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Date
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M7 - Winter Break
Arithmetic & Expressions
Practice
NO CALCULATORS!!
Think Through Math
Multiplying Fractions
There are two pathways loaded in TTM (Chapter 2, Chapter 3, or Ratios – not the first one on the list) that you are
expected to complete before returning to school on January 4th. Show your work in your composition book and use the
tools that are available, such as the live tutor and glossary. Be sure to record your questions as well as calculations.
Only completed TTM lessons and pathways will count toward your grade. Remember, they cannot be made up later so
complete them while you can. Pathways will disappear when you have completed them.
Multiply. Express your answer in simplest form. Show each step of your work to receive full credit.
1.
2.
3.
5.
6.
7. − 10.
9. − 11. − 17. − −1 4.
12. 15. −3 2 18. 1 −2 8. − 14. −2 13. −1 4 16. −2 −3 19. −2 −3 20.
−1 Example 1
Example 2
Multiply − by the reciprocal of
Dividing Fractions
Rewrite as a division expression.
Multiply by the reciprocal of
.
.
Multiply the numerators and
denominators.
Multiply the numerators and the
denominators.
Divide the numerator and
denominator by the GCF, 6.
Divide the numerator and the
denominator by the GCF, 3.
Simplify.
Simplify.
Write as a negative integer, when
possible.
Evaluate each quotient. Give your answer in simplest form. Show each step of your work to receive full credit.
1.
÷ 5. − ÷ 19.
÷
6.
÷ − 3.
20.
4. − ÷ 11. −2 ÷ −1 14. −4 ÷ 1 17.
÷
7. − ÷ 10. 1 ÷ −3 13. −3 ÷ 4 16.
9. − ÷ − 2.
15.
18.
21.
8.
12.
÷ − ÷ − Multiplying Decimals
Show each step of your work and clearly justify your thinking to receive full credit.
1. 6.411.3
2. 8.310.1
3. 4.522.9
4. 12.332.1
5. 13.635.6
6. 18.920.1
7. −6.38(−0.4)
8. −4.3(−1.5)
9. 19.3(−0.6)
10. 5.39(−1.6)
11. (−5.3)(−2.8)
12. (−22.9)(3.1)
13. 7.85(−3.6)
14. 3.58.02
15. 9.60.75
16. 6.057.2
17. 15.40.17
18. 345.6
19. 12.986.4
20. 15.427
Decimals & Long Division
Example 1
'(. ') ÷ (−'. *)
Example 2
',. ,* ÷ (−'. -)
Make the divisor a whole number by
multiplying both the divisor and the
dividend by 10.
Make the divisor a whole number by
multiplying both the divisor and the
dividend by 10.
Place the decimal point in the quotient
above the decimal point in the dividend.
Place the decimal point in the quotient
above the decimal point in the
dividend.
Quotient will be negative because
Positive ÷ Negative = Negative.
Quotient will be negative because
Positive ÷ Negative = Negative.
13.14 ÷ (−1.8) = −7.3
16.68 ÷ (−1.2) = −13.9
Evaluate each quotient using long division. Show each step of your work to receive full credit.
1. 36.45 ÷ 8.1
2. 91.14 ÷ 2.17
3. 9.225 ÷ 0.75
4. 2.31 ÷ 0.15
5. 38.54 ÷ 8.2
6. 15.4 ÷ 2.75
7. 0.205 ÷ 4.1
8. 34.83 ÷ 8.6
9. 22.54 ÷ 2.45
10. 46.92 ÷ 5.1
11. 12.98 ÷ 4
12. −36.9 ÷ 4.5
13. 159.12 ÷ (−3.4)
14. −49.14 ÷ (−6.3)
15. 12.376 ÷ 0.52
16. (−23.49) ÷ 0.9
17. 11.36 ÷ (−1.6)
18. 5.49 ÷ (−6.1)
19. −73.53 ÷ 0.9
20. (−54.96) ÷ (−1.2)
Simplifying and Expanding Algebraic Expressions
Simplify each expression. If already simplified, explain why. Then identify the algebraic and constant terms,
like terms, and coefficients in each expression.
1. 3 + 7/ + 3/ + /
2. 20 + 51 − 0 + 60
3. 62 − 23 + 7
4. 4 + 34 + 84 + 2
5. 51 − 25 + 35 − 5
6. / + / + 3 + 4
7. 0 + 50 + 20 + 30
8. 76 − 26 + 36 + 46
9. 21 + 41 − 31 + 51
Simplify each expression. Show evidence of your mathematical reasoning.
1. 67 − 37 + 87 − 7
2. 108 + 48 − 88 − 38
3. 92 + 42 − 52 + 32
4. 12/ − 4/ + 3/ + 5/
5. 12 − 8 + 55 + 45 − 65
6. 20 + 78 − 12 − 58 + 88
7. 92 + 11 − 82 − 6 + 52
8. 18 + 43 − 9 + 83 − 113
9. 20 + 59 + 109 − 20 − 149
10. 20 + 128 − 78 − 8
11. 6/ + 15 + 9/ − 10/ − 8
12. : + 9 + 10: − 5 − 4:
13. 30 + 26 + 41 + 20
14. 51 + 25 + 31 + 45
15. 26 − 6 + 40 − 31
16. 50 + 26 + 60 − 26
17. 8ℎ − 47 + 57 + 2ℎ
18. 58 + 4< − 68 + 6<
19. 74 − 6= − 54 + 3=
20. 30 + 21 − 50 + 1
State whether each pair of expressions are equivalent. Show mathematical evidence to support your thinking.
1. 8> + 2>and3> + 4> + 3>
3. 73 − 2and2 − 73
2. 94and9 + 4
4. 57 − 27and
B
Expand each expression by applying distributive property. Show evidence of your mathematical reasoning.
1. 5(0 + 3)
2. 3(6 + 4)
3. 6(1 − 2)
4. 4(5 − 5)
5. 3(2C + 4)
6. 7(69 − 2)
7. 8(3 − 27)
8. 9(7 + 4ℎ)
9. 3(29 − 4)
10. 5(37 − 7)
11. 4(C + 5)
12. 5(68 + 1)
13. 7(: − 9)
14. −5(/ + 8)
15. −4(5/ + 3)
16. −7(2/ − 7)
17. −(2/ + 4)
18. 4(/ − 6)
19. 3(/ − 4)
20. 3(24 − 5)
21. 8(37 − 9)
22. −2(/ − 4)
23. −3(8 − 2ℎ)
24. −5(38 + 4)
25. Think First. Jordan writes 3(4/ − 8) is equivalent to
12/ − 8. Explain why his expansion is NOT correct.
26. Think First. Write an expression for the area of
these shapes.
Expand and simplify each expression. Show each step of your work to receive full credit.
1. 5(2/ + 4) + 3/
2. 3(4 + 2) + 4
3. 8(2: + 4) − 6:
4. 2(87 + 2) − 137
5. 5(3D − 1) + D
6. 3(42 + 2) + 2
7. 3/ + 2(/ + 5)
8. 6 + 4(/ + 3)
9. 4/ + 2(/ − 5)
10. 5/ − 2(/ − 8)
11. 3 0 + 2 + 5
12. 6 6 − 3 − 6
13. 0.4(3 + 3) + 0.8/
14. 0.3(4 + 5) − 0.14
15. 3(/ + 7) + 6(3/ + 4)
16. 4(2/ + 5) + 3(3/ − 4)
17. 4(3/ + 2) + 6(4/ + 3)
18. 6(/ + 7) − 3(/ + 4)
19. 3(8/ − 4) + 4(2/ + 5)
20. 6(5/ + 7) − 2(/ − 4)
21. 5(/ + 7) − 2(/ − 9)
22. 6(4 − 8) − 3(/ + 5)
23. −8(3/ + 7) − 3(2/ + 8)
24. −9(8/ − 5) − 7(8/ − 9)
25. 11(6 − 2) + 3(6 + 6)
26. 9(8 − 4) + 3(38 − 1)
27. 8(27 + 2) − 8(27 − 2)
28. −7(114 + 2) − 12(4 − 4)
29. 6(21 + 2) + 3(1 + 4) + 131
30. 3(ℎ − 8) + (ℎ + 6) − 2ℎ
31. −2(−83 − 10) − 6(−103 − 3)
32. 5(9 − 2D + 2) − 3(9 − D + 22)
33. −9(−9 + 64) − 5(7 + 44)
34. Think First. Work out what each of the bricks
at the bottom simplify to, then add the 2 bricks
next to each other to give the brick above them.
Factor each expression. Remember, look for factors that each term have in common.
1. 6/ + 9
2. 120 + 20
3. 356 − 15
4. 107 − 5
5. 21ℎ + 35
6. 118 − 55
7. 18 + 90
8. 600 + 206 − 301
9. 2< − 108
10. 60 − 186
11. 82 − 123
12. 3/ +15