Numbers and Fractions

Question 0

Integers

Answer 0

-3,-2,-1,0,1,2,3

Like whole numbers but have negatives. Still no fractions

Question 1

Whole Numbers

Answer 1

0, 1, 2, 3, …

No negatives or partial numbers like fractions

Question 2

Rational numbers

Answer 2

Any number that can be written as a fraction except those with zero in the denominator. Includes integers, fractions and whole numbers

p/q: p and q are integers, q is not zero

Question 3

Irrational numbers

Answer 3

A real number that can’t be written as a simple fraction, no clear ratio(nal)

Some Square roots are irrational
3.14159…=?/?
Decimal goes on forever without repeating

Question 4

Real numbers

Answer 4

Any rational, irrational, integer or whole number

Question 5

Choose the correct statement:

A. no rational numbers are integers
B. All irrational numbers are real numbers
C. No irrational numbers are real numbers
D. All integers are whole numbers

Answer 5

B

Question 6

What are som tasks that students use number lines for?

Answer 6

Counting
Math operations
Measuring
Graphing
Estimating

Question 7

When showing inequalities in a number line, what is the difference between an empty dot and a filled in dot?

Answer 7

Empty dot shows that number is not included in the solution (x>5)

Solid dot shows it is included in solution (x>=5)

Question 8

Communicative property

Answer 8

ORDER
For multiplication and addition order is not important

4+7=7+4. 8x3=3x8

If you live in a community, it doesn’t matter where, you’re still part if community

Question 9

Associative property

Answer 9

Grouping not important when adding or multiplying

3 + (4+7)=(3+4)+7
2(83)=(28)3

You spend time with your associates in a group

Question 10

True or False:

Associative and commutative properties work with subtraction and division?

Answer 10

False. Order and grouping make a big difference while subtracting and dividing

Question 11

Identity property

Answer 11

Any number plus zero equals that number 4+0=4

Any number times one equals that number 8*1=8

The number wants to be the same; it wants to be itself

Question 12

Multiplicative property of zero

Answer 12

Any number times 0 is 0

8*0=0

Question 13

Distributive property

Answer 13

Combines addition/subtraction and multiplication for expanding or simplifying expressions with parenthesis

a(b+c)=ab+ac
a(b-c)=ab-ac

Question 14

Prime numbers

Answer 14

Have exactly two factors, one and the number itself.

Prime numbers up to 25
2,3,5,7,11,13,17,19,23

Question 15

Composite numbers

Answer 15

Have more than two factors, but not an infinite number or factors (like zero)

All even numbers except two are composite numbers

Question 16

Divisibility rules:

2

Answer 16

Numbers divisible by 2 are even or end in zero

Question 17

Divisibility rules:

3

Answer 17

First find sum of digits. If sum is divisible by 3, then whole number is divisible by three

837
8+3+7=18=3*6

Question 18

Divisibility rules:

4

Answer 18

If the final two digits of a number greater than 100, than number is divisible by four

1,072
Last two digits 72 are divisible by four, so whole number is divisible by 4

Question 19

Divisibility rules:

5

Answer 19

If number ends in zero or 5 it is divisible by 5

Question 20

Divisibility rules:

6

Answer 20

Must be divisible by both 2 and 3, therefore it must be an even number whose sum is divisible by three

Ex: 534
It is even do it’s divisible by 2 and the sum of the digits, 12, is divisible by three so it is divisible by 6

Question 21

Divisibility rules:

8

Answer 21

Only useful for numbers greater than 1,000. A number divisible by 8 ends with a three-digit number divisible by 8

Ex: 7,488
488 is divisible by 8 and 61, so whole number can be divided by 8

Question 22

Divisibility rules:

9

Answer 22

Similar to
Rule for 3. Sum of digits must be able to be divided by 9.

Ex: 72,954
7+2+9+5+4=27 which is divisible by 9

Question 23

What must be in place before adding or subtracting fractions and mixed numbers?

Answer 23

A common denominator

Question 24

When should you convert mixed numbers to improper fractions?

Answer 24

When multiplying or dividing, but not for addition and subtraction

Question 25

What is the process for multiplying fractions?

Answer 25

1 convert to improper fraction

2. Try to cancel out shared factors (any factors shared in both the denominator and numerator can be cancelled even if not in the same fraction)
3. Multiply straight across in both numerator and denominator
4. Simplify fraction to express it in its lowest terms

Question 26

What is the process of dividing fractions?

Answer 26

Same as multiplication, but multiply by the reciprocal (flip fraction upside down)

3/4 ➗ 2/3 = 3/4 x 3/2
10 ➗ 2= 10 x 1/2