Rational Numbers Worksheets Grade 7

Rational Numbers Worksheets for Grade 7 provide students with ample practice and reinforcement of key concepts related to rational numbers. These worksheets are designed to help students understand and work with entity and subject effectively, allowing them to develop a strong foundation in math.

  Solving Equations with Rational Expressions Worksheet

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  Order of Operations Worksheets 5th

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  3 Grade Math Worksheets

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  6th Grade Math Worksheets Multiplication

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  Positive Negative Integers and Absolute Value

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  Rational Numbers Worksheets

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  Comparing Decimals Worksheet 4th Grade

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  Menstrual Period Funny Cartoons

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  Multiplication of Exponents and Division Worksheets

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  Order of Operations Worksheets 5th Grade Math

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  Fraction Number Line Chart

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  Multiplying and Dividing Powers of 10 Worksheet

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  Multiplying and Dividing Powers of 10 Worksheet

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  Multiplying and Dividing Powers of 10 Worksheet

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Define a rational number.

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, a rational number is any number that can be written in the form a/b, where a and b are integers and b is not equal to zero.

Give an example of a rational number that is also an integer.

An example of a rational number that is also an integer is 3. Since an integer can be expressed as a fraction with a denominator of 1 (e.g., 3 = 3/1), it is considered a rational number.

Provide two examples of rational numbers that are not integers.

One example of a rational number that is not an integer is 0.5, since it can be expressed as a fraction: 1/2. Another example is -1.75, which can be written as -7/4. Both of these numbers can be represented as a ratio of two integers, demonstrating that they are rational numbers that are not integers.

What is the difference between a rational number and an irrational number?

A rational number is a number that can be expressed as a fraction of two integers, while an irrational number is a number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion. In simple terms, rational numbers can be written as a ratio of two integers, while irrational numbers cannot.

Can a rational number be written as a fraction? Explain.

Yes, a rational number can be written as a fraction. This is because a rational number is any number that can be expressed as the ratio of two integers where the denominator is not zero. By definition, a fraction represents a division of two integers, making rational numbers a subset of fractions. Therefore, every rational number can be written in the form of a fraction.

State whether 1/2 is a rational number or not. Justify your answer.

Yes, 1/2 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are both integers. In this case, 1 (numerator) and 2 (denominator) are both integers, so 1/2 is a rational number.

Can a rational number be positive, negative, or zero? Give an example for each.

Yes, a rational number can be positive, negative, or zero. For example, 3 is a positive rational number, -2 is a negative rational number, and 0 is a rational number that is neither positive nor negative.

How can you determine if a given decimal is a rational number or not?

To determine if a given decimal is a rational number, you can check if the decimal either terminates (stops) or repeats (has a pattern that repeats indefinitely). If the decimal terminates or repeats, then it is a rational number. If the decimal does not terminate or repeat, then it is an irrational number.

Explain how to compare and order rational numbers.

To compare and order rational numbers, first convert them to a common denominator if necessary. Then, simply compare the numerators of the fractions. The rational number with the larger numerator is greater. If the numerators are the same, compare the denominators – the smaller denominator indicates the greater value. When ordering rational numbers, arrange them from least to greatest or vice versa based on the comparison. Remember to convert mixed numbers to improper fractions for accurate comparison.

Provide an example where adding two rational numbers results in an irrational number.

An example of adding two rational numbers to obtain an irrational number is \( \frac{1}{2} + \frac{1}{2} = 1 \). This sum, 1, is an irrational number because it cannot be expressed as a ratio of two integers.