Summer 2009
I am anxioulsy awaiting a chance to go see Transformers and can’t wait to see the new Harry Potter. I have been totally relaxing and reading a book or two. Did you see that Suton went 50th in the draft? What have the rest of you been up to?
Our Multiplication and Division Integer Algorithm
1. Look at the problem to see if the numbers are positive or negative.
2. If you are multiplying a positive and a negative then you multiply as usual and the answer will be negative.
3. If you are multiplying two negatives then you multiply as usual and the answer will be positive.
4. If you are dividing a positive and a negative then you divide as usual and your answer will be negative.
5. If you are dividing two negatives then you divide as usual and your answer will be positive.
+ x + = + + ÷ + = +
+ x - = - + ÷ - = -
- x + = - - ÷ + = -
- x - = + - ÷ - = +
Our Subtraction of Integers Algorithm
Our Subtraction of Integer Algorithm
1. Look at the problem to see what numbers are positive and negative.
2. If you are subtracting a positive, then you can rewrite it as adding a negative.
Ex. 3 – 5= 3 + -5 -6 – 3= -6 + -3
3. If you are subtracting a negative, then you can rewrite it as adding a positive.
Ex. 5 - - 4= 5 + 4 -7 - -3= -7 + 3
4. Solve the problem using your addition algorithm. (See below)
Subtracting a Positive = Adding a Negative
Subtracting a Negative = Adding a Positive
We also discussed in class an alternative way to think about subtracting integers-
If both signs are the same, find the difference between the two numbers, and then if the second number is bigger than the first your answer will be negative.
Ex. -5 - -6= 1 7 – 9 = -2 4 – 2= 2
If the signs are different, add the absolute value of the numbers, and then the sign of the first number becomes the sign of your answer.
Ex. 5 - -6= 11 -6 – 4 =-10
Adding Positive & Negative Numbers
Our Addition of Integer Algorithm
1. Look at the problem to see which numbers are positive and negative.
2. If both numbers have the same sign, add the two numbers together and then put the same sign on your answer.
Ex. 3+ 4 =7 -2+ -7= -9
3. If both numbers have different signs, subtract the two numbers and then the sign of the number that is furthest away from zero will be the sign of your answer.
Ex. -7 +5= -2
Dividing Decimals Algorithm
Dividing Decimals Algorithm
1. Look at the problem to see where the decimals are located.
2. Move the decimal in the divisor to make it into a whole number.
3. Move the decimal in the dividend the same number of times as you did in your divisor.
4. Put the decimal in my answer (quotient), based on where it is in the dividend.
5. Divide the problem.
Shapes & Designs
We have switched gears and are taking a much needed break from fractions to learn about Geometry. We have been writing many vocabulary words and today we took some notes about special triangles and quadrilaterals.
Equilateral Triangles= all sides are equal and all angles are equal.
Isosceles Triangle= two sides are equal and two angles are equal.
Scalene Triangle= no sides are equal and no angles are equal.
Square= all sides are equal and all angles are 90 degrees.
Rectangle= opposite sides are equal and all angles are 90 degrees.
Parallelogram= opposite sides are equal & parallel and opposite angles are equal.
Rhombus= all sides are equal.
Trapezoid= has at least one set of parallel sides.
So a square is also a rectangle, parallelogram, rhombus and a trapezoid.
Our Fraction Division Algorithm Using Common Denominators
2nd & 3rd hour 2008
1) Look at the problem to see if there are whole numbers and/or mixed numbers.
2) Change whole numbers and/or mixed numbers to improper fractions.
ex. 3 2/3= 11/3 or 5= 5/1
3) Change the fractions to equivalent fractions with the same denominator.
ex. 9/1 divided by 4/5= 45/5 divided by 4/5=
4) Divide the 1st numerator by the second numerator ( 1st numerator is the numerator of your answer and the 2nd numerator is the denominator of your answer).
ex. 45/5 divided by 4/5= 45/4
5) Simplify your answer.
ex. 45/4= 11 1/4
Our Fraction Division Algorithm Using Reciprocals
2nd& 3rd hr 2008
1) Look at the problem for mixed numbers and/or whole numbers.
2) Change mixed numbers and whole numbers to improper fractions
ex. 3 2/3= 11/3 and 5=5/1
3) Change the second fraction to its RECIPROCAL and change the problem to a multiplication problem.
ex. 5/6 divided by 12/1= 5/6 x 1/12
4) Multiply the fractions- numerator by numerator and denominator by denominator
ex. 5 x 1= 5 and 6 x 12 =72 so your answer would be 5/72
5) Simplify the answer if needed.
3rd hour’s Fraction Multiplication Algorithm
1. Look at the problem to see if there are any mixed numbers or whole numbers.
2. If there are mixed numbers and/or whole numbers then change them to improper fractions.
Ex. 2 2/3 =8/3 or 4= 4/1
3. Now you can solve the problem by taking the numerator x numerator to get your answer’s numerator.
Ex. 3/4 x 5/1= 15/
4. Next take the denominator x denominator to get your answer’s denominator.
Ex. 3/4 x 5/1= 15/4
5. SIMPLIFY!!
Ex. 15/4 =3 3/4
2nd hour’s Fraction Multiplication Algorithm
1. Look at the problem to see if there are any mixed numbers or whole numbers.
2. If there are mixed numbers and/or whole numbers then you need to change them to improper fractions.
Ex. 2 1/3 =7/3 or 4= 4/1
3. You can then solve your problem by taking the numerator x numerator to get the numerator of your answer.
Ex. 2/3 x 7/1= 14/
4. Next you multiply the denominators to get the denominator of your answer.
Ex. 2/3 x 7/1= 14/3
5. SIMPLIFY!!
Ex. 14/3 =4 2/3
