Unit 1: Number and Operations: Practice Activity 1images.carsondellosa.com/media/cd/pdfs/Activities/Samplers/1581_sb… · Math Engagement Grade 7 ... Number and Operations: Practice

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CD-1581

Mark Twain Media/Carson-Dellosa Publishing LLC

Mark Twain Media/Carson-Dellosa Publishing LLC

CD-1581

• NCTM Standards based• Multiple grade-appropriate opportunities• Practice targeting each skill• Assessment/standardized- test format

Printed in the USA

Math Engagement: Grade 7

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Name: Date:

1581-EB © Mark Twain Media, Inc., Publishers

Skill:.Understanding.numbers,.ways.of.representing.numbers,.relationships.among.num-bers,.and.number.systems

Unit 1: Number and Operations: Practice Activity 1

Name the place of the number in bold. Example: 8,652.03 The bold number is in the tens place.

..1. 4,867,291 .6. 0.593

..2. 31,281,471 ..7. 8,507,211

..3. 1,689,740 ..8. 25,609.45.

..4. 51,087,481 ..9. 26.158.

..5. 1,792.31. . 10. 0.0046

Write each number in word form. Example: 7,901,052.5 The number written in word form is seven million, nine hundred one thousand, fifty-two and five tenths.

11. 4,786,921

12. 33,781,441

13. 2,468,291

14. 17,264,521

15. 452.097

Write each number in standard form. Example: The number forty-two million, three hundred ten thousand, four hundred five is written in standard form as 42,310,405.

16. seven hundred million

17. sixteen thousand, four hundred eighty-eight

18. seventy-five thousand, four

19. sixty-five million, fifty-eight

20. one hundred seventy-three and thirteen hundredths

WAKE-UP.WORD.PROBlEM: Arlene saved $21 in June, $58 in July, and $63 in August. Peggy saved four times as much as Arlene during the same three-month period. How much money did Peggy save?



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Just.a.Tip: If you have trouble determining the larger number, try converting each fraction and/or decimal to a percent, ratio, and/or decimal. Then compare the num-bers again.

Put the decimals in order from least to greatest.

..1. 0.066, 7.62, 0.092, 0.041

..2. 7.28, 0.826, 0.043, 0.034

..3. 0.27, 2.7, 0.789, 0.045

..4. 0.321, 32.1, 3.21, 4.05

..5. 0.78, 0.75, 0.65, 0.29

Put the decimals in order from greatest to least.

..6. 0.011, 0.012, 1.5, 15.7

..7. 0.068, 0.072, 0.077, 0.61

..8. 0.65, 0.56, 5.75, 0.290

..9. 0.395, 0.405, 30.7, 2.35

10. 4.11, 0.276, 0.288, 0.028

Put the fractions in order from least to greatest.

11. , , ,

12. , , ,

Put the fractions in order from greatest to least.

13. , , ,

14. , ,

15. , , ,



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In a number such as 52, the 5 is the base and the 2 is the exponent. The exponent indi-cates how many times the base is to be multiplied. For example, in 52, the 2 tells you to multiply the 5 two times. 52 = 5 x 5 = 25. When a base number has an exponent, the base number is said to be raised to the in-dicated power, so 52 is read as “5 to the second power.”

Just.a.Tip:.Any base raised to the zero power equals one. 30 = 1, 100 = 1Any base raised to the first power equals the base. 31 = 3, 101 = 10

Raise the following bases to the indicated powers.

..1. 62 ..6. 102

..2. 84 ..7. 103

..3. 27 ..8. 104

..4. 51 ..9. 105

..5. 90 10. 106

Scientific.notation is a way to write large numbers in a smaller space using exponents to indicate the powers of 10. First move the decimal point just to the right of the number in the farthest left place. Then you multiply that number by 10 raised to the number of decimal places you moved over.

Example: 3,829 Move the decimal point to 3.829. The number can now be written as 3.829 x 103. You can check the number by multiplying 3.829 x (10 x 10 x 10) = 3.829 x 1,000 = 3,829. If you have a number like 700, you can drop the zeros when writing scientific notation. 700 = 7 x 102

Rewrite each number in scientific notation.

11. 900 16. 78,410,000,000

12. 500,000 17. 768.7

13. 2,704,000 18. 80,000,000

14. 65.81 19. 3,000

15. 400,000,000 20. 6,842,700,000



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Write each decimal in number form.

..1. nine tenths ..4. sixty-three hundredths

..2. seventeen hundredths ..5. one and four tenths

..3. eight tenths ..6. seventy-two thousandths

Just.a.Tip: You can divide the numerator by the denominator to find each fraction in decimal form.

Find a decimal equal to each fraction.

..7.

..8.

..9.

10.

11.

12.

13.

14.

15.



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Unit 1: Number and Operations: Assessment 1

Mark the answer that names the value of each number in bold.

..1. 268,749 ❍ A. six million ❍ B. six hundred thousand ❍ C. six thousand ❍ D. sixty thousand

..2. 13,741,268 ❍ A. three million ❍ B. three hundred thousand ❍ C. thirty thousand ❍ D. thirty-seven million

Mark the answer that shows each number in word form.

..3. 17,642,741 ❍ A. seven million, six hundred forty-two thousand, seven hundred forty-one ❍ B. seventeen million, six hundred thousand, seven hundred and forty-one ❍ C. seventeen million, six hundred forty-two thousand, seven hundred forty-one ❍ D. seventeen million, six hundred forty-two, seven hundred forty-one

..4. 387,291,202 ❍ A. three hundred eighty-seven billion, two hundred ninety-one thousand, two hundred

two ❍ B. three hundred eighty-seven million, two hundred ninety-one thousand, two hundred

two ❍ C. three hundred eighteen million, two hundred ninety-one thousand, two hundred

two ❍ D. three hundred eighty-seven million, two hundred nineteen thousand, two hundred

two

Mark the answer that shows each number in standard form.

..5. seventeen million, eight hundred ninety-two ❍ A. 17,892 ❍ B. 17,892,000 ❍ C. 17,000,892 ❍ D. 17,000,802

..6. four hundred thousand, six hundred one ❍ A. 400,610 ❍ B. 4,000,601 ❍ C. 400,601 ❍ D. 4,060,001



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Mark the answer that puts the decimals in order from least to greatest.

..7. 0.051, 0.51, 0.63, 0.74 ❍ A. 0.51, 0.63, 0.74, 0.051 ❍ B. 0.051, 0.51, 0.63, 0.74 ❍ C. 0.051, 0.51, 0.74, 0.63 ❍ D. 0.74, 0.63, 0.51, 0.051

Mark the answer that puts the decimals in order from greatest to least.

..8. 0.29, 0.41, 0.44, 0.027 ❍ A. 0.44, 0.41, 0.027, 0.29 ❍ B. 0.027, 0.29, 0.41, 0.44 ❍ C. 0.027, 0.44, 0.41, 0.027 ❍ D. 0.44, 0.41, 0.29, 0.027

Mark the answer that puts the fractions in order from least to greatest.

..9. , , ,

❍ A. , , ,

❍ B. , , ,

❍ C. , , ,

❍ D. , , ,

Mark the answer that puts the fractions in order from greatest to least.

10. , , ,

❍ A. , , ,

❍ B. , , ,

❍ C. , , ,

❍ D. , , ,

Unit 1: Number and Operations: Assessment 1 (cont.)

Mark the answer that shows each decimal in number form.

11.. seven and eight tenths ❍ A. 7.08 ❍ B. 7.80 ❍ C. 78.0 ❍ D. 7.18

12. forty-eight hundredths ❍ A. 0.48 ❍ B. 0.048 ❍ C. 4.8 ❍ D. 48.0

Mark the decimal that is equivalent to each fraction.

13. ❍ A. 0.045 ❍ B. 0.21 ❍ C. 0.50 ❍ D. 0.45

14. ❍ A. 7.50 ❍ B. 0.725 ❍ C. 0.025 ❍ D. 0.75

Mark the answer that expresses the following number in scientific notation.

15. 9,025,000,000 ❍ A. 9,025 x 105

❍ B. 9.025 x 106

❍ C. 9.025 x 109

❍ D. 9.025 x 1010



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Skill:.Understanding.the.meanings.of.operations.and.how.they.relate.to.one.another


Just.a.Tip: It is important to know the order in which you should perform arith-metic operations. First, do any operations in parentheses and perform any ex-ponentiation. Next, perform multiplication and division from left to right. Finally, perform addition and subtraction from left to right.

Solve each problem. Do not use a calculator.

..1. 8 x 16 ÷ 2 =

..2. 25 x 4 ÷ 10 =

..3. 27 - 4 x 6 =

..4. 38 - 5 x 12 =

..5. 48 ÷ 2 + 24 ÷ 6 =

..6. 9 x 9 ÷ 9 =

..7. 17 + 7 x 6 =

..8. 90 - 22 x 4 =

..9. 56 ÷ 2 + 88 =

10. 78 - 14 - 25 =

11. 35 + 44 =

12. 30 - 22 x 5 =

13. 7(36 ÷ 4) ÷ (8 - 5) =

14. (12 - 7)2 x (4 + 5) =

15. (32 + 4) ÷ (21 - 18)2 =

Extension.Activity: Have students write three problems and exchange with their classmates to solve each set of problems.



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Just.a.Tip: Remember to substitute the correct value for each variable.

Perform exponentiation first. If a constant and a variable are written together, perform the multiplication or division indicated in that grouping first before con-tinuing with other multiplication or division.

Example: If b = 4 and d = 3, 12/b x 2d = 3 x 6 = 18 NOT 12 ÷ 4 x 2 x 3 = 18

Evaluate each algebraic expression if b = 4, c = 7, and d = 3.

..1. 3b + c 2 - 4 =

..2. bc4 =

..3. 9c - 2b =

..4. 24 x b ÷ 2d =

..5. c + c + c - d =

..6. 7c + b 2 =

..7. 8d 3 =

..8. 12b + 2d ÷ 6 =

..9. 6b - 2d =

10. b/2 - 18 x 4 =

11. bc2 =

12. 5c x 4b - 2d =

13. 9d + 2bd 2 =

14. (c - d) x b3 =

15. (c2 + 5) ÷ d =



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Use the order of operations to evaluate each expression.

Just.a.Tip: Work inside the parentheses before doing anything else.

..1. 18 + 4(22 - 8) =

..2. (45 - 4) x 6 =

..3. (82 + 12) - 24 =

..4. 8(12 - 8) + 42 + 8(10 - 2) =

..5. 6(18 - 6) + 35 + 5(18 - 6) =

..6. 32 + 6(14 - 7) =

..7. (63 + 4(12 - 2)) - (34 - 6) =

..8. (45 + 8(18 - 4)) - (28 - 6) =

..9. 5(14 x 9) - 8 =

10. 8(12 x 12) - 15 =

11. 8(6 - 4) + 28 =

12. 12(15 - 5) + 38 =

WAKE-UP.WORD.PROBlEM: Charlene saves the money she usually spends on snacks for six weeks. The first week she saves $0.85. The second week she saves twice as much money as the first week, the third week she saves three times as much money as the first week, the fourth week she saves four times as much, the fifth week she saves five times as much, and the sixth week she saves six times as much. How much money does Charlene save during the entire six weeks?



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The radical sign over a number called the radicand means you are to find the square root of the radicand. The square.root is the number that, when squared (multiplied by itself), equals the radicand. Each number has two square roots, a positive number and a nega-tive number.

Example: 81 = 9 or -9 or ±9 9 x 9 = 81 -9 x -9 = 81

Find the square roots of each number without using a calculator.

1. 25

.2.. 16

3. 4

4.. 36

5. 100

6. 121

7. 9

8. 81

9. 49

10. 64

Give the square roots of each number. You may use a calculator. Round the roots to the thou-sandths place.

11. 12

12. 24

13. 18

14. 0.5

15. 2



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Evaluate each expression. Do not use a calculator. Mark the correct answer.

..1. 186 ÷ 14 x 6 = ❍ A. 79.71 ❍ B. 7.791 ❍ C. 79.851 ❍ D. 78.87

.2. 98 - 26 x 14 = ❍ A. 798 ❍ B. -798 ❍ C. 476 ❍ D. -70

Evaluate each expression if a = 12, b = 16, and c = 8. Mark the correct answer.

..3. 4a ÷ 6 x 9 = ❍ A. -72 ❍ B. 68 ❍ C. 72 ❍ D. 70

..4. 4ab2 ÷ 0.02 = ❍ A. 6.140 ❍ B. 61.440 ❍ C. 61,440 ❍ D. 614,400

Use the order of operations to evaluate each expression. Mark the correct answer.

..6. 45(12 x 12) - 43

❍ A. 6.446 ❍ B. 6,418 ❍ C. 6,416 ❍ D. 6,787

..7. (122 + 18) x 15 = ❍ A. 2,430 ❍ B. 2,441 ❍ C. 2,034 ❍ D. 2,450

Find the square root of the number. Mark the correct answer.

..5. 42 + b/c - = ❍ A. 48

❍ B. 43

❍ C. 44

❍ D. 43

..8. 42(18 - 6) + 181 = ❍ A. 685 ❍ B. 586 ❍ C. 605 ❍ D. 698

..9. 188 ❍ A. ±13.51 ❍ B. ±13.71 ❍ C. ±13.81 ❍ D. ±5.261

10. 18 ❍ A. ±4.76 ❍ B. ±4.004 ❍ C. ±4.24 ❍ D. ±424



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Name: Date:


Skill:.Computing.fluently.and.making.reasonable.estimates


Solve each problem.

..1. 0.295 + 0.148 = ..7. + =

..2. 0.076 - 0.021 = ..8. + =

..3. 4.12 + 8.07 = ..9. + =

..4. 6.08 - 0.74 = 10. 2- 1 =

..5. 0.396 - 0.271 = 11. 3- 1 =

..6. 5.897 - 4.128 = 12. 5 + 1 =

Just.a.Tip: An algorithm is a sequence of steps that leads to a desired result. Some algorithms, like long division, can involve many steps.

Analyze each algorithm.

13. 2,978 ÷ 18 = 20. 2,158 ÷ 19 =

14. 7,429 ÷ 21 = 21. 32,746 ÷ 24 =

15. 52.86 ÷ 14 = 22. 4,769 ÷ 13 =

16. 2,179 ÷ 5 = 23. 57.80 ÷ 6 =

17. 43.20 ÷ 12 = 24. 1,442 ÷ 6 =

18. 8,261 ÷ 17 = 25. 36,215 ÷ 4 =

19. 7,389 ÷ 15 =



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Name: Date:


Skill:.Computing.fluently.and.making.reasonable.estimates


Analyze each algorithm.

..1. 0.489 - 0.006 = ..6. 6 x 5 =

..2. 0.297 + 0.328 = ..7. 0.465 x 0.212 =

..3. 4,265 ÷ 27 = ..8. 7.02 x 0.61 =

..4. 3,781 ÷ 19 = ..9. 1x 1 =

..5. 2 x 1 = 10. 1,275 ÷ 4 =

WAKE-UP.WORD.PROBlEM: Theresa wants to divide 1,568 marbles into 18 piles. How many marbles will Theresa put in each pile? How many, if any, marbles will be left over?

Just.a.Tip: A proportion is a statement that two fractions are equal. To solve a proportion, find the number that keeps the statement equal.

Example: = To find x, cross multiply 4 x 2, and then divide by 8. x = 1

Solve each proportion. Show your work.

11. = . 16. =

12. = . 17. =

13. = . 18. =

14. = . 19. =

15. = . 20. =

4 x8 2


56 x 4 2

12 24 b 6

68 x 2 4

18 y 9 45

90 y10 8

21 x 3 6

12 y36 27

8 y5 3

36 x 6 12

58 112 2 y

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Unit 1: Number and Operations: Practice Activity 1images.carsondellosa.com/media/cd/pdfs/Activities/Samplers/1581_sb… · Math Engagement Grade 7 ... Number and Operations: Practice