Download “Helpful Hints”

Summer Math
“Helpful Hints”
Place Value and Rounding Tips:
When asked to round a number, please underline the number in that place value. Then look to its right – if the number
to its right is a 5 or greater, then the number you underlined will go up one; if the number to its right is less than 5, then
the number you underlined will stay the same. http://www.math.com/school/subject1/lessons/S1U1L3GL.html
Adding and Subtracting with Decimals Tips:
Rule: LINE UP YOUR DECIMALS!!! You must put zeroes above or below “lonely” digits when subtracting.
Examples:
a.)15.7 + 6.3 = 15.7
+ 6.3
22.0
b.) 9.3 – 2.56 =
9.30
-2.56
6.74
Dividing a decimal by a whole number:
RULE: Decimal goes straight up to the quotient (answer).
EXAMPLE:
24.03
2|48.06
Dividing by a Decimal:
Example: click here http://www.math.com/school/subject1/lessons/S1U1L6GL.html
Multiplying Decimals: http://www.math.com/school/subject1/lessons/S1U1L5GL.html
Practice with Decimals: http://aaamath.com/dec.htm
Integer Tips:
http://www.math.com/homeworkhelp/HotSubjects_integers.html
INTEGERS
RULE!
Addition & Subtraction
- If the signs are alike, add and take that sign.
- If the signs are different, subtract and take the sign of the “bigger” number.
- If you have "double negatives" then you must circle the negatives and change the sign to a
plus sign. (like: 5 – -3 will become 5 + 3)
Examples: -2 + -3 = -5
+
4 +
+
3 = +7
+
6 + -2 = +4
Examples: -6 – -3 becomes -6 + +3 which equals: -3
Multiplication & Division
-
Multiply or Divide like normal.
When you get your answer, THEN you decide if the answer will be positive or negative
If the signs are alike, your answer will be positive.
If the signs are different, your answer will be negative.
Examples:
-5(+2) = -10
-4
2 = -2
-2(-3) = +6
-10
-5 = 2
Integer Practice: http://aaamath.com/alg.htm
(-5)2 = +25
How to Add and Subtract Positive and Negative Numbers
If a number has no sign it usually means that it is a positive number.
Rule
Example
+(+)
3+(+2) = 3 + 2 = 5
−(−)
6−(−3) = 6 + 3 = 9
+(−)
7+(−2) = 7 − 2 = 5
−(+)
8−(+2) = 8 − 2 = 6
Two like signs become a positive sign
Two unlike signs become a negative sign
If both numbers are positive or both numbers are negative, add and keep the sign.
If one number is positive and the another number is negative:
If the positive number is larger, subtract the numbers, and then put the positive sign in front of the result. For example,
-3 - - 8 = ?. You would convert the problem to – 3 + 8 = ? The result would be +5.
If the negative number is larger, subtract the numbers and then put the negative sign in front of the result. For
example, + 3 + -5 = ? You would convert the problem to +3 – 5 = ? Subtract 3 from 5 to get 2, then add a negative sign
for your result: -2.
Example: What is 5+(−2) ?
+(−) are unlike signs (they are not the same), so they become a negative sign.
5+(−2) = 5 − 2 = 3
Example: What is 25−(−4) ?
−(−) are like signs, so they become a positive sign.
25−(−4) = 25+4 = 29
Example: What is −6+(+3) ?
+(+) are like signs, so they become a positive sign.
−6+(+3) = −6 + 3 = -3
How to Multiply and Divide Positive and Negative Numbers
***** Here Are The Rules *****
You multiply or divide integers just as you do whole numbers, except you must keep track
of the signs.
If the signs are the SAME, then the answer is POSITIVE.
If the signs are DIFFERENT, then the answer is NEGATIVE.
Example: What is - 25 . (−4) ?
−(−) are like signs, so they become a positive sign.
−25 x (−4) = +100
Example: What is +5
.
(−2) ?
+(−) are unlike signs (they are not the same), so they become a negative sign.
+5 x (−2) = -10
Example: What is (−6)
.
+3 ?
− (+) are unlike signs, so they become a negative sign.
(−6) x +3 = −18
Example: What is - 35 . (−7) ?
−(−) are like signs, so they become a positive sign.
−35 ÷ (−7) = +5
Example: What is +50 ÷ (−2) ?
+(−) are unlike signs (they are not the same), so they become a negative sign.
+50 ÷ (−2) = -25
Example: What is (−6) ÷ +3 ?
− (+) are unlike signs, so they become a negative sign.
(−6) ÷ +3 = -2
Order of Operations-PEMDAS Tips:
http://www.math.com/school/subject2/lessons/S2U1L2GL.html
Do the operations in parentheses first.
Solve any exponents that may be in the problem
Then multiply or divide from left to right.
Then add or subtract from left to right
Parentheses
Exponents
Multiply
Divide
Add
Subract
Please Excuse My Dear Aunt Sally
One and Two-Step Equation Tips: Do the inverse operation to get a variable by itself
Examples:
http://www.math.com/school/subject2/lessons/S2U3L1GL.html
Practice:
http://aaamath.com/equ.htm
Fraction Tips:
Multiplying Fractions:
RULE: Multiply the numerators and the denominators straight across
Example: http://www.math.com/school/subject1/lessons/S1U4L4GL.html
**Shortcut** sometimes you can “cross simplify” before you multiply! This will give you small numbers to work with.
Example: http://www.math.com/school/subject1/lessons/S1U4L4EX.html
Dividing Fractions:
RULE: Multiply by the reciprocal (multiplicative inverse).
In middle school language:
Step 1: Change the sign to “times”
Step 2: Flip the back fraction over
Step 3: multiply straight across
Example: http://www.math.com/school/subject1/lessons/S1U4L8GL.html
Adding and Subtracting Fractions:
RULE: You MUST have common denominators BEFORE you can add or subtract. Once you have common denominators,
only add or subtract the numerators (your denominator will stay the same)
Question to ask yourself:
Do I have common denominators?
IF YOU ANSWERED YES,
simply add or subtract the numerators,
the denominator will stay the same
IF YOU ANSWERED NO,
1.) Find a common denominator (you can
multiply the denominators that you have
to get a common denominator)
2.)To get new numerators, multiply by the
number that can be multiplied to make
the denominators a true statement
(whatever you do to the
bottom, you do to the top)
EXAMPLE:
http://www.math.com/school/subject1/lessons/S1U4L3GL.html