1. A student said, "To find the value of $$ 109.2 \div 6 $$, I can divide 1,092 by $$ 60 . " $$ $$ \begin{array}{ll} ext { a) Do you agree with this } & ext { b) Calculate the quotient of } \ ext { statement? Explain your } & 109.2 \div 6 ext { using any method of } \ ext { reasoning } & ext { your choice. }\end{array} $$ 2.a. Write two division expressions that have the same value as $$ 61.12 \div 3.2 $$. b. Find the value of $$ 61.12 \div 3.2 $$. Show your reasoning. 3. $$ \begin{array}{l} ext { A bag of pennies weighs } 5.1 ext { kilogram. Each penny weighs } 2.5 ext { grams. About how } \ ext { many pennies are in the bag? SELECT ONE ANSWER } \ ext { A. } 20\end{array} $$ B. 200 C. 2,000 D. 20,000

Question

1. A student said, "To find the value of $$ 109.2 \div 6 $$, I can divide 1,092 by $$ 60 . " $$ $$ \begin{array}{ll}	ext { a) Do you agree with this } & 	ext { b) Calculate the quotient of } \ 	ext { statement? Explain your } & 109.2 \div 6 	ext { using any method of } \ 	ext { reasoning } & 	ext { your choice. }\end{array} $$ 2.a. Write two division expressions that have the same value as $$ 61.12 \div 3.2 $$. b. Find the value of $$ 61.12 \div 3.2 $$. Show your reasoning. 3. $$ \begin{array}{l}	ext { A bag of pennies weighs } 5.1 	ext { kilogram. Each penny weighs } 2.5 	ext { grams. About how } \ 	ext { many pennies are in the bag? SELECT ONE ANSWER } \ 	ext { A. } 20\end{array} $$ B. 200 C. 2,000 D. 20,000

UpStudy AI · Accepted Answer

1.  
a) The student’s method is correct. By multiplying both the dividend and the divisor by the same nonzero factor, the quotient remains unchanged. In this case, multiplying by 10 converts  
$$
109.2 \div 6 \quad\text{to}\quad \frac{109.2 \times 10}{6 \times 10} = \frac{1092}{60}.
$$

b) To calculate  
$$
109.2 \div 6,
$$  
we can use the equivalent expression  
$$
\frac{1092}{60}.
$$  
Dividing $$1092$$ by $$60$$ gives  
$$
1092 \div 60 = 18.2.
$$

2.  
a) One way to write equivalent division expressions for  
$$
61.12 \div 3.2
$$  
is to multiply both the dividend and the divisor by the same number to eliminate decimals. For example, multiplying by 10 gives  
$$
611.2 \div 32,
$$  
and multiplying by 100 gives  
$$
6112 \div 320.
$$

b) To compute  
$$
61.12 \div 3.2,
$$  
we can use either equivalent expression. Using the version with the decimals removed by multiplying by 10:  
$$
61.12 \div 3.2 = 611.2 \div 32.
$$  
Now, performing the division, we see that  
$$
32 \times 19.1 = 611.2,
$$  
so  
$$
61.12 \div 3.2 = 19.1.
$$

3.  
We are given that a bag of pennies weighs $$5.1$$ kilograms and each penny weighs $$2.5$$ grams. First, convert the weight of the bag to grams:  
$$
5.1\,\text{kg} = 5100\,\text{g}.
$$  
The number of pennies in the bag is  
$$
\text{Number of pennies} = \frac{5100\,\text{g}}{2.5\,\text{g per penny}} = 2040.
$$  
Since 2040 is closest to 2000 among the answer choices, the correct answer is Option C (2,000).
1. a) Yes, the student is correct. Multiplying both numbers by 10 turns $$109.2 \div 6$$ into $$1092 \div 60$$, which simplifies the division. b) $$ 109.2 \div 6 = 18.2 $$ 2. a) $$ 61.12 \div 3.2 = 611.2 \div 32 \quad \text{and} \quad 6112 \div 320 $$ b) $$ 61.12 \div 3.2 = 19.1 $$ 3. There are approximately 2,000 pennies in the bag.

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