numbers & operations

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