D125 Mathematics for Elementary Educators I
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Free D125 Mathematics for Elementary Educators I Questions
What is the place value of 7 in 4,728?
- Tens
- Hundreds
- Thousands
- Ten thousands
Explanation
In the number 4,728, the digits are arranged as follows: 4 (thousands), 7 (hundreds), 2 (tens), and 8 (ones). The 7 is in the hundreds place, which means its place value is 700. Therefore, the correct answer is hundreds.
Correct Answer Is:
Hundreds
In a lesson on rational numbers, which of these is NOT a rational number?
- 1/2
- 0.75
- √4
- √2
Explanation
Rational numbers are numbers that can be expressed as the quotient of two integers, with a nonzero denominator. 1/2 and 0.75 can be written as fractions (1/2 and 3/4), and √4 = 2, which is also rational. However, √2 cannot be expressed as a fraction of two integers; it is an irrational number. Therefore, the number that is NOT rational is √2.
Correct Answer Is:
√2
What are the next two numbers in the sequence with a rule of adding 25 and a starting number of 400?
- 425, 450
- 425, 450
- 425, 450
- 425, 450
Explanation
The sequence starts at 400 and follows a rule of adding 25 to each term to get the next. Starting from 400, the first term plus 25 gives 425, and adding 25 again gives 450. Therefore, the next two numbers in the sequence are 425 and 450.
Correct Answer Is:
425, 450
Which type of numbers cannot be represented as the quotient or fraction of two integers?
- Whole numbers
- Rational numbers
- Real numbers
- Irrational numbers
Explanation
Numbers that cannot be written as a quotient of two integers are called irrational numbers. These numbers cannot be expressed in the form (p/q), where ( p ) and ( q ) are integers and q ≠ 0. Their decimal representations are non-terminating and non-repeating. Examples include π, √2, and e. Because irrational numbers do not fit the definition of a rational fraction, they are the correct choice.
Correct Answer Is:
Irrational numbers
Which of the following numbers are prime numbers? (Choose all that apply)
- 39
- 47
- 27
- 73
Explanation
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Checking the options: 39 can be divided by 3 and 13, so it is not prime; 47 has no divisors other than 1 and 47, so it is prime; 27 can be divided by 3 and 9, so it is not prime; 73 has no divisors other than 1 and 73, so it is prime. Therefore, the numbers 47 and 73 are prime.
Correct Answer Is:
47, 73
What is the process for multiplying decimals?
- Divide the decimal places
- Add the decimal places
- Multiply as you would with whole numbers and consider decimal places
- Subtract the decimal places
Explanation
To multiply decimals, first ignore the decimal points and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in both original numbers and place the decimal in the product so that it has the same total number of decimal places. This ensures the product correctly reflects the magnitude of the decimals. Therefore, the correct answer is the option that describes multiplying like whole numbers and adjusting for decimal places.
Correct Answer Is:
Multiply as you would with whole numbers and consider decimal places
What is the least common multiple of 15 and 40?
- 120
- 60
- 30
- 80
Explanation
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. The multiples of 15 include 15, 30, 45, 60, 75, 90, 105, 120, … and the multiples of 40 include 40, 80, 120, … The smallest number common to both lists is 120. Therefore, the correct answer is the option that identifies 120 as the LCM.
Correct Answer Is:
120
How do you simplify a fraction to its lowest terms?
- Add the numerator and denominator
- Divide the numerator and denominator by the same number
- Multiply the numerator and denominator by the same number
- Find an equivalent fraction with no common factors
Explanation
To simplify a fraction to its lowest terms, you divide both the numerator and the denominator by their greatest common factor. This process reduces the fraction to an equivalent form in which the numerator and denominator share no further common factors besides 1. Simplifying in this way keeps the value of the fraction the same while expressing it in its simplest form. Therefore, the correct option is the one that describes dividing both parts of the fraction by the same number.
Correct Answer Is:
Divide the numerator and denominator by the same number
A teacher uses a scenario where a child has 3/4 of a pizza and eats 1/4. What fraction remains?
- 1/6
- 2/4
- 1/4
- 3/8
Explanation
The child starts with 3/4 of a pizza and eats 1/4. To find what remains, subtract the eaten portion from the total: 3/4 − 1/4 = 2/4. This fraction can also be simplified to 1/2, but based on the given options, the correct representation is 2/4. Therefore, the fraction of pizza that remains is 2/4.
Correct Answer Is:
2/4
What is an Integer?
- 1/3
- -3
- 0.5
- 2.5
Explanation
An integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals. Examples include -3, 0, 1, and 5. Integers are used in counting and measurement and are distinct from numbers with fractional parts like 1/3, 0.5, or 2.5. Therefore, the correct answer is the option that represents a whole number with no fractional or decimal component.
Correct Answer Is:
-3
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