Download Math 9 – Assignment – Real Numbers

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Math 9 – Assignment –
Operations with Real Numbers and Square Roots
Show all work for all questions where possible.
1. Marion and her 5 friends bought 3 pizzas. Each person ate
3
of a
8
pizza. How much pizza is left?
1
of their money
4
3
1
on gas,
of their money on food and hotels, and
of their money
5
8
on tourist attractions.
2. During their vacation, the Robichaud family spent
a) What fraction of their money did they spend altogether?
b) If they had $1840 before their vacation started, how much
money did they spend on gas, food, hotels, and tourist
attractions? How much is left over?
4. Which statements are always true, sometimes true, or always
false? Give examples to prove your answers.
a) If you subtract a negative rational number from another
negative rational number, the result is always less than zero.
b) The sum of two natural numbers is greater than each of the two
numbers.
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c) When you subtract a rational number from another rational
number, you get an integer.
d) The square of a rational number that is not zero is negative.
e) The product of two negative rational numbers is greater than
each of the two original numbers.
f) The product of two rational numbers is zero.
g) All rational numbers can be expressed in a decimal form.
h) All numbers in a decimal form are rational numbers.
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5. Complete the magic square. The sum of the numbers in a row, in a
column, and along the diagonal must be equal.
168.2
161
31.4
24.2
67.4 81.8
53
103.4
45.8 96.2
110.6
89
153.8
146.6
126
6.
Simplify each radical.
a)
36
b)
300
c)
18
d)
2 75
e)
28
f)
9 32
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Challenge Question.
To find the principal square root of any perfect square, subtract the
odd numbers in ascending order until the result is zero as shown.
The number of subtractions will give you the square root of the
number you started with.
Example
36 – 1 = 35
35 – 3 = 32
32 – 5 = 27
27 – 7 = 20
20 – 9 = 11
11 – 11 = 0
There are six subtractions so the square root of 36 is 6.
Use the same method to find the principal square root of each
number. Show your work and explain why this method works.
a) 289
d) 1089
b) 576
c) 784