Arithmetic Flashcards
Multiplying fractions
multiply numerators by each other and denominators by each other.
Dividing fractions
Flip the numerator and the denominator of the fraction that your dividing by, then multiply.
Adding Fractions
you can add fractions only when they have the same denominator. When you add, add only the numerator, NOT the denominators
What is the common denominator
When you have to find a common number that the numbers in the fraction share in order to add and subtract.
Subtraction fractions
only subtract the numerator with a common denominator.
Reducing Fractions
Whenever there is a common factor in the numerator and denominator, you can reduce the fraction by removing the factor from both parts of the fraction.
Canceling
when ever you have to multiply two or more fractions, you should cancel common factors before you multiply. Similar to reducing.
ex. (1/2)(2/1) = 1/1
Comparing fractions
One way to compare fractions is to re-express them with a common denominator. Or convert them to decimals.
What is a mixed number
consist of an integer and a fraction. For example 1(3/4)
Improper fraction
when the numerator is greater than the denominator.
To convert an improper fraction
to a mixed number, divide the numerator by the denominator. the number of whole times that the denominator goes into the numerator will be the integer portion of the improper fraction. the remainder will be the fraction
Adding and subtracting mixed numbers
first add/ subtract the integer parts, next add/subtract the fractional parts. When subtracting and the mixed number is smaller than the fraction then convert it to an improper fraction. and continue.
Setting up a ratio
to find a ratio put the number associated with the word of on the top and the quantity associated with the word to on the bottom and reduce.
ex. the ratio of 20 oranges to 12 apples is 20/12= 5/3
Part to part ratios and part to whole ratios
if the parts add up to a whole, a part to part ratio can be turned into two part to whole ratios. by putting each number in the original ratio over the sum of the numbers.
ex ratio of males to females is 1 to 2 -> 1/3
Solving a proportion
to solve a proportion, cross multiply
Changing fractions to decimals
divide the denominator of the fraction into the numerator
Changing decimals to fractions
to change decimals to fractions put the digits to the right of the decimal point in the numerator. to figure the denominator we put a 1 in the denominator and followed it with as many zeros as there were digits to the right of the decimal point.
Addition and subtraction of decimals
you add and subtract decimals the same way you add and subtract whole numbers. just make sure the decimal points are lined up.
Multiplication of decimals
multiply decimals as if they were whole numbers and worry about the decimal points later. To place the decimal point in the answer count the number of digits to the right of the decimal point of each number, then place the decimal in the answer of the sum.
Division of decimals
express the division in fractional form. then make both the numerator and denominator a whole number by multiplying it by 10. then divide the denominator into the numerator.
Rounding decimals to nearest place
to round a decimal to the nearest place, look at the digit immediately to the right of that place. if the digit 5 or greater round up. if its 4 or less round down.
Percent
any percent can be expressed as a fraction with the denominator of 100. percent means per one hundred.
convert a percent to a decimal
just drop the percent symbol and divide the number by 100.
percent formula
percent=part/whole
percent x whole=part
percent increase
%increase= amount of increase/original whole(%100)
ex if X is 10% greater than Y then X is 110% of Y
percent decrease
%decrease= amount of decrease/original whole(%100)
ex if X is 70% less than Y, then X is 30% of Y
New whole
new whole= original whole +- amount of change
Averages
to find the average set of numbers , add them up and divide by the number of terms (the number of numbers)
average= sum of the numbers/number of terms
Using the average to find the sum
sum= (average) x (number of terms)
Finding the missing number when given the average
to find a missing number when you’re given the average, use the sum.
ex. If the average of four numbers is 7. then 4 x 7= 28. if the numbers given are 3,5,6 they =14, 28-14= 7. which makes 7 the fourth number.
Probability
the probability of an event is the possible number of desired outcomes divided by the total number of possible outcomes. its numerical value is always less than or equal to one. the probability of two independent events both occurring is the product of the individual probabilities.
