Mathematics Exam Study Guide: Fractions, Decimals, and Place Value

Vocabulary flashcards covering fraction classifications, conversions, number line placement, expanded form, and arithmetic operations based on the exam study guide.

Proper Fraction

A fraction in which the bottom number (denominator) is greater than the top number (numerator), such as $\frac{4}{5}$, $\frac{3}{4}$, and $\frac{2}{3}$.

Improper Fraction

A fraction in which the top number (numerator) is greater than the bottom number (denominator), such as $\frac{3}{2}$, $\frac{4}{3}$, and $\frac{5}{4}$.

Mixed Fraction

A number consisting of an integer (whole number) combined with a fraction, such as $2\frac{1}{2}$ and $3\frac{3}{4}$.

Equivalent Fractions

Fractions that represent the exact same numerical value or quantity despite having different numerators and denominators.

Fraction-to-Decimal Conversion

The mathematical operation of expressing a fraction as a decimal by dividing the numerator by the denominator (e.g., $\frac{3}{8}$, $\frac{3}{10}$, $\frac{8}{4}$, and $\frac{4}{8}$).

Decimal-to-Fraction Conversion

The mathematical process of rewriting a terminating decimal as a fraction over a power of $10$ and simplifying (e.g., $3.48$, $0.742$, $0.0003$, and $0.345$).

Mixed and Improper Fraction Conversion

The process of converting mixed numbers into improper fractions (such as $3\frac{1}{4}$ and $5\frac{3}{4}$) and converting improper fractions into mixed numbers (such as $\frac{29}{4}$ and $\frac{8}{3}$).

Number Line Representation of Fractions

The method of plotting fractional and mixed values (such as $\frac{3}{8}$, $\frac{5}{10}$, $2\frac{1}{2}$, and $4\frac{1}{8}$) at their corresponding locations along a graduated line.

Expanded Form

A method of writing quantities by separating each digit into its individual place value, applied to whole numbers (e.g., $34{,}256$, $89{,}432$, $102{,}342$, and $4{,}320{,}001$) and decimal numbers (e.g., $0.3428$ and $0.39269$).

Decimal and Multi-Digit Addition

The process of computing sums by aligning values vertically according to place value and decimal points (e.g., $543.8 + 3.03 + 0.432 + 3$ and $643.8 + 39.58 + 59.326$).