PRAXIS 5164 COMPREHENSIVE EXAM 2026 QUESTIONS
AND ANSWERS RATED A+
✔✔repeat decimals to fractions - ✔✔multiply recurring decimal by 10n (n=number of
recurring decimals)
subtract the recurring decimal by your product to eliminate recurring part
solve for x
✔✔ratio - ✔✔compares two numbers by division
can be expressed x to y, x:y, x/y
✔✔rate - ✔✔a ratio that compares two quantities measured in different units
✔✔unit rate - ✔✔a rate with a denominator of 1.
✔✔scale factor - ✔✔the ratio used to enlarge or reduce similar figures
✔✔discount total - ✔✔take percent discount and divide by 100
multiply by original price
subtract your product by original price
✔✔discount - ✔✔(original price - new price)/original price x 100%
✔✔mark up - ✔✔(selling price - cost)/cost x 100%
✔✔taxes - ✔✔take percent tax and divide by 100
multiply that by overall price
add answer to overall price
✔✔tip - ✔✔same as tax or
move decimal one place to left (10%) and double or triple for 20%/30% tip
✔✔simple interest - ✔✔A=P(1+rt)
a - final amount
p - initial principle balance
r - annual interest rate
t - time in years
✔✔percent error - ✔✔absolute value of measured value - actual value over actual value
then multiply by 100
✔✔map scale - ✔✔write down map scale
fill in the measure that you know under like unit
cross multiply for the missing term
, ✔✔divisible by 2 if - ✔✔last digit is even
✔✔divisible by 3 if - ✔✔sum of digits is divisible by 3
✔✔divisible by 4 if - ✔✔the number formed by the last 2 digits is divisible by 4
✔✔divisible by 5 if - ✔✔integer ends in 5 or 0
✔✔divisible by 6 if - ✔✔number is divisible by 2 and 3
✔✔divisible by 7 if - ✔✔double the value of the last digit and subtract from the leftover
number. the result is divisible by 7
✔✔divisible by 8 if - ✔✔The last three digits are divisible by 8
✔✔divisible by 9 if - ✔✔sum of digits is divisible by 9
✔✔prime number - ✔✔a whole number that has exactly two factors, 1 and itself.
✔✔composite number - ✔✔A number with more than two factors
✔✔factor tree - ✔✔take original number
split into two factors
repeat until you get all prime numbers
✔✔greatest common factor - ✔✔the greatest of the common factors of two or more
numbers
15: 1 3 5 15
35: 1 5 7 35
GCF (15,35)=5
✔✔least common multiple - ✔✔smallest number that is a multiple of two or more
numbers
3: 3 6 9 12 15
5: 5 10 15 20
LCM(3,5) = 15
✔✔simplifying radicals - ✔✔factor tree list numbers under radical
circle in pairs
✔✔multiply or divide inequality by a negative - ✔✔Reverse the direction of the
inequality
AND ANSWERS RATED A+
✔✔repeat decimals to fractions - ✔✔multiply recurring decimal by 10n (n=number of
recurring decimals)
subtract the recurring decimal by your product to eliminate recurring part
solve for x
✔✔ratio - ✔✔compares two numbers by division
can be expressed x to y, x:y, x/y
✔✔rate - ✔✔a ratio that compares two quantities measured in different units
✔✔unit rate - ✔✔a rate with a denominator of 1.
✔✔scale factor - ✔✔the ratio used to enlarge or reduce similar figures
✔✔discount total - ✔✔take percent discount and divide by 100
multiply by original price
subtract your product by original price
✔✔discount - ✔✔(original price - new price)/original price x 100%
✔✔mark up - ✔✔(selling price - cost)/cost x 100%
✔✔taxes - ✔✔take percent tax and divide by 100
multiply that by overall price
add answer to overall price
✔✔tip - ✔✔same as tax or
move decimal one place to left (10%) and double or triple for 20%/30% tip
✔✔simple interest - ✔✔A=P(1+rt)
a - final amount
p - initial principle balance
r - annual interest rate
t - time in years
✔✔percent error - ✔✔absolute value of measured value - actual value over actual value
then multiply by 100
✔✔map scale - ✔✔write down map scale
fill in the measure that you know under like unit
cross multiply for the missing term
, ✔✔divisible by 2 if - ✔✔last digit is even
✔✔divisible by 3 if - ✔✔sum of digits is divisible by 3
✔✔divisible by 4 if - ✔✔the number formed by the last 2 digits is divisible by 4
✔✔divisible by 5 if - ✔✔integer ends in 5 or 0
✔✔divisible by 6 if - ✔✔number is divisible by 2 and 3
✔✔divisible by 7 if - ✔✔double the value of the last digit and subtract from the leftover
number. the result is divisible by 7
✔✔divisible by 8 if - ✔✔The last three digits are divisible by 8
✔✔divisible by 9 if - ✔✔sum of digits is divisible by 9
✔✔prime number - ✔✔a whole number that has exactly two factors, 1 and itself.
✔✔composite number - ✔✔A number with more than two factors
✔✔factor tree - ✔✔take original number
split into two factors
repeat until you get all prime numbers
✔✔greatest common factor - ✔✔the greatest of the common factors of two or more
numbers
15: 1 3 5 15
35: 1 5 7 35
GCF (15,35)=5
✔✔least common multiple - ✔✔smallest number that is a multiple of two or more
numbers
3: 3 6 9 12 15
5: 5 10 15 20
LCM(3,5) = 15
✔✔simplifying radicals - ✔✔factor tree list numbers under radical
circle in pairs
✔✔multiply or divide inequality by a negative - ✔✔Reverse the direction of the
inequality
