D125 Mathematics for Elementary Educators I
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Free D125 Mathematics for Elementary Educators I Questions
What is a rational number?
- A number formed by dividing two integers
- A prime number
- A whole number
- An irrational number
Explanation
A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. This means rational numbers include fractions, terminating decimals, and repeating decimals. The defining characteristic is the ability to write the number in the form p/q, where p and q are integers. Therefore, the correct answer is the option that describes this relationship.
Correct Answer Is:
A number formed by dividing two integers
79.9 is what percent of 159.8?
- 30%
- 60%
- 50%
- 40%
Explanation
To find what percent 79.9 is of 159.8, divide 79.9 by 159.8 and multiply by 100: (79.9/159.8) * 100 = 50%. This calculation shows that 79.9 is exactly half of 159.8, or 50 percent. Therefore, the correct answer is the option that represents 50%.
Correct Answer Is:
50%
11 is what percent of 97?
- 15.5%
- 8.7%
- 11.34%
- 20.3%
Explanation
To determine what percent 11 is of 97, divide 11 by 97 and multiply by 100: (11/97) * 100 = 11.34%. This calculation converts the ratio of 11 to 97 into a percentage. Therefore, the correct answer is the option that equals 11.34%.
Correct Answer Is:
11.34%
Convert the mixed number 2 1/3 to an improper fraction:
- 5/3
- 7/3
- 6/3
- 2/3
Explanation
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part and add the numerator: 2 × 3 + 1 = 6 + 1 = 7 Place this over the original denominator: 7/3. Therefore, 2 1/3 as an improper fraction is 7/3.
Correct Answer Is:
7/3
What is the rule for a number pattern with the following first four terms: 1, 11, 21, 31, ...?
- Odd number
- Even number
- Prime number
- Composite number
Explanation
The given sequence increases by 10 with each term: 1, 11, 21, 31, … This pattern shows that each term is 10 more than the previous term. The rule describes the type of numbers in the sequence, which are all odd numbers because adding 10 to an odd number results in another odd number. Therefore, the correct answer is the option that identifies the sequence as odd numbers.
Correct Answer Is:
Odd number
Which numbers are considered rational?
- Numbers with infinite decimal expansions
- Numbers that cannot be represented as a fraction of two integers
- Numbers that can be expressed as a quotient of two integers
- Numbers that continue without repeating
Explanation
Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This includes integers, fractions, and terminating or repeating decimals. Numbers that cannot be expressed as a fraction of integers, such as non-repeating and non-terminating decimals, are irrational. Therefore, the correct answer is the option that identifies rational numbers as those that can be expressed as a quotient of two integers.
Correct Answer Is:
Numbers that can be expressed as a quotient of two integers
What is a Composite Number?
- 5
- 3
- 7
- 12
Explanation
A composite number is an integer greater than 1 that has more than two factors, meaning it can be divided evenly by numbers other than 1 and itself. Unlike prime numbers, which have exactly two factors, composite numbers can be broken down into smaller positive integers through multiplication. In this case, 12 has factors such as 2, 3, 4, and 6 in addition to 1 and 12, making it a composite number. Therefore, the correct answer is the option that identifies 12 as a composite number.
Correct Answer Is:
12
A recipe calls for 2/3 cup of sugar per batch. For 3/4 of a batch, how much sugar?
- 1/2 cup
- 6/12 cup
- 5/7 cup
- 1/4 cup
Explanation
Explanation
To find the amount of sugar for 3/4 of a batch, multiply the fraction of the batch by the amount of sugar per full batch:
(2/3) × (3/4) = 6/12 = 1/2
Therefore, for 3/4 of a batch, the student would need 1/2 cup of sugar.
Correct Answer Is:
1/2 cup
A teacher asks students to find the greatest common factor (GCF) of 12 and 18 to simplify a fraction. What is the GCF?
- 3
- 6
- 9
- 12
Explanation
The greatest common factor (GCF) is the largest number that divides exactly into two or more numbers. For 12 and 18, the factors of 12 are 1, 2, 3, 4, 6, 12, and the factors of 18 are 1, 2, 3, 6, 9, 18. The largest factor they have in common is 6. Therefore, the GCF of 12 and 18 is 6.
Correct Answer Is:
6
25.7 is what percent of 141?
- 18.16%
- 20.3%
- 15.5%
- 12.7%
Explanation
To find what percent 25.7 is of 141, divide 25.7 by 141 and then multiply the result by 100. The calculation is (25.7/141) * 100 = 18.16%. This gives the percentage representation of 25.7 relative to 141. Therefore, the correct answer is the option that matches 18.16%.
Correct Answer Is:
18.16%
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