Find two numbers whose quotient is between, then estimate the quotient of 100 ÷ 7.
The Correct Answer and Explanation is:
Find two numbers whose quotient is between two whole numbers, then estimate the quotient of 100 ÷ 7.
Solution:
First, we are asked to estimate the quotient of 100 ÷ 7. Since 7 does not divide evenly into 100, we need to find two whole numbers that the quotient falls between.
Let’s begin by thinking:
- 7 × 14 = 98
- 7 × 15 = 105
We see that 98 is less than 100, and 105 is greater than 100. Therefore, the quotient of 100 ÷ 7 is between 14 and 15.
Now we can estimate:
100 ÷ 7 ≈ 14.29
So, the exact quotient is approximately 14.29, but since we are estimating, we can say that 100 ÷ 7 is about 14 or a little more than 14.
Explanation:
When dividing numbers that do not result in a whole number quotient, it is helpful to estimate by finding two products that are close to the dividend (in this case, 100). We start by multiplying 7 by various whole numbers to find which products come closest to 100 without exceeding it.
We find that 7 multiplied by 14 equals 98, which is just under 100, and 7 multiplied by 15 equals 105, which is just over 100. This tells us that 100 divided by 7 must fall between 14 and 15.
Estimation is a useful skill in everyday life because it allows us to quickly approximate answers without needing exact calculations. For example, if someone has 100 pieces of candy to share equally among 7 people, each person would get a little more than 14 pieces.
By understanding multiplication facts and using them to bracket our quotient between two known products, we develop a strong sense of number relationships, which is a key part of mathematical reasoning.
Final Estimate:
100 ÷ 7 ≈ 14.3
