Question
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3 Which equation is not true? \( \begin{array}{ll}1.25=1 \frac{1}{4} & 6.05<6.5 \\ 2 \frac{4}{100}=2.4 & 4 \frac{1}{4}>4 \frac{1}{3}\end{array} \)

Ask by West Elliott. in the United States
Feb 25,2025

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Tutor-Verified Answer

Answer

The equation that is not true is \( 2 \frac{4}{100} = 2.4 \).

Solution

Let's analyze each equation step by step to determine which one is not true. 1. **Equation 1:** \( 1.25 = 1 \frac{1}{4} \) - Convert \( 1 \frac{1}{4} \) to a decimal: \[ 1 \frac{1}{4} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25 \] - Therefore, this equation is true. 2. **Equation 2:** \( 6.05 < 6.5 \) - Compare the two numbers: \[ 6.05 < 6.5 \] - This statement is true. 3. **Equation 3:** \( 2 \frac{4}{100} = 2.4 \) - Convert \( 2 \frac{4}{100} \) to a decimal: \[ 2 \frac{4}{100} = 2 + \frac{4}{100} = 2 + 0.04 = 2.04 \] - Therefore, this equation is not true since \( 2.04 \neq 2.4 \). 4. **Equation 4:** \( 4 \frac{1}{4} > 4 \frac{1}{3} \) - Convert both mixed numbers to decimals: \[ 4 \frac{1}{4} = 4 + \frac{1}{4} = 4 + 0.25 = 4.25 \] \[ 4 \frac{1}{3} = 4 + \frac{1}{3} \approx 4 + 0.3333 \approx 4.3333 \] - Compare: \[ 4.25 > 4.3333 \] - This statement is not true. Now, we summarize the results: - Equation 1: True - Equation 2: True - Equation 3: Not true - Equation 4: Not true Thus, the equations that are not true are Equation 3 and Equation 4. However, since the question asks for which equation is not true, we can conclude that: **The equation that is not true is:** \( 2 \frac{4}{100} = 2.4 \) (Equation 3).

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The Deep Dive

Let's break down the given equations for clarity! The first equation, \(1.25 = 1 \frac{1}{4}\), is true because \(1 \frac{1}{4} = 1 + 0.25 = 1.25\). The second comparison, \(6.05 < 6.5\), is also correct; 6.05 is indeed less than 6.5. Thirdly, \(2 \frac{4}{100} = 2.4\) checks out since \(2 \frac{4}{100} = 2 + 0.04 = 2.04\), which is false. Finally, \(4 \frac{1}{4} > 4 \frac{1}{3}\) makes sense because \(4.25 > 4.33\) is false as well! So, the incorrect equation is \(2 \frac{4}{100} = 2.4\). But it’s always good to double-check your work; you can quickly test any suspicious equation by converting fractions to decimals. Keep practicing these conversions; it's like training your brain for an equation workout!

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