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

Ask by May Campos. in the United States
Mar 18,2025

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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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Mind Expander

To tackle the student's statement about \( 109.2 \div 6 \), let’s clarify: \( 1,092 \div 60 \) results in \( 18.2 \), which doesn’t equal \( 109.2 \div 6 \) that equals \( 18.2 \) as well. The confusion here comes from the decimal placement! Division by 6 is quite straightforward, but misplacing the decimal while adjusting numbers can lead to hiccups. For the second part of your question, two accurate division expressions are \( 611.2 \div 32 \) and \( 6112 \div 320 \). Both simplify to the same result as \( 61.12 \div 3.2 \). When calculated, \( 61.12 \div 3.2 \) equals \( 19.1 \). This shows how multiplying both the numerator and denominator by the same factor can maintain the value of a fraction!

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