Divisibility Rules

Divisibility Rules

A number is divisible by …

• 2, if the ones digit is even (0, 2, 4, 6, 8)

–Example: 58 because there is an 8 in the ones place


• 3, if the sum of its digits is divisible by 3

–Example: 81 because 8 + 1 = 9 and 9 is divisible by 3


• 4, if the last 2 digits are divisible by 4

–Example: 832 because 32 is divisible by 4


• 5, if the ones digit is a 0 or a 5

–Example: 1025 because there is a 5 in the ones place


• 6, if the number is divisible by 2 AND 3

–Example: 48 • There is an 8 in the ones place so it is divisible

by 2• 8 + 4 = 12 and 12 is divisible by 3, so 48 is

divisible by 3


• 9, if the sum of the digits is divisible by 9

–Example: 468 because 4 + 6 + 8 = 18 and 18 is divisible by 9


• 10, if the ones digit is a zero–Example: 2010 because the ones digit is a 0


• 10, if the number ends in zero–Example: 50 because the number ends in zero

Fractions

• To simplify fractions – you need to find the greatest common factor of the numbers–Use your divisibility rules to help you –Example:

3

2

36

24

• Equivalent Fractions: are fractions that have the same value OR simplify to the given fraction

–Example: both fractions reduce to 18

12

15

10

3

2

• To simplify fractions – you need to find the greatest common factor of the numbers–Use your divisibility rules to help you –Example:

3

2

36

24

Improper Fractions &

Mixed Numbers

Improper Fractions

• An Improper Fraction is one where the numerator is larger than denominator

Convert Improper Fractions to Mixed Numbers

• To convert and improper fraction into a mixed number follow these 3 steps:1. .Divide the numerator by the denominator2. Turn your remainder into a fraction3. Reduce your fraction to simplest form

Examples1. .

2. .

3. .

4. .

6

17

2

9

6

39

8

15

2

14

6

52

2

16

8

71

Mixed Numbers

• A mixed number is a special fraction that has a whole number and a fraction

Convert Mixed Numbers to Improper Fractions

• To convert and improper fraction into a mixed number follow the recycling method:1. .Multiply the denominator by the whole number2. .Add the numerator to the product found in

previous step.3. Place the sum found in Step 2 over the old

denominator in your mixed number

Use the “Recycling Method” to help us with this…

1. .

2. .

3. .

4. .

3

25

6

52

2

11

5

38

6

17

3

17

2

3

5

43

• We can also remember to not get M.A.D. when we have to convert mixed numbers to improper fractions…..

M ultiplyAddDenominator (keep same one)

Adding &

Subtracting.

Fractions

1. Fractions need to have common denominators in order to add or subtract them. If they do skep to step #3

2. To get common denominator: find lowest common denominator (LCD)

3. Create equivalent fractions with he least common denominator (LCD)

4. Add or subtract the numerators. Then add or subtract the whole numbers (if they are mixed numbers)

5. For some subtraction problems you may need to borrow one whole in order to subtract. Do this and write the fraction as an improper fraction

6. .Write your fraction with the common denominator answer

7. .Reduce your answer to simplest form (if your solution is an improper fraction, make it into a mixed number)

Examples1. .

2. .

3. .

4. .

5. .

6. .

7. .

18

11

18

7 1

12

7

12

2

12

11

25

21

12

2

18

174

30

1115

12

21

211

10

31

12

113

5

4

25

7

7

36

3

24

18

135

3

210

10

76

3

14

5

23

Multiplying &

Dividing.

Fractions

1. If the fractions are mixed numbers, make them into improper fractions

2. To divide you must Keep, Switch, Flip. Keep the first fraction, Switch the multiplication sign to division, Flip the other fraction to its reciprocal

3. You cross simplify to make it a simpler problem

4. Multiply the numerators and then multiply the denominators

5. .Reduce your answer to simplest form (if your solution is an improper fraction,

make it into a mixed number)

Examples1. .

2. .

3. .

4. .

5. .

6. .

7. .

8. .

9. .

4

115

4

33

10

7

9

2

55

9

45

74

31

5

419

153

4

28

179

4

15

11

25

3

18

5

9

77

7

42

2

14

9

7

7

2

5

24

3

44

12

15

9

127

14

14

3

22

5

3

285

32

Fractions Decimals

Convert Decimals to Fractions

• Write the decimal the way you say it.

– Example: 0.25 “Twenty-five hundredths

• Reduce the fraction to simplest form.

– Example:

100

25

100

25

4

1

Convert Fractions to Decimals

• Divide the numerator by the denominator.

• Use long division.

• Check with your calculator.

– Example: 11

218.

Examples1. .

2. .

3. .

4. .

5. .

6. .

7. .

8. .

9. .

10. .

11

22.0

100

37

375.4

03.7 5

4

10

8

50

19

6.0

8.6

3

2

100

99

5

46

8.0

38.0

8

34

99.0502.0

500

251

1000

502

81.0

100

81

Rational Numbers

Rational Numbers• Rational Numbers terminate or repeat.–How do we know if a number is terminating or

repeating number? Convert the number to a decimal.

–Terminating numbers are numbers that end or stop.

• Example: 0.75, 2,

–Repeating numbers are numbers that have a repeating pattern.

• Example:11

2

,8

55

33

,3

2,18.0

Examples1. .

2. .

3. .

4. .

5. .

6. .

7. .

8. .

6

2

44

5

10

Terminating Repeating

Neither

3

2

Terminating

TerminatingTerminating

55

21 Repeating

Neither

Documents

Divisibility Rules