ATI TEAS 7 FULL STUDY GUIDE MATH
Fundamentals of Mathematics
I. Fractions
A. Basic Terminology
1. Numerator: The top number of a fraction, indicating the number of parts
being considered.
2. Denominator: The bottom number of a fraction, indicating the total number
of equal parts.
B. Types of Fractions
1. Proper Fraction: A fraction where the numerator is smaller than the
denominator.
o Example: 53
2. Improper Fraction: A fraction where the numerator is larger than or equal
to the denominator.
o Example: 37
3. Mixed Number: A number consisting of a whole number and a proper
fraction.
o Example: 241
C. Converting Between Improper Fractions and Mixed Numbers
1. Improper Fraction to Mixed Number:
o Step 1: Divide the denominator into the numerator.
o Step 2: The quotient becomes the whole number.
o Step 3: The remainder becomes the numerator of the proper
fraction.
o Step 4: The denominator remains the same.
o Example: 25=221 (5 divided by 2 is 2 with a remainder of 1)
2. Mixed Number to Improper Fraction:
o Step 1: Multiply the whole number by the denominator.
o Step 2: Add the numerator to the result from Step 1. This becomes
the new numerator.
o Step 3: The denominator remains the same.
, o Example: 221=2(2×2)+1=25
D. Least Common Denominator (LCD)
The smallest number that is a multiple of the denominators of all fractions
being compared.
E. Converting Decimals to Fractions
1. Step 1: Write the decimal as a fraction with the decimal as the numerator
and 1 as the denominator.
o Example: 0.37=10.37
2. Step 2: Multiply the numerator and denominator by 10n, where n is the
number of decimal places.
o Example: 0.37×100100=10037 (two decimal places, so multiply by
100)
3. Step 3: Reduce the fraction to its simplest form if possible.
o Example: 10037 (cannot be reduced further)
F. Converting Fractions to Decimals
1. Step 1: Divide the numerator by the denominator.
2. Step 2: Add zeros after the decimal point in the dividend as needed.
3. Step 3: Continue the division until there is no remainder or the decimal
repeats.
G. Converting Decimals to Percentages
1. Multiply the decimal by 100 and add a percent sign (%).
o Example: 0.75×100%=75%
2. Move the decimal point two places to the right.
o Example: 0.75→75%
H. Converting Percentages to Decimals
1. Remove the percent sign (%) and divide the number by 100.
o Example: 45%=10045=0.45
2. Move the decimal point two places to the left.
o Example: 45%→0.45
I. Converting Fractions to Percentages
Fundamentals of Mathematics
I. Fractions
A. Basic Terminology
1. Numerator: The top number of a fraction, indicating the number of parts
being considered.
2. Denominator: The bottom number of a fraction, indicating the total number
of equal parts.
B. Types of Fractions
1. Proper Fraction: A fraction where the numerator is smaller than the
denominator.
o Example: 53
2. Improper Fraction: A fraction where the numerator is larger than or equal
to the denominator.
o Example: 37
3. Mixed Number: A number consisting of a whole number and a proper
fraction.
o Example: 241
C. Converting Between Improper Fractions and Mixed Numbers
1. Improper Fraction to Mixed Number:
o Step 1: Divide the denominator into the numerator.
o Step 2: The quotient becomes the whole number.
o Step 3: The remainder becomes the numerator of the proper
fraction.
o Step 4: The denominator remains the same.
o Example: 25=221 (5 divided by 2 is 2 with a remainder of 1)
2. Mixed Number to Improper Fraction:
o Step 1: Multiply the whole number by the denominator.
o Step 2: Add the numerator to the result from Step 1. This becomes
the new numerator.
o Step 3: The denominator remains the same.
, o Example: 221=2(2×2)+1=25
D. Least Common Denominator (LCD)
The smallest number that is a multiple of the denominators of all fractions
being compared.
E. Converting Decimals to Fractions
1. Step 1: Write the decimal as a fraction with the decimal as the numerator
and 1 as the denominator.
o Example: 0.37=10.37
2. Step 2: Multiply the numerator and denominator by 10n, where n is the
number of decimal places.
o Example: 0.37×100100=10037 (two decimal places, so multiply by
100)
3. Step 3: Reduce the fraction to its simplest form if possible.
o Example: 10037 (cannot be reduced further)
F. Converting Fractions to Decimals
1. Step 1: Divide the numerator by the denominator.
2. Step 2: Add zeros after the decimal point in the dividend as needed.
3. Step 3: Continue the division until there is no remainder or the decimal
repeats.
G. Converting Decimals to Percentages
1. Multiply the decimal by 100 and add a percent sign (%).
o Example: 0.75×100%=75%
2. Move the decimal point two places to the right.
o Example: 0.75→75%
H. Converting Percentages to Decimals
1. Remove the percent sign (%) and divide the number by 100.
o Example: 45%=10045=0.45
2. Move the decimal point two places to the left.
o Example: 45%→0.45
I. Converting Fractions to Percentages
