FDP Flashcards
When should you use decimals or percentages? When should you use fractions?
Fractions for multiplication and division, decimals and percents for everything else
D& P= for addition, subtraction, estimations and comparing numbers
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What are digits? integers? non integers?
digits: 0-9 inclusive
integers: counting #s (whole #s) can be - or +. Can be classified by # of digits they contain
nonintegers: non counting #s, have a decimal or fraction
Name the place value of each digit: 452.87168
4- hundreds, 5- tens 2-ones 8-tenths 7-hundredths 1- thousandths 6-ten thousandths 8- hundred thousandths
round 892.1624 to each nearest digit
digit 5 or greater round next number up. if lower, leave
simplify: .876x10^3
87. 423x10^10
what are the rules for multiplying and dividing?
876, 874230000000
multiplying by positive powers moves dec to right, dividing moves it to the left
neg powers: multiplying moves left, dividing moves to the right
how do you multiply decimals quickly?
.0003 x 40000
move decimals of each number but in opposite direction to get answer (12).
what is the divisor and what is the dividend?
divisor- one outside of division sign
dividend- the number that is being divided.
How do you perform the strategy of testing cases for data sufficiency?
- What possible cases are allowed? Read facts in question, and ask what would make the statement sufficient.
- Choose numbers for the first statement that make the first statement true. Solve, then answer the question
- Try to prove the statement insufficient by testing another number.
If in a value question you get a different value then it is insufficient. In a yes/no question sometimes yes and sometimes no=insufficient
Make sure to test numbers with diff properties: e.g. odd, even, prime, zero, negative, or a fraction
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what are proper fractions? improper?
Proper fractions are between -11 can be negative.
Improper are greater than 1, can be written as mixed numbers. can also be negative
When is a fraction’s value increasing? when is it decreasing?
positive fractions: when the numerator is increasing and denom stays the same.
decreasing when denominator increases while the numerator stays the same.
How do you multiply fractions?
multiply tops and multiply bottoms. simplify before you multiply
How do you add fractions?
find a common denominator, add top number only
how do you divide fractions?
use reciprocal of the divisor to multiply
How do you divide double decker fractions e.g. (1/2)/(3/4)
Double decker dividing: change fraction sign into a division sign and multiply by reciprocal
or multiply by common denominator
((1/2) x 4)/ ((3/4)4)= 2/3
How do you compare fractions?
Which is greater: 7/9 or 4/5
Cross multipliy and have the value next to the numerator of that value:
7/9 CM 4/5
7x5=35
4x9=36
How do you simplify complex fractions: (15+10)/5
do not split the denominator. Simplify the fraction first. You can Split the numerator
How do you know when two fractions are reciprocals?
multiply them, they should equal 1.
How do you make multiplying by percents easier?
7% of 50?
Split the percents out into 50, 10, 5 and 1% of original number to make it easier or use fractions.
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what do you think when you see “What is the price change?”
Percent change= change in value/original value Always think of the original value as 100%.
Increased by 10%, then new price is 110% of original.
If you decrease, subtract the decrease from from 100 to get the new price.
How do you solve a Successive Percent change problem?
Calculate each change separately.
percents cannot be added together first. Pick a number (100 for the price).
OR multiply the percentages together .
How do you solve compound interest problems?
What does the total amount equal?
Total amount= P(1+(r/n))^nt P= principal n=number of times a year r=rate (decimal) t= number of years
some can be solved as successive percent problems
How do you double a ratio?
Top is multiplied by 2, bottom stays the same.
When should you use smart numbers?How do you solve PS problems with Smart Numbers?
- If the problem talks about a number but never supplies a value for it in the problem or unknown and you have to pick a variable- they can be turned into an arithmetic problem instead with a smart number.
- Have a percentage, fraction or decimal in the answer
- Choose smart numbers to replace the unknowns
- Solve the problem using your chosen smart numbers: 100 is a good number for percent problems.
- Find a match in the answers. use the smart number in the answer choices and if the answer comes out is a match to the answer in which you solved then you have the correct answer.
Which smart numbers should you choose when dealing with a fraction problem?
Choose the smallest common denominator of the fractions given.
How do you solve smart number problems with variables?
- Choose SN for each variables. if they are not connected, youll need to pick more than one.
- Solve
- Find a match in the answers
What are the guidelines for choosing SN?
Do not pick 0 or 1.
Do not pick numbers that appear elsewhere
IF you have to choose multiple numbers, choose different numbers, with different properties.
What is an unknown multiplier for ratios?
It is the multiplier for each part in the ratio to get the actual number of units that are present.
Draw a ratio table to find the unknown multiplier and solve for only what is needed
If you need the absolute total number, then add the ratio with multiplier up.
Take a look at the Answer choices and make sure they are all a multiple of the multiplier or the ratio numbers so that you can eliminate any that are not.
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When you see a relative value in DS e.g. “what fraction of the total pies sold last month were apple pies?” What should you think?
Ratio: ap:tp. If a statement gives relative information (percent or fraction), it may be enough information to solve.
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What should you do when you have multiple ratios?
Find a common term and find the least common denominator of that term to solve for the other parts in the ratio. FDP102
What do you do if a DS asks for a ratio and they supply alg equations?
Try to get the equation to represent : x/y. Ratios are a representation of division. So you should be able to get the equation to values of x/y, if not, it is NS
When estimating, what should you keep in mind?
Which way you round. If you round up for 1 number, you might try to round down on the second numbers so that your estimation is closer to an answer choice.
Estimate when the answers are relatively far apart, you can estimate
estimate when the problem asks to estimate/approx
estimate using benchmarks: e.g. if question says she got 12% off, then try with. 10%, and 20%. If the answers are less than 10 or more than 20%, then you know to eliminate them
how do you make dividing by decimal easier?
if decimal is in divisor, switch it over to the dividend and move the decimal in the same direction.
How do you move a fraction closer to 1?
Add the same number to the numerator and denominator. A proper fraction will increase as it gets closer to one. An improper faction will decrease in value.
What is the first step when multiplying fractions?
Simplify first!
how do you simplify double decker fractions?
1/2 / 3/4
Flip and multiply. Or multiply top & bottom numerator by common denominator
What is 7% of 50?
Building fractions: Find 5% and 1%.
5%=2.5
1%= .5
1%= .5
How do you use an unknown multiplier?
Assign a variable for the multiplier and apply it to every element in the ratio (even the total)
Solve for the unknown multiplier and then substitute it back to find the actual values.
What is the smart number process?
- pick the sn and put a box around it
- plug it into the question, do the arithmetic and circle it.
- then do all of the answer choices until you get your circled number
What should you do if you see easy percentages in a word problem?
Convert it to fractions. The GMAT is hinting it.
What is the good/evil twin elimination method?
Look at the answer choices. if two are the +/- of a number or if you add them/subtract them you get the main sum in the question, that means one is a good twin and one is the evil twin. You can eliminate the other answer choices.
In this case, always choose the good twin! The evil twin is there in case you solve for the wrong variable or make a common mistake
Compare Fractions
which is greater?
3/5 or 4/7
use a modified version of the double cross. multiply 3x7=21 and 4x5=20 so 3/5 is greater. Use the cross to add fractions:
1/4+1/3=
1(3) + 4(1)=7
4(3)=12
