Number Sense week 1

Question 1

Define Integers:

Answer 1

Any positive or negative number

Question 2

Where can integers be found?

Answer 2

thermometers, money, directions, sports scores

Question 3

What is an opposite number?

Answer 3

Any pair of numbers that are the same numerical distance from 0

Question 4

Give examples of an opposite number pair:

Answer 4

-3, and 3

Question 5

List the integer rules when multiplying or dividing:

Answer 5

a) two of the same operations make a positive
i. 2 negatives make a positive
ii. 2 positives make a positive

b) a pair of opposite operations make a negative
i. 1 negative and 1 positive make a negative
ii. 1 positive and 1 negative make a negative

Question 6

Solve.

+3) (-2

Answer 6

= (-6)

- one negative and one positive make a negative

Question 7

Solve.

-1) (-2) (-3

Answer 7

= (-6)

- the two negatives make a positive, becomes one negative one positive; makes a negative

Question 8

When subtracting, which way do we move on the number line?

Answer 8

To the left

Question 9

When adding, which way do we move on the number line?

Answer 9

To the right

Question 10

Define double signs:

Answer 10

When two operations are side by side

Question 11

Give an example of double negative signs:

Answer 11

x - (-y)

Question 12

Give an example of double positive signs:

Answer 12

a + (+b)

Question 13

What do two double negative signs cancel out to make?

Answer 13

Two negatives make a positive (addition)

Question 14

What do two double positive signs cancel out to make?

Answer 14

Two positives make a positive (addition)

Question 15

What does one positive sign and one negative double sign cancel out to make?

Answer 15

One negative and one positive make a negative (subtraction)

Question 16

Solve.

8 + (-5)

Answer 16

8 + (-5)
+ / - cancel out to become subtraction
8 - 5
= 3

Question 17

Solve.

-3 - (-7)

Answer 17

-3 - (-7)
- / - cancel out to become addition
-3 + 7
= 4

Question 18

What does BEDMAS stand for?

Answer 18

B - Brackets
E - Exponents
D - Division
M - Multiplication
A - Addition
S - Subtraction

Question 19

Define the order of operations:

Answer 19

A set of rules specifying which mathematical operations to evaluate before another.

Question 20

What is the acronym used in the order of operations?

Answer 20

BEDMAS

Question 21

Define rational number:

Answer 21

Any number that can be written as a quotient (division/fraction)

Question 22

How would you solve 1.65 to become a quotient of an integer?

Explain.

Answer 22

1.65 x 100/100
= 165/100
= 33/20.
We can multiply by 100/100 because it has two zeros, and 1.65 has two decimal places

Question 23

Give an example of a mixed fraction:

Answer 23

2 1/3

Question 24

Give an example of an improper fraction:

Answer 24

8/3

Question 25

What do we do with the negative symbol when converting a mixed fraction to an improper fraction?
Explain.

Answer 25

Nothing. All that is done with it is it is brought over to the final solution.

Question 26

How do we convert a fraction from mixed to improper?

Answer 26

Multiply the whole number by the denominator and add it to the numerator

Question 27

Why would 5/10 not be an appropriate final answer? What would the correct answer be?

Answer 27

Because it isn’t simplified to lowest terms.

Final answer would be 1/2.

Question 28

State the rules when multiplying and dividing fractions:

Answer 28

1. Finding a common denominator isn’t necessary
2. Must follow integer rules - (-)(-) = (+) etc.
3. Always should convert to improper fractions before evaluating
4. Multiply numerators together
5. Multiply denominators together

Question 29

What is cross cancelling used for?

Explain how.

Answer 29

It is used to make fractions smaller before evaluating.

Finding Greatest Common Factor (GCF)
between diagonal numbers in a fraction
(numerator and denominator- or vice versa),
and reducing to how many times the shared factor can fit into the numbers

Question 30

How do we solve dividing factors?

Answer 30

Convert to multiplication: flip the second fraction so the denominator is now the numerator, and vice versa

Question 31

Can cross cancelling work with any kind of problem?

Why or why not?

Answer 31

NO. Only multiplication, and only when the reciprocals (diagonal numbers) share a greatest common FACTOR that can fit into both numbers

Question 32

Finish the sentence:

Cross cancelling only works when…

Answer 32

It is used in multiplication fractions & diagonally

Question 33

Define Greatest Common Factor (GCF):

Give an example.

Answer 33

The biggest number that can fit evenly into a set of numbers.
The GCF between 5 and 10 is 5.
5 would become 1, and 10 would reduce to 2

Question 34

Define Lowest Common Multiple (LCM):

Give an example.

Answer 34

The smallest number that a set of numbers can all fit into evenly.
The LCM between 4, 2, and 14 is 28.

Question 35

Define a prime number:

Give an example.

Answer 35

A prime number is a number that only has 2 other smaller numbers that can fit into itself. The number itself, and 1.
5 is a prime number

Question 36

Define a composite number:

Give an example.

Answer 36

Has more than 2 other smaller numbers that can fit into itself.
10 is a composite number