Real World Math

Question 1

Fractions - Reducing and Expanding

Answer 1

Express the numerator and denominator as products of their factors then cancel factors that are common to both. You can only reduce across a multiplication sign.

Question 2

Fractions - Adding and Subtracting

Answer 2

With a common denominator - easy to do! Just add or subtract the numerator and put over the common denominator.
With different denominators you have to start by finding a common denominator.
Bowtie technique

Question 3

Fractions - Bowtie Technique

Answer 3

When adding and subtracting fractions you can use the Bowtie Technique. Multiply the denominators of each fraction - this gives you a common denominator. Then multiply the denominator of each fraction by the numerator of the other. Take these numbers and add or subtract them - depending on what the question asks you to do. Reduce if necessary. 2/3 + 3/4 = 3x4, 4x2, 3x3, = 8/12 + 9/12 = 17/12

Question 4

Fractions - Multiplication

Answer 4

Just multiply straight across - first numerator by 2nd, and first denominator by second

Question 5

Fractions - Division

Answer 5

Just like multiplying, but before you do turn the second fraction upside down. Flip and multiply

Question 6

Fraction - Fractions in Fractions

Answer 6

Just re-write the expression horizontally. 7/ 1/4 = 7 / 1/4 = 7/1 x 4/1 = 28/1 = 28

Question 7

Fractions - Comparing Fractions

Answer 7

Find a common denominator, sure, but you can also use a variant of the bowtie technique. Don’t multiply denominators - just the denominators and numerators. The fraction with the larger product in its numerator is the greater fraction. 3/7 and 7/12 - 123 = 36 77 = 49, thus 7/12 is bigger

Question 8

Fractions - Converting Mixed Numbers

Answer 8

Mixed number is a number that is represented as an integer and a fraction. Multiply the denominator of the fraction by the integer and then add that result to the numerator, and then put the whole thing over the denominator. 2 2/3 = 3x2+2/ 3 or 8/3

Question 9

Fractions - Decimals

Answer 9

To turn a fraction into its decimal equivalent divide the numerator by the denominator.

Question 10

Set up for Quant Comp with Variables

Answer 10

A a b c d B
x= y=
x= y=
x= y=

Question 11

Comparing Decimals

Answer 11

Line the numbers up by their decimal points
Fill in the missing zeros

0.00099 and 0.001

0. 00099
1. 00100

Question 12

Decimals and Digits

Answer 12

0.123
0 is the units digit
1 is the tenths digit
2 is the hundredths digit
3 is the thousandths digit

Question 13

Percent Change

Answer 13

Percentage increase / decrease

Percent Change = (Difference / Original) * 100

If the question asks you to find the percent increase then the original number is the smaller number. If the questions asks you to find the percent decrease then the original number is the larger number.

Question 14

Ratios

Answer 14

Ratios express a part to part relationship - fractions express part to the whole.
GRE may express rations in several ways:
x : y
the ratio of x to y
x is to y

Question 15

Every fraction can be a ratio, and vice versa

Answer 15

A ratio of 1:2 means that the total of all the parts is either 3 or a multiple of 3, so the ratio of 1:2 can be expressed as the fraction 1/3. Likewise a fraction 1/3 means that we are looking at one part of out a total three so the other part must be 2 - that means the ratio is 1:2.
Treat a ratio like a fraction - anything you can do to a fraction, you can also do to a ratio. You can cross-multiply, find common denominators, reduce, and so on.

Question 16

Finding the Total with Ratios

Answer 16

Add the numbers in a ratio to find the total. A ratio of 2:1 means there are three total parts.

Question 17

Ratio Box

Answer 17

x y total
ratio 1 2 3
multiply by 8 8 8
actual numbers 8 16 24

Question 18

Proportion

Answer 18

A proportions is an equivalent relationship between two fractions or ratios. Thus, 1/2 and 4/8 are proportionate because they are equivalent fractions.

Question 19

Averages

Answer 19

The average of a list of numbers is the sum of all numbers in the list divided by the numbers of the list.
Average = total / # of things

Question 20

Average Pie

Answer 20

Average Pie helps organize your info

                      Total divide                                      divide
      # of things  x  Average

Question 21

Median

Answer 21

The median is the middle value in a list of numbers; above and below the median lie an equal number o values. If the list contains an even number of integers, the median is an average of the two middle numbers.

Question 22

Mode

Answer 22

The mode is the number in the list of numbers that occurs the most frequently

Question 23

Range

Answer 23

The range is the difference between the greatest and the least numbers in a list of numbers.
2, 6, 13, 3, 15, 4, 9 The range = 15-2 = 13

Question 24

Standard Deviation

Answer 24

When you see the phrase standard deviation or normal distribution draw a bell curve and fill in the percentages:
2% -(-2 SD)- 14% -(-1 SD)- 34% -(Mean)- 34% -(+1 SD)- 14% -(+2 SD)- 2%. Standard deviations are in even increments.

Question 25

Standard Deviation - Negative

Answer 25

Even if a list of numbers contains negative integers while the other doesn’t does not mean one list has a negative standard deviation. SD is defined as the distance a point is from the mean, so it can never be negative. ETS will never ask you to calculate standard deviation - you need the mean to calculate the standard deviation.

Question 26

Rate - Rate Pie

Answer 26

Rate problems are similar to average problems.

         Distance or Amount divide                                      divide
                  Time x  Rate

Question 27

Charts

Answer 27

Don’t start with the questions - start with the charts.
Look for information in titles
Look for asterisks, footnotes, parentheses, and small print.
Keep an eye out for funny units.