Math Assessment Reviewer - Operations on Decimals and Fractions

Vocabulary flashcards reviewing key mathematical concepts, rules, and procedures regarding operations on decimals, powers of 10, fractions, and mixed numbers.

Powers of 10 Greater Than 1

Powers of 10 such as $1, 10, 100, 1000\dots$

Powers of 10 Less Than 1

Powers of 10 such as $0.1, 0.01, 0.001\dots$

Multiplying Decimals by a Power of 10 Greater Than 1

A procedure where the decimal point is moved to the right according to the number of zeroes in the power of 10 (e.g., $100 \times 8.5 = 850$).

Multiplying Decimals by a Power of 10 Less Than 1

A procedure where the decimal point is moved to the left according to the number of decimal places in the power of 10 (e.g., $0.01 \times 1.58 = 0.0158$).

Dividing Decimals by a Power of 10 Greater Than 1

A procedure where the decimal point is moved to the left according to the number of zeroes in the power of 10 (e.g., $3.5 / 10 = 0.35$).

Dividing Decimals by a Power of 10 Less Than 1

A procedure where the decimal point is moved to the right according to the number of decimal places in the power of 10 (e.g., $5.3 / 0.1 = 53$).

Dividing a Whole Number by a Decimal

Moving the decimal point of the divisor to make it a whole number, moving the decimal point of the dividend as many times as the divisor was moved while adding zeroes, and dividing (e.g., $15 / 0.75 = 20$).

Dividing a Decimal by a Whole Number

Dividing normally while keeping the divisor as a whole number, where the divisor cannot be a decimal.

Dividing a Decimal by a Decimal

Moving the decimal point of the divisor to make it a whole number, moving the decimal point of the dividend as many times as the divisor, and then dividing (e.g., $56.7 / 0.9 = 63$).

Least Common Denominator (LCD)

The common denominator found when adding or subtracting fractions with different denominators (e.g., for denominators $4$ and $3$, the $\text{LCD} = 12$).

Addition and Subtraction of Mixed Numbers

Adding or subtracting whole numbers along with fractions, requiring that the denominators of the fractions be equal before operating.

Borrowing in Fraction Subtraction

A step in fraction subtraction used when the minuend's numerator is smaller than the subtrahend's numerator, requiring borrowing from the whole number.

Repeating Decimal

A decimal whose quotient contains digits that repeat indefinitely.

Terminating Decimal

A decimal in which the repeating digit is $0$ (e.g., $2.50$, normally written as $2.5$).

Ellipsis in Decimals

Three dots ($\dots$) used to indicate that a decimal's digits repeat indefinitely (e.g., $0.333\dots$).

Repeating Bar

A horizontal line placed over digits ($\overline{x}$) to indicate which numbers repeat in a decimal (e.g., $0.\overline{3}$).

Steps in Multiplying Decimals

A three-step procedure: 1) Ignore decimal points, 2) Multiply normally as whole numbers, and 3) Count skipped decimal places in factors and move the decimal point in the product accordingly.

Addition and Subtraction of Decimals

The process of adding or subtracting decimal numbers by lining up decimal points and adding zeroes if needed to avoid confusion.