ACCUPLACER Arithmetic Preparation Lesson 2.1 Fractions Classifying Reducing Converting

FUNDAMENTALS OF FRACTIONS: REDUCING, CONVERTING & CLASSIFYING

LECTURE NOTES

FUNDAMENTAL OF FRACTIONS: CLASSIFICATION, REDUCTION AND DECIMAL CONVERSION

Vocabulary and Definitions:

A fraction: can be defined as two quantities expressed as on divided by the other. The Numerical quantity on the top is the Numerator and the numerical quantity on the bottom is the Denominator. A fraction can be expressed in different ways such as 2/5, $\frac{2}{5}$ .

A Proper Fraction: A proper fraction is one where the numerator is smaller than the numerator. $\frac{3}{5}{\rm{ is proper since 3 < 5}}{\rm{.}}$

Improper Fractions: A fraction where the numerator is greater than the denominator $\frac{8}{5}{\rm{ is improper since 8 > 5}}{\rm{.}}$ .

Compound Fractions or Mixed Numbers: A fraction expressed as a whole number and a proper fraction.

$\begin{array}{l} 5\frac{1}{2}{\rm{ is a mixed number because it is composed of a whole number 5 and mixed}}\\ {\rm{proper fraction }}\frac{1}{2}. \end{array}$

Equivalent Fractions: Fractions that are all reduce to the same fraction when reduced to lowest terms

$Ex.\,\,\frac{4}{8},\,\,\frac{{12}}{{24}},\frac{{10}}{{20}}{\rm{ are equivalent fractions since they all reduce to }}\frac{1}{2}$ .

Undefined Fractions: A fraction with a non-zero numerator divided by zero.

$\frac{5}{0}{\rm{ is undefined since the 5}} \ne {\rm{0 is divided by 0}}{\rm{.}}$

Indeterminate Fraction: If the numerator and the denominator are 0, it is an indeterminate fraction

$\frac{0}{0}{\rm{ is indeterminate since the numerator and denominator are zero}}{\rm{.}}$

REDUCING FRACTIONS TO LOWEST TERMS

Strategy for Reducing Fractions

1: Decompose the numerator and the denominator to a product of primes.

2: Divide out common factors between the numerator and the denominator.

3: Multiply the numerator and denominators left. The resulting fraction is the fraction in lowest terms

CONVERTING FRACTIONS TO DECIMALS AND DECIMALS TO FRACTIONS

Strategy for Converting Fractions to Decimals

Express the fraction in standard division notation with the numerator (top dog) goes in the division bars (dog house). The denominator goes outside. If the fraction is a mixed number convert it to an improper fraction.
Divide using the regular long division algorithm until terms terminate, repeat, or reach the specified number of decimal places in the problem.
Multiply the numerator and denominators left. The resulting fraction is the fraction in lowest terms

CONVERTING FRACTIONS TO DECIMALS AND DECIMALS TO FRACTIONS

Strategy for Converting Fractions to Decimals

Express the fraction in standard division notation with the numerator (top dog) goes in the division bars (dog house). The denominator goes outside. If the fraction is a mixed number convert it to an improper fraction.
Divide using the regular long division algorithm until terms terminate, repeat, or reach the specified number of decimal places in the problem.

ACCUPLACER ARITHMETIC PREP COURSE LESSONS

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COMPLETE PLACER ARITHMETIC PREP COURSE LINKS

Lesson 1.1 Operations on Whole and Decimals Numbers Adding and Subtracting
Lesosn 1.2 Multiplying Decimals and Whole Numbers
Lesson 2.1 Basics of Fractions, Classifying, Reducing, & Converting to Decimals

Arithmetic Section

According to the college board The Arithmetic algebra "test measures your ability to perform basic arithmetic operations and to solve problems that involve fundamental arithmetic concepts. There are 17 questions on the Arithmetic tests, divided into three types.
• Operations with whole numbers and fractions: Topics included in this category are addition, subtraction, multiplication, division, recognizing equivalent fractions and mixed numbers, and estimating.
• Operations with decimals and percents: Topics include addition, subtraction, multiplication, and division with decimals. Percent problems, recognition of decimals, fraction and percent equivalencies, and problems involving estimation are also given.
• Applications and problem solving: Topics include rate, percent, and measurement problems; simple geometry problems; and distribution of a quantity into its fractional parts." -Source collegeboard.com