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Which expression is equivalent to \( \frac{12}{7} \) ? \( \begin{array}{ll}\text { (A) } 12-7 & \text { (B) } 7-12 \\ \text { (c) } 12 \div 7 & \text { (D) } 7 \div 12\end{array} \) Kamaria lives on a ranch with 4 horses. She feeds the horses a total of 10 pounds of oats. Each horse gets the same amount of oats. How many pounds of oats does each horse get? Use a visual model and an equation to support your answer.

Ask by Bartlett Wyatt. in the United States
Feb 27,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Each horse gets 2.5 pounds of oats.

Solution

1. To find an expression equivalent to 12/7, notice that 12/7 means "12 divided by 7." This corresponds to option (C) 12 ÷ 7. 2. For the horses: Kamaria has 4 horses and 10 pounds of oats. To determine how much oats each horse gets, we set up the division problem:   x = amount of oats per horse   4 × x = 10   x = 10 ÷ 4 = 2.5 Each horse gets 2.5 pounds of oats. Visual Model: Imagine 10 identical oat pieces (or 10 pounds represented by a bar divided into 10 equal parts). We need to divide these 10 parts equally among 4 horses. One way to visualize is to draw a rectangle divided into 4 equal sections (each section representing each horse). Then, distribute the 10 parts as evenly as possible among the 4 sections. Since 10 cannot be evenly split into whole numbers, each section gets 2 whole parts and the remaining 2 parts are further divided equally, giving each horse an extra 0.5 part. Summing up, each horse gets 2 + 0.5 = 2.5 pounds of oats. Thus, both the equation and the visual model confirm that each horse receives 2.5 pounds of oats.

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Mind Expander

To find how many pounds of oats each horse gets, we can use a simple equation: if Kamaria has 4 horses and they share 10 pounds of oats equally, we can express this as \(x = \frac{10}{4}\), where \(x\) is the amount of oats each horse receives. Simplifying \( \frac{10}{4} \) gives us \( \frac{5}{2} \) or 2.5 pounds of oats per horse. A visual model could show a circle divided into four equal parts, each labeled with 2.5 to illustrate that each horse gets the same portion. Now, regarding the first expression question, the correct option equivalent to \( \frac{12}{7} \) is \( 12 \div 7 \), which corresponds to option (C). The choice (A) is a subtraction and not related to the original fraction, while (B) results in a negative number. Choice (D) gives a fraction less than 1, demonstrating how each option carries different meanings mathematically!

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