Properties of Real Numbers
To which set of numbers does the number belong?
–55
natural numbers
whole numbers
integers ✅
irrational numbers
Between which two numbers will √10 lie on the number line?
10 and 10.5
pi and 4 ✅
0 and pi
14/5 and 31/10
Which number lies between 4.3 and 4.5 on the number line?
4 1/5
√5
4 7/20 ✅
4.06
Name the property of real numbers illustrated by the equation.
2 • (√8 • 7) = (2 • √8) • 7
Distributive Property
Associative Property of Multiplication ✅
Commutative Property of Multiplication
Associative Property of Addition
An integer is always a rational number.
true ✅
false
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Great job on your test! Here are the explanations for each question:
1. The number -55 belongs to the set of integers since it is a negative whole number.
2. The square root (√) of 10 lies between pi and 4 on the number line. This is because pi (approximately 3.14) is less than the square root of 10 (approximately 3.16), and 4 is greater than the square root of 10.
3. The number 4 7/20 lies between 4.3 and 4.5 on the number line. This can be determined by converting the mixed number 4 7/20 into its decimal equivalent, which is approximately 4.35.
4. The property of real numbers illustrated by the equation 2 • (√8 • 7) = (2 • √8) • 7 is the Associative Property of Multiplication. This property states that the grouping of numbers in a multiplication equation does not affect the end result. In this case, the numbers are grouped differently, but the product remains the same.
5. An integer is always a rational number. This is true because a rational number is defined as any number that can be expressed as a fraction of two integers. Since integers can be expressed as a fraction with a denominator of 1, they are rational numbers.
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