Basic Operations of Arithmetic

 

 

Addition

 

                        Addend

             

+                      Addend

_________

                     

                        Sum  

 

 

Subtraction

 

 

                        Minuend

             

-                       Subtrahend

_________

                     

                        Difference

 

 

Multiplication

 

                        Factor

             

x                      Factor

_________

                     

                        Product

 

 

Division

 

                           

                  Quotient              

Divisor     Dividend                     Dividend   = Quotient

                                                     Divisor

                                                            

                                                     Dividend ¸ Divisor = Quotient

 

 

Tests for Divisibility

 

 

Number

Rule for Divisibility

1

Every number is divisible by 1

2
The last digit of the number can be divided by 2

4

The last two digits of the number can be divided by 4

8

The last three digits of the number can be divided by 8

5

The last digit is 5 or 0

10

The last digit is 0

3

The sum of the digits of the number can be divided by 3

6

The number can be divided by 2 and 3

9

The sum of the digits of the number can be divided by 9

 

 

Prime Numbers

 

A prime number is an integer greater than 1 whose only whole number factors are itself and 1.  The following is a list of the first 100 prime numbers.

 2                                 101                              233                              383

 3                                 103                              239                              389

 5                                 107                              241                              397

 7                                 109                              251                              401

11                                113                              257                              409

13                                127                              263                              419

17                                131                              269                              421

19                                137                              271                              431

23                                139                              277                              433

29                                149                              281                              439

31                                151                              283                              443

37                                157                              293                              449

41                                163                              307                              457

43                                167                              311                              461

47                                173                              313                              463

53                                179                              317                              467

59                                181                              331                              479

61                                191                              337                              487

67                                193                              347                              491

71                                197                              349                              499

73                                199                              353                              503

79                                211                              359                              509

83                                223                              367                              521

89                                227                              373                              523

97                                229                              379                              541

 

 

Fractions, Decimals, and Percent

 

Fractions

 

Numerator

Denominator

 

Reciprocal                              Flip the fraction

Mixed number                        A whole number and a fraction

 

To multiply fractions:             Cross cancel

                                                Multiply

To divide fractions:                Copy fractions

                                                Flip the second fraction (reciprocal)

                                                Cross cancel

                                                Multiply

 

 

Equivalents

 

 

Percent

Fraction

Decimal

100 %

1 whole

1.0

50 %

½

0.5

25 %

¼

0.25

75 %

¾

0.75

10 %

1/10

0.1

20 %

1/5

0.2

30 %

3/10

0.3

40 %

2/5

0.4

60 %

3/5

0.6

80 %

4/5

0.8

1 %

1/100

0.01

2 %

1/50

0.02

4 %

1/25

0.04

5 %

1/20

0.05

150 %

1 ½

1.5

250 %

2 ½

2.5

125 %

1 ¼

1.25

33 1/3 %

1/3

0.333

66 2/3 %

2/3

0.666

 

To change from a fraction to a percent:

Divide the numerator by the denominator.


To change a fraction to a percent:

Multiply by 100%.


 


To change a decimal to a fraction:

Read the number.  Write what you read and simplify.


 


To change a decimal to a percent:

Multiply by 100%.

62.4 = 6240%

62.4 x 100% = 6240%

 

To change a percent to a fraction:

Divide by 100% and simplify.


 


To change a percent to a decimal

Divide by 100%.


 



Study Guide for Equations

 

1.                  Get variables together and numbers together.

2.                  What you do to one side of the equation, you also must do to the other side of the equation.

3.                  Solve equations by using the inverse (opposite) operation.

4.                  Check all equations by substitution.

 

If equation is:

Solve by:

Addition

Subtraction

Subtraction

Addition

Multiplication

Division

Division

Multiplication

 


 

 



Word Problems

 

 

Word Problem Key Words

 

Sum:  total, together, after, joined

 

Difference:  profit, before, minus, comparisons: more than, less

 

Product:  of, times, double

 

Quotient:  each, average

 

 

Word Problem Thinking Patterns

 

Some                                   if missing, subtract

+Some more                        if missing, subtract

Total

 

 

Some                                   if missing, add

-Some went away                if missing, subtract

What’s left                           if missing, subtract

 

 

Larger                                   Later (in time)

-Smaller                                 -Earlier                                  

Difference                              Difference

 

 

Part

          +Part

          Whole

Measurement

 

 

 

Time:                                                    Weight:                                                   

 

1 minute = 60 seconds                                    1 lb = 16 oz

1 hour = 60 minutes                                        1 ton = 2000 lb

1 day = 24 hours

1 year = 12 months                                          Length:

1 year = 365 days                                  

1 leap year = 366 days                                    1 foot = 12 inches

1 decade = 10 years                                         1 yard = 3 feet

1 score = 20 years                                                       = 36 inches

1 century = 100 years                                       1 mile = 5280 feet

                                                                                     =1760 yards

 

 

Metric Conversions:

 

10 millimeters = 1 centimeter

100 centimeters = 1 meter

1000 millimeters = 1 liter

1000 meters = 1 kilometer

1000 grams = 1 kilogram

 

1 inch = 2.54 centimeters

 

Liquids:

 

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 oz

1 pint = 16 oz

3 teaspoons = 1 tablespoon


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