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) …
Improper Fraction to Mixed Number
We have been learning how to change a mixed number to an improper fraction and from an improper fraction to a mixed number. For example, 13/7 = 1 6/7. 7 goes into 13 1 whole time with 6 left over, so 1 is your whole number 6 is your numerator and 7 stays as your denominator. Here is another example, 3 2/3 =11/3 because 3/3 equals 1 whole so 9/3 equals 3 wholes, then you add the numerator to 9 and that answer becomes your numerator and the denominator stays the same.
They all received notes to put in their binders so they can do this in the future.
Equivalent Fractions
Knowing how to find an equivalent fraction is extremely important.
Equivalent fractions are fractions that look different but are equal. For example, 1/2=2/4.
We have been working with our fraction benchmarks to help us understand equivalent fractions. Some of our benchmarks include- 1/2, 1/4, 1/3, 3/4, 2/3, 0 & 1.
3/4 x 2/2= 6/8
