Rational Numbers Worksheet Practice

Are you a middle school student looking to strengthen your understanding of rational numbers? Look no further than our collection of rational numbers worksheets. These practice sheets are designed to help you dive deep into this mathematical concept, allowing you to build a solid foundation for solving problems involving fractions, decimals, and percents.

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What is a rational number?

A rational number is a number that can be expressed as a fraction where the numerator and denominator are both integers and the denominator is not zero. This includes both positive and negative whole numbers, fractions, and decimals that either terminate or repeat.

Give an example of a rational number.

One example of a rational number is 2/3, as it can be expressed as a fraction where the numerator (2) and denominator (3) are both integers.

Is zero a rational number? Why or why not?

Yes, zero is a rational number. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers and the denominator is not zero. In the case of zero, it can be written as 0/1, where 0 is an integer and 1 is a non-zero integer. Therefore, zero meets the criteria to be classified as a rational number.

Explain how to convert a fraction into a decimal.

To convert a fraction into a decimal, divide the numerator (top number) by the denominator (bottom number). The result will be the decimal equivalent of the fraction. If the division doesn't result in a whole number, you can either round to a specific decimal place or leave the decimal as a fraction.

How can you determine if a decimal is a rational number?

A decimal is a rational number if it either terminates (has a finite number of digits after the decimal point) or if it repeats a pattern of digits infinitely. This means that if you can express the decimal as a fraction of two integers (a/b), then it is a rational number. On the other hand, if the decimal is non-terminating and non-repeating (like pi or the square root of 2), then it is an irrational number.

Can a rational number be negative? Provide an example.

Yes, a rational number can be negative. For example, -3/4 is a rational number as it can be expressed as a fraction where both the numerator and denominator are integers. This number is negative because the numerator is negative while the denominator is positive.

What is the difference between a terminating decimal and a repeating decimal?

A terminating decimal is a decimal number that has a finite number of digits after the decimal point, meaning it ends or terminates. On the other hand, a repeating decimal is a decimal number that has a pattern of one or more digits that repeat infinitely after the decimal point. In other words, a terminating decimal stops at a certain point, while a repeating decimal goes on forever with a repeating pattern of digits.

Explain the concept of equivalent fractions in relation to rational numbers.

Equivalent fractions are fractions that represent the same value even though they may look different. In the context of rational numbers, equivalent fractions can be created by multiplying or dividing both the numerator and denominator of a fraction by the same non-zero number. This means that even though the fractions may have different numerators and denominators, they still represent the same part of a whole or set. For example, 1/2 is equivalent to 2/4 because when simplified, they both represent half of a whole. Working with equivalent fractions enables us to compare and perform operations on rational numbers more easily.

How do you add or subtract rational numbers?

To add or subtract rational numbers, you simply need to the same process as with integers. Add or subtract the numerators to get the new numerator, while keeping the denominators the same. This allows you to perform addition or subtraction of fractions with ease by ensuring that the denominators are identical. Remember to simplify the final answer if possible by reducing it to its simplest form.

Provide an example of a rational number that is not an integer.

One example of a rational number that is not an integer is 1/2. This fraction represents the division of the integer 1 by the integer 2, resulting in a rational number that is not a whole number.