Adding and Subtracting Rational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

How do you add two rational numbers with different denominators?

Back

To add two rational numbers with different denominators, find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators.

Front

What is the result of subtracting a negative number from a negative number?

Back

Subtracting a negative number from a negative number is equivalent to adding the absolute value of that negative number.

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that sum over the original denominator.

Front

What is the process for subtracting fractions?

Back

To subtract fractions, ensure they have a common denominator, then subtract the numerators and keep the denominator the same.

Front

What is the significance of the sign in front of a number when performing addition or subtraction?

Back

The sign indicates whether the number is positive or negative, which affects the overall result of the operation.

Front

How do you simplify the result of adding or subtracting fractions?

Back

To simplify the result, divide the numerator and the denominator by their greatest common divisor (GCD).

Front

What is the first step in solving an application problem involving rational numbers?

Back

The first step is to carefully read the problem to identify the quantities involved and the operations required.

Front

How do you handle mixed numbers in addition and subtraction?

Back

Convert mixed numbers to improper fractions before performing addition or subtraction.

Front

What is the result of adding a positive number to a negative number?

Back

The result depends on the absolute values of the numbers; if the positive number is larger, the result is positive, and if the negative number is larger, the result is negative.