Number Sense week 1 Flashcards
Define Integers:
Any positive or negative number
Where can integers be found?
thermometers, money, directions, sports scores
What is an opposite number?
Any pair of numbers that are the same numerical distance from 0
Give examples of an opposite number pair:
-3, and 3
List the integer rules when multiplying or dividing:
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
Solve.
+3) (-2
= (-6)
- one negative and one positive make a negative
Solve.
-1) (-2) (-3
= (-6)
- the two negatives make a positive, becomes one negative one positive; makes a negative
When subtracting, which way do we move on the number line?
To the left
When adding, which way do we move on the number line?
To the right
Define double signs:
When two operations are side by side
Give an example of double negative signs:
x - (-y)
Give an example of double positive signs:
a + (+b)
What do two double negative signs cancel out to make?
Two negatives make a positive (addition)
What do two double positive signs cancel out to make?
Two positives make a positive (addition)
What does one positive sign and one negative double sign cancel out to make?
One negative and one positive make a negative (subtraction)
Solve.
8 + (-5)
8 + (-5)
+ / - cancel out to become subtraction
8 - 5
= 3
Solve.
-3 - (-7)
-3 - (-7)
- / - cancel out to become addition
-3 + 7
= 4
What does BEDMAS stand for?
B - Brackets E - Exponents D - Division M - Multiplication A - Addition S - Subtraction
Define the order of operations:
A set of rules specifying which mathematical operations to evaluate before another.
What is the acronym used in the order of operations?
BEDMAS
Define rational number:
Any number that can be written as a quotient (division/fraction)
How would you solve 1.65 to become a quotient of an integer?
Explain.
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
Give an example of a mixed fraction:
2 1/3
Give an example of an improper fraction:
8/3
What do we do with the negative symbol when converting a mixed fraction to an improper fraction?
Explain.
Nothing. All that is done with it is it is brought over to the final solution.
How do we convert a fraction from mixed to improper?
Multiply the whole number by the denominator and add it to the numerator
Why would 5/10 not be an appropriate final answer? What would the correct answer be?
Because it isn’t simplified to lowest terms.
Final answer would be 1/2.
State the rules when multiplying and dividing fractions:
- Finding a common denominator isn’t necessary
- Must follow integer rules - (-)(-) = (+) etc.
- Always should convert to improper fractions before evaluating
- Multiply numerators together
- Multiply denominators together
What is cross cancelling used for?
Explain how.
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
How do we solve dividing factors?
Convert to multiplication: flip the second fraction so the denominator is now the numerator, and vice versa
Can cross cancelling work with any kind of problem?
Why or why not?
NO. Only multiplication, and only when the reciprocals (diagonal numbers) share a greatest common FACTOR that can fit into both numbers
Finish the sentence:
Cross cancelling only works when…
It is used in multiplication fractions & diagonally
Define Greatest Common Factor (GCF):
Give an example.
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
Define Lowest Common Multiple (LCM):
Give an example.
The smallest number that a set of numbers can all fit into evenly.
The LCM between 4, 2, and 14 is 28.
Define a prime number:
Give an example.
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
Define a composite number:
Give an example.
Has more than 2 other smaller numbers that can fit into itself.
10 is a composite number
