SAT- Math
How do you convert from part-to-part ratios to part-to-whole ratios?—
ANSWER--If the parts add up to the 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. For example, if the ratio of males to
females is 1 to 2, then the males-to-people ratio is 1/ (1+2) = 1/3 and the
females-to-people ratio is 2/ (1+2) = 2/3
In other words, 2/3 of all the people are female.
How do you solve a proportion?—ANSWER--To solve a proportion, cross
multiply.
For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
,How do you solve a problem involving rates?—ANSWER--To solve a rate
problem, use the units to keep things straight. For example, if asked: If
snow is falling at the rate of one foot every four hours, how many inches of
snow will fall in seven hours?
Your setup would be:
1 foot/ 4 hours = x inches/ 7 hours
12 inches/ 4 hours = x inches/ 7 hours
4x = 12 x 7
x = 21
What is the average rate and how do you find it?—ANSWER--Average rate is
not simply the average of the rates.
Average A per B = Total A/ Total B, so
Average Speed = Total distance/ Total time
For example, to find the average speed for 120 miles at 40 mph and 120
miles at 60 mph, don't just average the two speeds. First, figure out the
total distance and the total time. The total distance is 120 + 120 = 240
miles. The times are three hours for the first leg and two hours for the
© 2026 Copyright. All Rights Reserved. This document is
protected by copyright law, Copyrighted By Brittie Donald
,second leg, or five hours total. The average speed, then, is 240/5 = 48 miles
per hour.
What is the formula used to find average?—ANSWER--To find the average of
a set of numbers, add them up and divide by how many there are.
Average = Sum of the terms / Number of the terms
How do you quickly find the average of a series of evenly spaced
numbers?—ANSWER--For evenly spaced numbers, the average is the
middle value. To find the average of evenly spaced numbers, just average
the smallest and the largest.
For example, the average of all the integers from 13 through 77 is the same
as the average of 13 and 77.
13 + 77/ 2 = 90/ 2 = 45
If you have an average of a series of numbers, how can you find their
sum?—ANSWER--Use the formula:
Sum = Average x Number of terms
If the average of 10 numbers is 50, then they add up to 10 x 50, or 500.
, How do you find the missing number in a series when you are given the
average?—ANSWER--To find a missing number when you're given the
average, use the sum.
Sum = Average x Number of Terms
For example, if the average of 4 numbers is 7, then the sum of those 4
numbers is 4 x 7, or 28. Suppose that 3 of the numbers are 3, 5, and 8.
These 3 numbers add up to 16 of that 28, which leaves 12 for the fourth
number.
How do you find the median of a set of numbers?—ANSWER--The median
of a set of numbers is the value that falls in the middle of the set.
For example, if you have 5 test scores, and they are 88, 86, 57, 94, and 73,
you must first list the scores in increasing or decreasing order: 57, 73, 86,
88, 94. The median is the middle number, or 86. If there is an even number
of values in a set (6 test scores, for instance), simply take the average of the
two middle numbers.
How do you calculate the total number of possibilities for several events to
occur?—ANSWER--The fundamental counting principle: If there are m
ways one event can happen and n ways a second event can happen, then
there are m x n ways for the 2 events to happen. For example, with 5 shirts
© 2026 Copyright. All Rights Reserved. This document is
protected by copyright law, Copyrighted By Brittie Donald
How do you convert from part-to-part ratios to part-to-whole ratios?—
ANSWER--If the parts add up to the 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. For example, if the ratio of males to
females is 1 to 2, then the males-to-people ratio is 1/ (1+2) = 1/3 and the
females-to-people ratio is 2/ (1+2) = 2/3
In other words, 2/3 of all the people are female.
How do you solve a proportion?—ANSWER--To solve a proportion, cross
multiply.
For example:
x/5 = 3/4
4x = 3 x 5
x = 15/4 = 3.75
,How do you solve a problem involving rates?—ANSWER--To solve a rate
problem, use the units to keep things straight. For example, if asked: If
snow is falling at the rate of one foot every four hours, how many inches of
snow will fall in seven hours?
Your setup would be:
1 foot/ 4 hours = x inches/ 7 hours
12 inches/ 4 hours = x inches/ 7 hours
4x = 12 x 7
x = 21
What is the average rate and how do you find it?—ANSWER--Average rate is
not simply the average of the rates.
Average A per B = Total A/ Total B, so
Average Speed = Total distance/ Total time
For example, to find the average speed for 120 miles at 40 mph and 120
miles at 60 mph, don't just average the two speeds. First, figure out the
total distance and the total time. The total distance is 120 + 120 = 240
miles. The times are three hours for the first leg and two hours for the
© 2026 Copyright. All Rights Reserved. This document is
protected by copyright law, Copyrighted By Brittie Donald
,second leg, or five hours total. The average speed, then, is 240/5 = 48 miles
per hour.
What is the formula used to find average?—ANSWER--To find the average of
a set of numbers, add them up and divide by how many there are.
Average = Sum of the terms / Number of the terms
How do you quickly find the average of a series of evenly spaced
numbers?—ANSWER--For evenly spaced numbers, the average is the
middle value. To find the average of evenly spaced numbers, just average
the smallest and the largest.
For example, the average of all the integers from 13 through 77 is the same
as the average of 13 and 77.
13 + 77/ 2 = 90/ 2 = 45
If you have an average of a series of numbers, how can you find their
sum?—ANSWER--Use the formula:
Sum = Average x Number of terms
If the average of 10 numbers is 50, then they add up to 10 x 50, or 500.
, How do you find the missing number in a series when you are given the
average?—ANSWER--To find a missing number when you're given the
average, use the sum.
Sum = Average x Number of Terms
For example, if the average of 4 numbers is 7, then the sum of those 4
numbers is 4 x 7, or 28. Suppose that 3 of the numbers are 3, 5, and 8.
These 3 numbers add up to 16 of that 28, which leaves 12 for the fourth
number.
How do you find the median of a set of numbers?—ANSWER--The median
of a set of numbers is the value that falls in the middle of the set.
For example, if you have 5 test scores, and they are 88, 86, 57, 94, and 73,
you must first list the scores in increasing or decreasing order: 57, 73, 86,
88, 94. The median is the middle number, or 86. If there is an even number
of values in a set (6 test scores, for instance), simply take the average of the
two middle numbers.
How do you calculate the total number of possibilities for several events to
occur?—ANSWER--The fundamental counting principle: If there are m
ways one event can happen and n ways a second event can happen, then
there are m x n ways for the 2 events to happen. For example, with 5 shirts
© 2026 Copyright. All Rights Reserved. This document is
protected by copyright law, Copyrighted By Brittie Donald
