Hailey tried to divide 92 by 5. Her work is shown below.
Which statements are true about Hailey's work? Check all that apply.
* Hailey found the correct quotient.
* The "1" in the quotient represents the number of tens in each of the 5 groups.
* Hailey placed the dividend and divisor in the wrong places in the problem.
* The "R2" represents the number of ones in each of the 5 groups.
* Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.
Answer (1)
Hailey correctly divides 92 by 5 using long division.
The quotient is 18, and the remainder is 2.
The '1' in the quotient represents 10, the number of tens in each group.
The true statements are: Hailey found the correct quotient; The "1" in the quotient represents the number of tens in each of the 5 groups; Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over. .
Explanation
Problem Analysis Let's analyze Hailey's work on the long division problem 92 d i v 5 . We need to determine if her steps and conclusions are correct. First, let's perform the long division ourselves to establish the correct answer.
Step-by-step Calculation When we divide 92 by 5, we first look at the tens place. How many times does 5 go into 9? It goes in 1 time. So, we write '1' in the tens place of the quotient. Then, we multiply 1 × 5 = 5 , and subtract 5 from 9, which gives us 4. We bring down the 2 from the ones place of the dividend, making it 42.
Continuing the Calculation Now, we ask: How many times does 5 go into 42? It goes in 8 times. So, we write '8' in the ones place of the quotient. Then, we multiply 8 × 5 = 40 , and subtract 40 from 42, which gives us 2. This means our quotient is 18 and our remainder is 2.
Evaluating the Statements Now, let's evaluate the given statements:
Hailey found the correct quotient. Hailey's quotient is 18 with a remainder of 2, which is the correct quotient. So, this statement is true.
The "1" in the quotient represents the number of tens in each of the 5 groups. The '1' in the quotient represents 1 ten, meaning there is 1 ten (or 10) in each of the 5 groups. So, this statement is true.
Hailey placed the dividend and divisor in the wrong places in the problem. Hailey placed the dividend (92) and divisor (5) in the correct places for long division. So, this statement is false.
The "R2" represents the number of ones in each of the 5 groups. The 'R2' represents the remainder, which is the number of ones left over after dividing as evenly as possible. It does not represent the number of ones in each of the 5 groups. So, this statement is false.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over. This accurately describes the first step in long division. We subtract 5 (representing 5 tens) from 9 (representing 9 tens) to see how many tens are left to bring down to the ones place. So, this statement is true.
Identifying True Statements Therefore, the true statements are:
Hailey found the correct quotient.
The "1" in the quotient represents the number of tens in each of the 5 groups.
Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.
Examples
Long division is a fundamental arithmetic operation used in various real-life scenarios. For example, imagine you're sharing a package of 92 candies equally among 5 friends. Using long division, you find that each friend gets 18 candies, and there are 2 candies left over. This concept extends to more complex situations, such as calculating unit prices at the grocery store (e.g., dividing the total cost of a package by the number of items to find the price per item) or determining monthly payments on a loan. Understanding long division helps in fair distribution and informed purchasing decisions.
