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The movenent of the progress bor moy be uneven becouse questions con be more nore or iess photoring rerof depending onyour orsmer An art teacher has \( 70 \frac{1}{2} \) pounds of clay and 20 students. Each student will get an equal amount of clay. How much clay does each student get? Write the answer as a mixed number. (141 1410 \( 3 \frac{21}{40} \) \( \frac{40}{141} \)

Ask by Rodriguez King. in the United States
Feb 03,2025

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Answer

Each student gets \(3 \frac{21}{40}\) pounds of clay.

Solution

Let's solve the problem step by step. **Problem:** An art teacher has \(70 \frac{1}{2}\) pounds of clay and 20 students. Each student will get an equal amount of clay. How much clay does each student get? Write the answer as a mixed number. **Step 1: Convert the mixed number to an improper fraction.** \[70 \frac{1}{2} = \frac{141}{2}\] **Step 2: Divide the total clay by the number of students.** \[ \frac{141}{2} \div 20 = \frac{141}{2} \times \frac{1}{20} = \frac{141}{40} \] **Step 3: Convert the improper fraction back to a mixed number.** \[ \frac{141}{40} = 3 \frac{21}{40} \] **Answer:** \[ 3 \frac{21}{40} \]

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The Deep Dive

To find out how much clay each student gets, you can divide the total amount of clay by the number of students. First, convert \( 70 \frac{1}{2} \) pounds of clay into an improper fraction. This equals \( \frac{141}{2} \). Now, divide this by 20, or \( \frac{141}{2} \div 20 \) which is the same as multiplying by the reciprocal, \( \frac{141}{2} \times \frac{1}{20} = \frac{141}{40} \). Converting this to a mixed number gives you \( 3 \frac{21}{40} \) pounds of clay per student. Remember, when performing division with fractions, it's always crucial to flip the second fraction and multiply. A common mistake is to forget to convert mixed numbers into improper fractions, which can lead to confusion and incorrect answers. Always double-check your steps and simplify whenever possible.

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