Which of the following correctly shows the quotient of 75 divided by 5?
5/75 = 12
75/5= 15
75÷5= 25
75÷5= 70
The Correct Answer and Explanation is :
The correct expression that shows the quotient of 75 divided by 5 is:
75 ÷ 5 = 15
Explanation
To understand why this is the correct answer, let’s break down the division process and its basic principles.
Division Concept: Division is one of the four fundamental arithmetic operations (along with addition, subtraction, and multiplication). It involves determining how many times one number (the divisor) fits into another number (the dividend). In this case, 75 is the dividend, and 5 is the divisor. When you divide 75 by 5, you are essentially asking how many groups of 5 can fit into 75.
Performing the Calculation: To perform the division, you can think of it in two ways: through repeated subtraction or by using multiplication.
- Repeated Subtraction: Start with 75 and repeatedly subtract 5 until you reach zero.
- 75 – 5 = 70 (1 group)
- 70 – 5 = 65 (2 groups)
- 65 – 5 = 60 (3 groups)
- 60 – 5 = 55 (4 groups)
- 55 – 5 = 50 (5 groups)
- 50 – 5 = 45 (6 groups)
- 45 – 5 = 40 (7 groups)
- 40 – 5 = 35 (8 groups)
- 35 – 5 = 30 (9 groups)
- 30 – 5 = 25 (10 groups)
- 25 – 5 = 20 (11 groups)
- 20 – 5 = 15 (12 groups)
- 15 – 5 = 10 (13 groups)
- 10 – 5 = 5 (14 groups)
- 5 – 5 = 0 (15 groups)
So, you can see that you can subtract 5 from 75 a total of 15 times before reaching zero. Therefore, 75 divided by 5 equals 15.
- Multiplication Check: Another way to confirm this is to reverse the process. If 75 divided by 5 equals 15, then multiplying the result (15) by the divisor (5) should give you back the original number (75):
- 15 × 5 = 75
Both methods confirm that the quotient of 75 divided by 5 is indeed 15.
Conclusion
Looking at the other options provided:
- 5/75 = 12: This is incorrect because dividing 5 by 75 does not equal 12.
- 75/5 = 25: This is incorrect; it is simply another way of saying 75 ÷ 5, but the result is still 15, not 25.
- 75÷5= 70: This is incorrect; dividing 75 by 5 does not yield 70.
Thus, the correct and valid representation of the quotient of 75 divided by 5 is 75 ÷ 5 = 15.