# Multiplying Fractions

**Our Algorithm for Multiplying Fractions**

- Look at the problem to see if there are whole numbers and/or mixed numbers.

2.If there are mixed numbers, then you change them to improper fractions by multiplying the denominator by the whole number and add the numerator to the answer and bring the denominator over.

Ex. 1 2/3 = 5/3

3.If there are whole numbers, then you change it to a fraction with 1 as the denominator.

Ex. 4 = 4/1

4. Multiply the two numerators and the two denominators.

Ex. 5/3 x 4/1 = 20/3

5. Then simplify the answer if needed.

Ex. 20/3 = 6 2/3

# Our Addition & Subtraction Algorithm 2011

**Our Fraction Addition Algorithm**

1) Look at the problem to see if the denominators are the same.

Ex. 1 ½ + 2 2/3 =

2) If the denominators are the same, then add the numerators together and keep the denominators the same.

3) If the denominators aren’t the same, then look to see what the denominator’s common multiple is.

Ex. 1 ½ + 2 2/3 =

4) Change the fractions to equivalent fraction with the same denominator.

Ex. 1 ½ + 2 2/3 = 1 3/6 + 2 4/6

5) Add the numerators and leave the denominator the same.

Ex. 3/6 + 4/6 = 7/6

6) If there are whole numbers, then add them together.

Ex. 1 + 2= 3

7) Combine your fraction answer with your whole number answer.

Ex. 3 7/6

8) Simplify your answer if needed.

Ex. 3 7/6 = 4 1/6

**Our Fraction Subtraction Algorithm**

1) Look at the problem to see if the denominators are the same.

Ex. 3 ¾ – 1 7/8=

2) If the denominators are the same, then subtract the numerators and keep the denominator’s the same.

3) If the denominators aren’t the same, then look to see what the denominators common multiple is.

Ex. 3 ¾ – 1 7/8=

4) Change the fractions to equivalent fraction with the same denominator.

Ex. ¾ – 7/8= 6/8 – 7/8

5) If the second fraction is larger than the first fraction then you need to borrow from the whole number.

Ex. 3 6/8 – 1 7/8= 2 14/8 – 1 7/8=

6) Subtract the numerators and leave the denominators the same.

Ex. 14/8 –7/8= 7/8

7) Subtract the whole numbers if there are any.

Ex. 2-1= 1

8) Combine your fraction answer with your whole number answer.

Ex. 1 7/8

9) Simplify your answer, if needed.

Ex. 1 7/8

# Order of Operations

**Order of Operations**

1) Parentheses ()

2) Exponents 4²

3) Multiplication/Division (from left to right)

4) Addition/Subtraction (from left to right)

Please Excuse My Dear Aunt Sally

Examples:

1) 2 + 3 x 6=

2) 3² + 5 – 7=

3) (19-5) ÷2=

4) 13 + 5² x 4=

# Divisibility Rules

**Useful Divisibility Rules**

**A number is divisible by 2 **if it is an even number.

**A number is divisible by 3 **if the sum of its digits are divisible by 3.

**A number is divisible by 4 **if its last two digits are divisible by 4.

**A number is divisible by 5 **if its last digit (ones place) is a zero or a five.

**A number is divisible by 6 **if it is divisible by both 2 and 3.

**A number is divisible by 9 **if the sum of its digits is divisible by 9.

**A number is divisible by 10 **if its last digit is a zero.

# Prime Time Notes

We are half way through our first book. There has been alot of vocabulary to keep track of so we came up with some notes to help us keep everything straight.

6 x 7 =42 6 & 7 are **factors **& **divisors **of 42.

42 is a **multiple** & a **product **of 6 & 7.

You can find the factors of a number by finding the numbers you multiply to get that number.

Ex. Factors of 30 are

1 x 30

2 x 15

3 x 10

5 x 6

This is the turn-around point.

**Common Factors** of 14 & 32

14- **1, 2**, 7, 14 1 & 2 are the common factors of 14 & 32

32- **1, 2,** 4, 8, 16, 32 **GCF (greatest common factor)** = 2

You can find the **multiples** by multiplying the number by other numbers.

Ex. Multiples of 6

6 (6×1), 12 (6×2), 18 (6×3), 24 (6×4), 30 (6×5) …

**Common Multiples** of 6 & 15

6- 6, 12, 18, 24, **30,** 36, 42, 48, 54, **60** …

15- 15, **30**, 45, **60**, 75, 90 …

30 & 60 are the common multiples of 6 & 15

**LCM (least common multiple)** = 30

**Prime vs. Composite**

A number cannot be both prime & composite.

A **prime number** has only 1 and itself as factors.

Ex. 2, 3, 5, 7, 11, 13 …

A **composite number** is number with more than two factors.

1 isn’t prime or composite. It is a special number.

2 is the only even number that is prime.

**Square Numbers**

**Square numbers** are numbers that have odd number factors because one of the factors is multiplied by itself.

Ex. 1 (1×1), 4 (2×2), 9 (3×3), 16 (4×4) …

# Our Addition and Subtraction Decimal Algorithm

1) Look at the problem.

Ex. 1.23 + 4.5= & 4.6 – 2.7=

2) Write the problem vertically and line up the decimals.

Ex. 1.23 4.16

+ 4.5 – 2.7

3) Add any zeros to hold place value if needed.

Ex. 1.23 4.16

+ 4.50 – 2.70

4) Add/Subtract right to left

Ex. 1.23 4.16

+ 4.50 – 2.70

5.73 1.46

5) Borrow if needed- see the second problem above.

# Our Fraction Division Algorithm

Our Fraction Division Algorithm w/ Common Denominators

1) Look at the problem to see if there are whole numbers and/ or mixed numbers.

Ex. 1¾ ÷ 2/3=

2) If there are whole numbers and/or mixed numbers then change them to an improper fraction.

Ex. 1¾ ÷ 2/3= 7/4÷2/3

3) Then change the fractions to common denominators.

Ex. Ex. 7/4÷2/3= 21/12 ÷ 8/12

4) Ignore the denominators and divide the first numerator by the second numerator- 1st numerator/2nd numerator

(You ignore the denominators because you are dividing a number by itself and that is equal to one.)

Ex. 21/12 ÷ 8/12= 21÷8 =21/8

5) Simplify your answer.

Ex. 21/8 = 2 5/8

# Long Division- the old school way

Many of the students have been struggling with division and want to learn what I call the old school way to divide. Even though I have been trying everyday to help them some of them are still not getting it so I foudn this link that they can go to that might help them.

http://www.wisc-online.com/objects/ViewObject.aspx?ID=ABM1001

Let me know if this helps.

# Our Dividing Fraction Algorithm- Reciprocal

- Look at the problem and then change any whole numbers and/or mixed numbers to an improper fraction.

2. Change the second fraction to its reciprocal and the division sign to a multiplication sign.

Ex. ½ / ¾ = ½ x 4/3 =

3. Multiply across.

Ex. 1 x 4 and 2 x 3

4. Simplify if needed.