = 725,000 15. 2.0×104 + 2.0×104 = 40,000 16. 6×107 × 2×10-3 = 120,000 17. 5 ÷ 1.0×10-6 = 5,000,000 18. 5 × 1.0×106 = 5,000,000

Ron Paul Curriculum 7th Grade Mathematics Solution Set #10 Rewrite the following numbers in scientific notation: 1. Fifty

5.0×101 5.0×102

2. Five hundred

3. Five hundred million

5.0×108

4. 0.000005

5.0×10-6

5. 239.241

2.39241×102

Write the following numbers in decimal notation: 6. 2.56×106 = 2,560,000 7. 2.56×10-6 = 0.00000256 8. 9.8432×102 = 984.32 9. 3.13×10-4 = 0.000313 10. 5.0×108 = 500,000,000 Use your calculator to solve the following problems: 11. 16 ÷ 1.9×10-10 = 84,210,526,315.8... 12. 4×107 × 2.2×10-7 = 8.8 13. 12 × 7.1×103 = 85,200 14. 6.78×104 ÷ 3.45×105 = 0.19652173913... In Ray’s New Higher Arithmetic, solve: 15-19. 6-8 and 11 on pp. 24-25 20-22. 11-13 on p. 29. 23-27. Solve “Examples for Practice”, problems 4-8 on p. 35.

28-31. Solve “Practical Problems”, problems 5-8 on pp. 35-36. Solve the following: 32. 74300 × 8640 = 641,952,000 33. 15712 × 98 = 1,539,776

Ron Paul Curriculum 7th Grade Mathematics Solution Set #11 In Ray’s New Higher Arithmetic, read pp. 43-44, and Cases II and III on pp. 49 & 50. Go to www.quizlet.com and find the flash card set “RPC6-021 - Division Table”. Make sure that you know all of the division flash cards, and study with them until you know them by heart. (Note: the division flash cards are the opposite of the multiplication flash cards). Solve the following division problems: 1. 567 ÷ 4 = 141 r. 3 2. 67642 ÷ 8 = 8,455 r. 2 3. 24767 ÷ 11 = 2251 r. 6 4. 60623 ÷ 12 = 5051 r. 11 5. 72456082 ÷ 2 = 36,228,041 6. 567 ÷ 100 = 5 r. 67 7. 67642 ÷ 10 = 6764 r. 2 8. 267350 ÷ 600 = 445 r. 350 9. 5670256 ÷ 2000 = 2835 r. 256 10. 427567 ÷ 700 = 610 r. 567

Ron Paul Curriculum 7th Grade Mathematics Solution Set #13 Write the following as powers, then use your calculator to solve: 1. 64 × 64 × 64 × 64 = 644 = 16,777,216 2. 5 to the 7th power = 57 = 78,125 3. 7 to the 5th power = 75 = 16,807 4. 2 to the 4th power = 24 = 16 5. 4 squared = 42 = 16 6. Twenty cubed = 203 = 8,000 7. Two to the fifth power = 25 = 32 8. 24 squared = 242 = 576 4

1 1 1 1 1 9. × × × =   = 0.0016 5 5 5 5 5 10. 0 to the 24th power = 024 = 0 11. 1 to the 18th power = 118 = 1 12. In your study notebook, make a table of the powers of two from 21 through 212. Powers of two are very common in mathematics, science, engineering, and computer science. It is a good idea to memorize the first twelve powers of two. 21

22

23

24

25

26

27

28

29

210

211

212

2

4

8

16

32

64

128

256

512

1024

2048

4096

Ron Paul Curriculum 7th Grade Mathematics Solution Set #14 Solve the following without using a calculator: 1. Square root of 49

7

2. Cube root of 8

2

3. Square root of 256

16

4. Cube root of 1000

10

5. Cube root of 216

6

6. 10th root of 0

0

7. 6th root of 1

1

Write the following roots with the radical symbol, then use your calculator to solve (if needed, write the first five digits after the decimal place): 8. 8th root of 256

8

256 = 2

9. 5th root of 243

5

243 = 3

10. 4th root of 99

4

99 = 3.15434... 2 = 1.41421...

11. Square root of 2 12. Cube root of 10

3

10 = 2.15443...

Answer the following without a calculator 13. What two integers is the square root of 50 between?

7 and 8

14. What two integers is the square root of 115 between?

10 and 11

15. What two integers is the square root of 10 between?

3 and 4

Ron Paul Curriculum 7th Grade Mathematics Solution Set #15 Use the method of short division to solve the following problems: 1. 3481 ÷ 8 = 435 r. 1 2. 8350 ÷ 9 = 927 r. 7 3. 7805332 ÷ 2 = 390,266 4. 2596 ÷ 12 = 216 r. 4 5. 6092312 ÷ 4 = 1,523,078 6. 213567 ÷ 100 = 2135 r. 67 7. 60794 ÷ 10 = 6079 r. 4 8. 39460 ÷ 200 = 197 r. 60 9. 4636923 ÷ 3000 = 1545 r. 1923 10. 395739 ÷ 500 = 791 r. 239 In Ray’s New Higher Arithmetic: 11-15. Solve problems 4-6 and 23-24 on pp. 46-47. Write the following as powers, then use your calculator to solve: 16. 9 to the 4th power

94 = 6,561

17. 2 to the 8th power

28 = 256 8

18. ½ to the 8 power

1 1 1 = 0.00390625   = 8 = 256 2 2

19. 567 to the 3rd power

5673 = 182,284,263

20. ‒5 to the 4th power

(‒5)4 = 625

21. ‒5 to the 5th power

(‒5)5 = ‒3125

th

Solve the following without using a calculator:

22. Square root of 144

12

23. Cube root of 27

3

24. Cube root of 64

4

25. Square root of 16

4

26. Square root of 121

11

Write the following roots with the radical symbol, then use your calculator to solve. (Write to the 5th decimal place if necessary):

27. 7th root of 2097152

7

2097152 = 8

28. 4th root of 65536

4

65536 = 16

29. 10th root of 1474578

10

1474578 = 4.13872...

30. Square root of 300

300 = 17.32050...

Ron Paul Curriculum 7th Grade Mathematics Solution Set #16 Solve the following using the correct order of operations: 1. 55 ‒ 4 × 7 = 27 2. 16 ‒ (9 + 7) = 0 3. 200 ÷ (10 ÷ 2) = 40 4. 200/2 × 10 ‒ 4 = 996 8. 15 × 12/4 ‒ 32 + 17 × 9 = 189 9. 3[2 + 4(5 ‒ 2)] = 42 2 2 10. 14 − 105 + 4 = 185

11.

45 35 + 10 = 1.8 = 25 35 − 10

12. 39 ‒ [20/4 + 2(3 + 6)] = 16 13.

16 + 9 + 9 =2 7

14.

9 (45 − 4 2 × 2) = 39

15. 16 ÷ 2 + 1 ‒ 8 × (‒2) ÷ 4 + 6 ‒ 5 = 14

Ron Paul Curriculum 7th Grade Mathematics Solution Set #19 Fill in the correct inequality to complete the following expressions: 1. 9 __ ‒10 3. 9/3 _>_ 9/(‒3) 4. 4 + (‒3) _>_ ‒4 + 3 5. 16 _>_ 15 6. 0 _0

9.

0>x

10.

x≥½

11.

3 > x > ‒3

14.

½>x>0

Ron Paul Curriculum 7th Grade Mathematics Solution Set #20 Solve the following using the correct order of operations: 1. 1000 ‒ 3 × 172 = 133 2. 3 × 4 ‒ 5 × 2 = 2 3. 200/2 × 10 ‒ 4 = 996 4.

2 × 12 + 9 = 15 12 ÷ 3

5. 24 + [18/2 + 8(3 ‒ 1)] ÷ 5 = 29 In Ray’s New Higher Arithmetic: 6-9. Solve problems 4-7 on p. 63. 10-11. Solve problems 3-4 in section 95 on p. 64. 12-13. Solve problems 1-2 on p. 73. 14-20. Solve problems 1-7 on p. 67. 21-25. Solve problems 1-5 on p. 70. Fill in the correct inequality to complete the following expressions: 26. 3 __ ‒12 28. 1.5 _ x

Ron Paul Curriculum 7th Grade Mathematics Solution Set #26 In Ray’s New Higher Arithmetic, read pp. 99-102. 1-3. Solve problems 1-3 on p. 102-103. In Ray’s New Higher Arithmetic, read “Case I” on pp. 103-104. 4-6. Solve problems 1-3 on p. 104. Fill in the correct inequality symbol for the following decimals to compare the value of the two decimals. If the two decimals are equal, use the “equals” sign: 7. 0.5 _