Fractions And Decimals Study Cards

Enhance Your Learning with Fractions and Decimals Flash Cards for quick understanding



Fraction

A number that represents a part of a whole or a ratio of two quantities, written in the form a/b where a is the numerator and b is the denominator.

Numerator

The top number in a fraction that represents the number of parts being considered.

Denominator

The bottom number in a fraction that represents the total number of equal parts in a whole.

Proper Fraction

A fraction where the numerator is less than the denominator, representing a value less than 1.

Improper Fraction

A fraction where the numerator is equal to or greater than the denominator, representing a value equal to or greater than 1.

Mixed Number

A whole number combined with a proper fraction, written in the form a b/c where a is the whole number, b is the numerator, and c is the denominator.

Equivalent Fractions

Fractions that represent the same value, but may have different numerators and denominators.

Common Denominator

A shared multiple of the denominators of two or more fractions, used to make them easier to compare or add/subtract.

Comparing Fractions

Determining which fraction is greater or smaller by finding a common denominator or using cross-multiplication.

Ordering Fractions

Arranging fractions in ascending or descending order based on their values.

Adding Fractions

Combining two or more fractions by finding a common denominator and adding their numerators.

Subtracting Fractions

Finding the difference between two fractions by finding a common denominator and subtracting their numerators.

Multiplying Fractions

Finding the product of two or more fractions by multiplying their numerators and denominators.

Dividing Fractions

Finding the quotient of two fractions by multiplying the first fraction by the reciprocal of the second fraction.

Decimal

A number that represents a part of a whole or a ratio of two quantities, written in the form of a decimal point followed by digits.

Tenths

The first place value after the decimal point in a decimal number, representing one-tenth of a whole.

Hundredths

The second place value after the decimal point in a decimal number, representing one-hundredth of a whole.

Thousandths

The third place value after the decimal point in a decimal number, representing one-thousandth of a whole.

Comparing Decimals

Determining which decimal is greater or smaller by comparing the digits from left to right.

Ordering Decimals

Arranging decimals in ascending or descending order based on their values.

Adding Decimals

Combining two or more decimals by aligning the decimal points and adding the digits.

Subtracting Decimals

Finding the difference between two decimals by aligning the decimal points and subtracting the digits.

Multiplying Decimals

Finding the product of two or more decimals by multiplying the digits without considering the decimal points, and then placing the decimal point in the correct position.

Dividing Decimals

Finding the quotient of two decimals by moving the decimal point in the divisor to the right until it becomes a whole number, then moving the decimal point in the dividend the same number of places to the right, and performing the division.

Converting Fractions to Decimals

Expressing a fraction as a decimal by dividing the numerator by the denominator.

Converting Decimals to Fractions

Expressing a decimal as a fraction by writing the digits after the decimal point as the numerator and the place value as the denominator.

Rounding Decimals

Approximating a decimal to a specified place value by looking at the digit to the right of the desired place value and rounding up or down based on its value.

Adding and Subtracting Fractions with Unlike Denominators

Combining or finding the difference between fractions that have different denominators by finding a common denominator and performing the operation on the numerators.

Multiplying and Dividing Fractions with Unlike Denominators

Finding the product or quotient of fractions that have different denominators by finding a common denominator, performing the operation on the numerators, and simplifying the result.

Adding and Subtracting Decimals with Unlike Place Values

Combining or finding the difference between decimals that have different place values by aligning the decimal points and performing the operation on the digits.

Multiplying and Dividing Decimals with Unlike Place Values

Finding the product or quotient of decimals that have different place values by multiplying or dividing the digits without considering the decimal points, and then placing the decimal point in the correct position.

Adding and Subtracting Mixed Numbers

Combining or finding the difference between mixed numbers by adding or subtracting the whole numbers separately, and then adding or subtracting the fractions separately.

Multiplying and Dividing Mixed Numbers

Finding the product or quotient of mixed numbers by converting them to improper fractions, performing the operation on the fractions, and then converting the result back to a mixed number.

Adding and Subtracting Fractions and Mixed Numbers

Combining or finding the difference between fractions and mixed numbers by converting the mixed numbers to improper fractions, finding a common denominator, and performing the operation on the numerators.

Multiplying and Dividing Fractions and Mixed Numbers

Finding the product or quotient of fractions and mixed numbers by converting the mixed numbers to improper fractions, finding a common denominator, performing the operation on the numerators, and simplifying the result.

Percent

A fraction or decimal expressed as a ratio out of 100, representing a part of a whole.

Percent to Decimal Conversion

Converting a percent to a decimal by dividing the percent value by 100.

Decimal to Percent Conversion

Converting a decimal to a percent by multiplying the decimal value by 100.

Percent to Fraction Conversion

Converting a percent to a fraction by writing the percent value as the numerator and 100 as the denominator, and then simplifying the fraction if possible.

Fraction to Percent Conversion

Converting a fraction to a percent by dividing the numerator by the denominator, multiplying the result by 100, and adding the percent symbol.

Percent Increase

The amount by which a quantity increases expressed as a percent of the original quantity.

Percent Decrease

The amount by which a quantity decreases expressed as a percent of the original quantity.

Simple Interest

The amount of money earned or paid on an initial investment or loan, calculated as a percentage of the principal amount.

Compound Interest

The amount of money earned or paid on an initial investment or loan, calculated based on the initial amount and the accumulated interest from previous periods.

Applications of Fractions and Decimals

Real-world scenarios where fractions and decimals are used to solve problems, such as measurements, money, and percentages.