Numbers & Operations
CRCT review
Real Numbers
All rational and irrational numbers – all numbers that can be expressed as a decimal
Rational Numbers Irrational Numbers
*natural numbers
*whole numbers
*integers
Natural Numbers
aka counting numbers
ex: 1, 2, 3, 4, …
Whole Numbers
The natural numbers and zero
ex: 0, 1, 2, 3, 4, …
Integers
The set of whole numbers and their opposites
ex: …-4, -3, -2, -1, 0, 1, 2, 3, 4…
Rational Numbers
A number that can be written as a/b, where a and b are integers and b doesn’t equal 0.
includes fractions, repeating/terminating decimals
ex: -1/4, 6/5, .0324, -3.272727
Irrational Numbers
non-terminating and non-repeating decimals Can’t be written as a/b
ex: 2.34567…,
All numbers that are not rational are irrational
Rational or Irrational?
1. -7.2
2. 1.004
3.
4.
5.
36
1.18
9
rational
rational
rational
rational
irrational
Absolute Value
The distance a number is from 0
= 8
= 0
= 4
= -10
8
0
4
10
Comparing/Ordering Rational Numbers
Write all numbers in the same form (all decimals, all fractions, or all percents)
EX. Order the numbers from greatest to least
2 1 14, , 25%, 1.5, 3 , -0.3, -2
3 2 4
.6 .25 3.5 2.25
1 2 13 , 1.5, , 25%, -0.3, -2 , -4
2 3 4
Adding Signed (+/-) numbers
1. When numbers being added have the same sign, add the numbers and write the sign with the answer
EX. 15 + 7 = 22 (-15) + (-7) = -22
2. When numbers being added have different signs:
-subtract the absolute values of the numbers
-use the sign of the number with the higher absolute value.
EX. -15 + 7 = -8 (-7) + 15 = 8
Subtracting Signed numbers
Add the opposite
Ex. -15 – 7 = -22
Multiplying/Dividing signed numbers
If there are an even number of (-), then the answer is (+)
EX. (-2)(3)(-4)
If there are an odd number of (-), then the answer is (-)
EX. (-2)(-3)(-4)
= 24
= -24
Adding/Subtracting Fractions
Must have a common denominator
1 3
45
6
12
3
12
10
13 13 = 4
12 12
Multiplying fractions
Must write as improper fraction Multiply the numerators Multiply the denominators
36 9 4 = = 1
20 5 5
Dividing Fractions
Write as improper fractions “When you have 2 fractions and you want to divide,
flip the second fraction and multiply.”
1 13 2
2 3
7 7
2 3
21 3 1 = = 1
14 2 2
Adding/Subtracting Decimals
Line up the decimals Add/subtract as normal Write the decimal point in the answer
Multiplying Decimals
Multiply as normal (ignore the decimals) Count how many spaces over you need to
place the decimal point in the answer
Dividing Decimals
If the divisor (outside the house) has a decimal point in it, then you have to move the decimal to the end.
Move the decimal point in the dividend (inside the house) the same number of places.
3.72 15.2
372 1520