Decomposition:

For questions 1-5, there are many solutions. Feel free to email me if you have any questions about your answers if they differ from these.

1. 50,000 + 4,000 + 90 + 3 OR (5 x 10,000) + (4 x 1000) + (9 x 10) + (3 x 1) OR (54 x 1000) + (9 x 10) + (3 x 1)

2. 3,000 + 300 + 0.6 OR (3 x 1000) + (3 x 100) + (6 x 0.1) OR (33 x 100) + (6 x 0.1)

3. 40,000,000,000 + 5,000,000,000 + 90,000,000 + 2,000,000 + 200,000 + 20,000 + 9,000 + 1 OR

(4 x 10,000,000,000) + (5 x 1,000,000,000) + (9 x 10,000,000) + (2 x 1,000,000) + (2 x 100,000) + (2 x 10,000) + (9 x 1000) + (1 x 1)

(45 x 1,000,000,000) + (92 x 1,000,000) + (229 x 1000) + (1 x 1)

(4 x 10¹⁰) + (5 x 10⁹) + (9 x 10⁷) + (2 x 10⁶) + (2 x 10⁵) + (2 x 10⁴) + (9 x 10³) + (1 x 10⁰)

4. 1 + 0.5 + 0.07 + 0.006 OR (1 x 1) + (5 x 0.1) + (7 x 0.01) + (6 x 0.001) OR (1 x 1) + (57 x 0.01) + (6 x 0.001)

5. 0.03 + 0.0004 OR (3 x 0.01) + (4 x 0.0001) OR (304 x 0.0001)

Composition:

1. 536

2. 3,430

3. 47,320

Scientific Notation:

1. 4.3 x 10²

2. 9.8798398 x 10⁷

3. 3.0944 x 10³

4. 5.06 x 10^-3

5. 8.9 x 10^-7

(1) Add or subtract as indicated.

1. 48372 + 394 = 48,766

2. 0.043 + 0.00065 = 0.04365

3. 283 - 0.035 = 282.965

4. 598-329 = 269

(2) Multiply.

1. 48 x 32 = 1536

2. 789 x 896 = 706,944

3. 56.3 x 2.22 = 124.986

4. 6.56 x 0.02 = 0.1312

(3) Divide. If the answer is not a whole number, write your answer in two ways: as a number with a remainder (ex. 123 R3) as well as a number with a fraction (123 ¼).

1. 328 ÷ 4 = 82

2. 236 ÷ 8 = 29 R4 or 29.5

3. 984 ÷ 12 = 82

4598 ÷ 17 = 270 R8 or 270 8/17

(1) Simplify:

1. 12/36 = 1/3

2. 3/21 = 1/7

3. 15/3 = 5

4. 6/42 = 1/7

(2) Convert from mixed numbers to improper fractions:

1. 1 3/6 = 9/6

2. 4 2/8 = 34/8 (simplifies to 17/4)

3. 6 6/7 = 48/7

(3) Convert from improper fractions to mixed numbers:

1. 15/3 = 5

2. 12/7 = 1 5/7

3. 65/7 = 9 2/7

(4) Operations:

1. 5/6 - 2/3 = 1/6

2. 4 1/5 + 3/6 - 3/8 = 519/120

3. 6/9 x 6/7 = 4/7

4. 8/2 ÷ 3 = 4/3

(5) Equivalent fractions (examples, you may have different ones)

1. 3 2/5 = 17/5 = 3 4/10 = 34/10

2. 4/7 = 8/14 = 16/28

3. 6/8 = 3/4 = 12/16

4. 14/8 = 1 6/8 = 7/4 = 1 3/4

(6) (Using addition) - Nicole used 1 cup of flour in total.

(7) (Using multiplication and subtraction) - Katie had 81/40 m of ribbon left over.

(8) (Using subtraction and division) - Each person gets 7/48 of the pie.

(1) George saved $132.

(2) 8 photos should be black and white.

(3) a) She has 36 GB still available

b) 33.6 GB are filled with photos

(4) a) The Harris family tipped 18%

b) Their total bill with tax and tip included was $94.32.

1. ½ or 50%

2. ¼ or 25%

3. Probability of pulling 2 red marbles is greater (6/50 < 9/50)

4. ½ or 50%

5. a) ¼ or 25%

b) 1/169

c) 52/867 or 6%

d) 25.5%

(1) Graph 1: Not linear - graph is not one straight-line going one way, there are two going different ways

Graph 2: Linear - graph is a straight line with negative slope

Graph 3: Not linear - graph is not a straight line

Graph 4: Linear - graph is straight line with positive slope

(2) and (3) - see photos below

(1) Mean = 163. 9, median = 164, and mode = 154

Extend: The mean would change (it would be equal to 165.09), and there would be two modes (151 and 152) instead of one mode. The median would not change because the value 164 would still be in the middle of the data set, because the changes do not change the position of the value of 164.

(2) Heights in the class - mean, so that all data is included; ice cream preferences - mode, because it is a categorical measure and we can say “vanilla” is the mode; income, median because the mean will be skewed due to outliers such as high-earners or part-time workers

(3) See image below: