Math Assessment Reviewer - Decimals and Fractions

Vocabulary flashcards covering mathematical operations on decimals, powers of 10, fraction arithmetic, and decimal classifications.

Alignment Rule for Decimal Addition and Subtraction

The requirement to align decimal points vertically when adding or subtracting, adding zeroes if needed to avoid confusion.

Multiplication of Decimals

A three-step process: 1. Ignore decimal points; 2. Multiply normally as with whole numbers; 3. Count total decimal places skipped in factors and place the decimal point accordingly in the final product.

Powers of 10 Greater than 1

Numbers such as 1, 10, 100, 1000\n\n\dots

Multiplying Decimals by Powers of 10 Greater than 1

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

Powers of 10 Less than 1

Numbers such as $0.1, 0.01, 0.001\dots$

Multiplying Decimals by Powers of 10 Less than 1

Moving the decimal point 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 Powers of 10 Greater than 1

Moving the decimal point to the left according to the number of zeroes in the power of 10 (e.g., $3.5 / 10 = 0.35$).

Dividing Decimals by Powers of 10 Less than 1

Moving the decimal point 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, then moving the decimal point of the dividend the same number of places to the right and adding zeroes as necessary (e.g., $15 / 0.75 = 20$).

Dividing a Decimal by a Whole Number

Dividing normally while keeping the decimal point aligned, under the rule that 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, then moving the decimal point of the dividend as many times to the right and adding zeroes if needed (e.g., $56.7 / 0.9 = 63$).

Least Common Denominator (LCD)

The smallest common denominator found when adding or subtracting fractions that do not have matching denominators.

Borrowing in Fraction Subtraction

The procedure used when subtracting fractions or mixed numbers if the minuend's numerator is smaller than the subtrahend's numerator, requiring borrowing $1$ from the whole number.

Repeating Decimal

A decimal quotient containing digits that repeat indefinitely, indicated using an ellipsis (...) or a repeating bar (-).

Terminating Decimal

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