Rational numbers and operations
Mathematics, Grade 8
Rational numbers and operations
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Rational numbers and operations
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Study Guide Rational numbers and operations Mathematics, Grade 8
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RATIONAL NUMBERS AND OPERATIONS • A rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. • An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. • A square root of a number is a number that when multiplied by itself will result in the original number. The square root of 4 is 2 because 2 · 2 = 4. A square root does not have to be a whole number. The square root of 1.44 is 1.2. • Any fraction can be changed into a decimal or percent and any decimal or percent can be changed into a fraction. This is because a decimal and a percent are based on the place values of tenths, hundredths, and thousandths etc., and most fractions can be changed to have a denominator of ten, hundred or thousand etc. • For the fractions that cannot easily be changed into 10, 100, or 1000, simple division will change the fraction into a decimal and then a percent. • Rational numbers can be added, subtracted, multiplied and divided. When a rational number in fraction form is added, subtracted, multiplied or divided, the rules for fractions are used. • When solving an equation or inequality with rational numbers, inverse operations are used. • Factors are numbers or variables that are multiplied together. The greatest common factor of two numbers or variables is the largest factor for both the numbers. The greatest common factor, or GCF, of 24 and 36 is 12. The GCF of 6x³ and 9x² is 3x² because 3 is the GCF of 6 and 9, and x² i s the GCF of x³ a nd x². © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use rational numbers and operations Any number is either rational or irrational. • One way to tell if a number is rational or irrational is to change it into a fraction. Any number that can be made into a fraction is rational. • Another way is to change the number into a decimal. If the decimal repeats or terminates, then it is rational. Otherwise it is irrational. For example, are the numbers, √8 and .12121212, rational or irrational? Ex. √8 = 2.828427125… it is irrational because it doesn't repeat or end. .12121212… it is rational because it repeats. • When comparing rational and irrational numbers, they should be changed into the same form, usually decimal form, and then compared. For example, order the numbers, √.5, 1/2, .8, (9/16), from least to greatest. To do this, the numbers must all be changed into the same form. Ex. 1/2 = .5 √.5 = .7071… .8 = .8 √(9/16) = .75 The correct order, from least to greatest, is 1/2, √.5, √(9/16), .8. • When rational and irrational numbers are used in equations and inequalities, the rules of fractions apply, such as adding and subtracting with common denominators. When solving, inverse operations are used. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
• Factors are numbers or variables that are multiplied. The greatest common factor or GCF of two numbers or variables is the greatest common factor for both of the numbers or variables. For example, what is the GCF of 16x4 and 14x²? Ex. The factors of 16x4 = 1, 2, 4, 8, 16 and x · x · x · x The factors of 14x² = 1, 2, 7, 14 and x · x The GCF would be 2x² because the number 2 is the GCF of the numbers 16 and 14, and x² is the GCF of the variables. Try This! 1. What are the following numbers written as fractions? .75 √9 8% √64/144 2. Are the following numbers rational or irrational? √3 .123123… √225 33 1/3% © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
3. What is the correct order from least to greatest for the following numbers? √.4 2/5 3/7 .6 4. Add the rational numbers: x/4 + 6x/4 = ? 5. Subtract the rational numbers: 4x/x - 2x/x = ? 6. Solve for x in the equation and inequality: (3/5)x = 9/25 x/-7 > -3 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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