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.
48372 + 394 = 48,766
0.043 + 0.00065 = 0.04365
283 - 0.035 = 282.965
598-329 = 269
(2) Multiply.
48 x 32 = 1536
789 x 896 = 706,944
56.3 x 2.22 = 124.986
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).
328 ÷ 4 = 82
236 ÷ 8 = 29 R4 or 29.5
984 ÷ 12 = 82
4598 ÷ 17 = 270 R8 or 270 8/17
(1) Simplify:
12/36 = 1/3
3/21 = 1/7
15/3 = 5
6/42 = 1/7
(2) Convert from mixed numbers to improper fractions:
1 3/6 = 9/6
4 2/8 = 34/8 (simplifies to 17/4)
6 6/7 = 48/7
(3) Convert from improper fractions to mixed numbers:
15/3 = 5
12/7 = 1 5/7
65/7 = 9 2/7
(4) Operations:
5/6 - 2/3 = 1/6
4 1/5 + 3/6 - 3/8 = 519/120
6/9 x 6/7 = 4/7
8/2 ÷ 3 = 4/3
(5) Equivalent fractions (examples, you may have different ones)
3 2/5 = 17/5 = 3 4/10 = 34/10
4/7 = 8/14 = 16/28
6/8 = 3/4 = 12/16
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) Order the following set of numbers from least to greatest.
See screenshot below (Set 1)
(2) Order the following set of numbers from greatest to least.
See screenshot below (Set 2)
(3) The number 0.1 represents one tenth (1/10), whereas 0.01 represents (1/100) and 0.001 represents (1/1000). As the denominator in the fraction gets bigger (10<100), the number itself gets smaller because you are dividing 1 by an increasingly large number.
½ or 50%
¼ or 25%
Probability of pulling 2 red marbles is greater (6/50 < 9/50)
½ or 50%
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
Questions (1) and (3) see photos below, question (2) check with Desmos Graphing Calculator
(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: