D125 Mathematics for Elementary Educators I
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Free D125 Mathematics for Elementary Educators I Questions
Which of the following represents the prime factorization of 96?
- 2^5 * 3
- 2^5 * 3^2
- 2^5 * 3^1
- 2^6 * 3^2
Explanation
To find the prime factorization of 96, divide it by the smallest prime numbers repeatedly. 96 ÷ 2 = 48, 48 ÷ 2 = 24, 24 ÷ 2 = 12, 12 ÷ 2 = 6, 6 ÷ 2 = 3. The remaining 3 is prime. Counting the factors, we have 2 multiplied 5 times and 3 multiplied once. Therefore, the prime factorization is 2^5 * 3, which matches the correct option.
Correct Answer Is:
2^5 * 3
81 is what percent of 162?
- 60%
- 50%
- 40%
- 30%
Explanation
To determine what percent 81 is of 162, divide 81 by 162 and multiply by 100 to convert the fraction to a percentage. The calculation: (81/162) * 100 = 50%. Therefore, 81 represents 50 percent of 162.
Correct Answer Is:
50%
Students are adding whole numbers: 247 + 189. What is the sum?
- 426
- 436
- 446
- 456
Explanation
Explanation
To add 247 and 189, align the digits by place value and add column by column:
7 + 9 = 16, write 6 and carry over 1
4 + 8 + 1 (carry) = 13, write 3 and carry over 1
2 + 1 + 1 (carry) = 4
So, the sum is 436. Therefore, the correct answer is 436.
Correct Answer:
436
In the number 45,672.9813, which digit is in the thousands place?
- 4
- 5
- 6
- 7
Explanation
In a number, the thousands place is the fourth digit to the left of the decimal point. In 45,672.9813, counting from right to left before the decimal, the digits are: 2 (ones), 7 (tens), 6 (hundreds), 5 (thousands). Therefore, the digit in the thousands place is 5.
Correct Answer Is:
5
A teacher asks students: 247 + 189 = ?
- 426
- 436
- 446
- 456
Explanation
To add 247 and 189, align the digits by place value and add column by column: 7 + 9 = 16 → write 6 and carry 1 4 + 8 + 1 (carry) = 13 → write 3 and carry 1 2 + 1 + 1 (carry) = 4 The sum is 436. Therefore, the correct answer is 436.
Correct Answer Is:
436
How do you divide fractions?
- Subtract the divisor
- Add the divisor
- Divide by the divisor
- Multiply by the reciprocal of the divisor
Explanation
Dividing fractions involves multiplying the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). The reciprocal of a fraction is obtained by swapping its numerator and denominator. This method converts the division problem into a multiplication problem, which is easier to solve while maintaining the correct value. Therefore, the correct answer is the option that describes multiplying by the reciprocal of the divisor.
Correct Answer Is:
Multiply by the reciprocal of the divisor
Which list contains all the positive factors of 56?
- 2, 4, 7, 8, 14, 28
- 1, 2, 4, 7, 8, 14, 28, 56
- 56, 112, 168, 224
- 2020267
Explanation
The positive factors of a number are all the integers that divide the number exactly without leaving a remainder. For 56, the factors are 1, 2, 4, 7, 8, 14, 28, and 56. The first option is missing 1 and 56; the third and fourth options include numbers that are not factors of 56. Therefore, the correct answer is the option that lists all factors including 1 and 56.
Correct Answer Is:
1, 2, 4, 7, 8, 14, 28, 56
What is the result of multiplying or dividing two negative numbers?
- An irrational number
- Zero
- A negative number
- A positive number
Explanation
When two negative numbers are multiplied or divided, the result is always positive. This happens because the negative signs cancel each other out during multiplication or division. The rule mirrors that of positive numbers, except the sign change occurs due to the interaction of the two negative values. Thus, combining two negatives through these operations yields a positive outcome.
Correct Answer Is:
A positive number
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
In a classroom using the area model for fractions, what fraction represents 2 wholes divided into 5 equal parts each, with 7 parts shaded?
- 7/5
- 14/5
- 7/10
- 2 2/5
Explanation
If each of the 2 wholes is divided into 5 equal parts, there are 2 × 5 = 10 parts in total. With 7 parts shaded, the fraction representing the shaded area is 7/10. Therefore, the correct answer is 7/10.
Correct Answer Is:
7/10
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