Finding the percent of a number
Ok, so we all know that a percent is a ratio that compares a number to 100. A percent is part of the whole that is 100. So, if you took a test that had 100 questions on it and you got 78 of them right, you got a 78/100. Or a 78%. You can find percents of numbers when you are given certain information. Let's look at some examples:
I like to use this proportion:
IS %
____ = _____
OF 100
I have the parts color-coded for a reason.
If you are asked to find what is 70% of 93, you can put this information into a proportion to find the amount.
WHAT IS 70% OF 93?
What is is in red because we don't know what 70% of 93 is. Therefore our is will be x. 70% is in purple because it has a percent sign next to it. OF 93 is in blue because the 93 is next to the word of. So now we are going to fill the numbers in the proportion and solve for x.
X 70
____ = _____
93 100
This problem is the same as saying 70 out of 100 is equal to what number out of 93?
Cross multiply and divide by 100 to find the missing number.
100X = 93 x 70
100X = 6510 Divide by 100.
100X = 6510
______ ______
100 100
X= 65.1
So, 65.1 is 70% of 93.
I like to use this proportion:
IS %
____ = _____
OF 100
I have the parts color-coded for a reason.
If you are asked to find what is 70% of 93, you can put this information into a proportion to find the amount.
WHAT IS 70% OF 93?
What is is in red because we don't know what 70% of 93 is. Therefore our is will be x. 70% is in purple because it has a percent sign next to it. OF 93 is in blue because the 93 is next to the word of. So now we are going to fill the numbers in the proportion and solve for x.
X 70
____ = _____
93 100
This problem is the same as saying 70 out of 100 is equal to what number out of 93?
Cross multiply and divide by 100 to find the missing number.
100X = 93 x 70
100X = 6510 Divide by 100.
100X = 6510
______ ______
100 100
X= 65.1
So, 65.1 is 70% of 93.
integers!
Adding and subtractingWhen adding positive integers, ummm, YOU KNOW HOW TO DO THAT ALREADY!!
When adding negative integers, add the absolute values, AND KEEP NEGATIVE! -7 + (-9) = -16 -100 + (-5) = -105 When adding integers with different signs, subtract the smaller absolute value from the larger, and keep the sign of the integer with the most power (larger absolute value or farther from 0). 10 + (-6) = 4 -29 + 13 = -16 When subtracting integers, KCO (keep, change, opposite), then follow the addition rules. Subtraction is the same as adding the opposite. It will give you the same result. For example: 10 - 8 =2 IS 10 + (-8) = 2 K C O 59 - (-10) = 69 IS 59 + 10 = 69 K C O -86 - (-20) = -66 IS -86 + 20 = -66 K C O |
Multiplying and dividingWhen the signs are the same, the product or quotient will be positive.
POSITIVE X POSITIVE = POSITIVE NEGATIVE X NEGATIVE = POSITIVE The same goes for division. When the signs are different, the product or quotient will be negative. POSITIVE X NEGATIVE = NEGATIVE NEGATIVE X POSITIVE = NEGATIVE The same goes for division. |
operations with rational numbers
Remember: rational numbers are numbers that can be written as ratios (like fractions). The denominator can never be 0 because YOU CANNOT DIVIDE BY 0!
Here are some examples of problems with rational numbers.
ADDING
-3 1/2 + (-2 4/5)
First, change mixed numbers to improper fractions (denominator x whole number + numerator)
-7/2 + (-14/5)
Next, find a common denominator for 2 and 5. This will be 10 because (2, 4, 6, 8, 10 and 5, 10) 10 is the first common multiple. Multiply the numerators by the factor you multiply the denominator by to get 10.
-35/10 + (-28/10)
Now, ignore denominators and handle numerators. Without denominators you will have this problem:
-35 + (-28) The signs are both negative, so just add the absolute values and keep negative.
-63
Now, pop the denominator back in and simplify!
-63/10 which is -6 3/10
SUBTRACTING
Let's use those same rational numbers, but this time we will subtract them. YOU WILL NOT GET THE SAME ANSWER!
-3 1/2 - (-2 4/5)
When subtracting integers we KCO (Keep, Change, Opposite). We do this because adding the opposite will get you the same result and it is easier to follow the addition rules for integers. You can use that handy-dandy number line.
- 3 1/2 + (2 4/5)
K C O
Now, change mixed numbers to improper fractions (denominator x whole number + numerator)
-7/2 + (14/5)
Next, find a common denominator for 2 and 5. This will be 10 because (2, 4, 6, 8, 10 and 5, 10) 10 is the first common multiple. Multiply the numerators by the factor you multiply the denominator by to get 10.
-35/10 + (28/10)
Now, ignore denominators and handle numerators. Without denominators you will have this problem:
-35 + (28)
The signs are different. Take the absolute values, subtract the integers, and keep the sign of the integer that has more power!! Which is -35. The sign will be negative.
-7
Now, pop the denominator back in and simplify!
-7/10 No simplifying needed!!
Here are some examples of problems with rational numbers.
ADDING
-3 1/2 + (-2 4/5)
First, change mixed numbers to improper fractions (denominator x whole number + numerator)
-7/2 + (-14/5)
Next, find a common denominator for 2 and 5. This will be 10 because (2, 4, 6, 8, 10 and 5, 10) 10 is the first common multiple. Multiply the numerators by the factor you multiply the denominator by to get 10.
-35/10 + (-28/10)
Now, ignore denominators and handle numerators. Without denominators you will have this problem:
-35 + (-28) The signs are both negative, so just add the absolute values and keep negative.
-63
Now, pop the denominator back in and simplify!
-63/10 which is -6 3/10
SUBTRACTING
Let's use those same rational numbers, but this time we will subtract them. YOU WILL NOT GET THE SAME ANSWER!
-3 1/2 - (-2 4/5)
When subtracting integers we KCO (Keep, Change, Opposite). We do this because adding the opposite will get you the same result and it is easier to follow the addition rules for integers. You can use that handy-dandy number line.
- 3 1/2 + (2 4/5)
K C O
Now, change mixed numbers to improper fractions (denominator x whole number + numerator)
-7/2 + (14/5)
Next, find a common denominator for 2 and 5. This will be 10 because (2, 4, 6, 8, 10 and 5, 10) 10 is the first common multiple. Multiply the numerators by the factor you multiply the denominator by to get 10.
-35/10 + (28/10)
Now, ignore denominators and handle numerators. Without denominators you will have this problem:
-35 + (28)
The signs are different. Take the absolute values, subtract the integers, and keep the sign of the integer that has more power!! Which is -35. The sign will be negative.
-7
Now, pop the denominator back in and simplify!
-7/10 No simplifying needed!!