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\( \frac { - 2 } { 4 } , \quad \frac { 8 } { 7 } , \quad \frac { - 1.2 } { 1.5 } , \quad 7.65 , \quad 2 \frac { 2 } { 5 } , \quad - 4.2 \)

Ask by Grant Garrett. in Malaysia
Mar 17,2025

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Answer

\[ \frac{-1}{2}, \quad \frac{8}{7}, \quad \frac{-4}{5}, \quad \frac{153}{20}, \quad \frac{12}{5}, \quad -\frac{21}{5} \]

Solution

1. Convert \( \frac{-2}{4} \) to simplest form: \[ \frac{-2}{4} = \frac{-1}{2} \] 2. The fraction \( \frac{8}{7} \) is already in its simplest form. 3. Simplify \( \frac{-1.2}{1.5} \): Multiply numerator and denominator by 10 to eliminate decimals: \[ \frac{-1.2}{1.5} = \frac{-12}{15} \] Now, divide both numerator and denominator by their greatest common divisor (3): \[ \frac{-12}{15} = \frac{-4}{5} \] 4. Express \( 7.65 \) as a fraction: Write it as \[ 7.65 = \frac{765}{100} \] Then simplify by noticing that both 765 and 100 are divisible by 5: \[ \frac{765 \div 5}{100 \div 5} = \frac{153}{20} \] 5. Convert the mixed number \( 2\frac{2}{5} \) to an improper fraction: Multiply the whole number by the denominator and add the numerator: \[ 2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \] 6. Express \( -4.2 \) as a fraction: Write it as \[ -4.2 = -\frac{42}{10} \] Now simplify by dividing numerator and denominator by 2: \[ -\frac{42}{10} = -\frac{21}{5} \] The final simplified forms are: \[ \frac{-2}{4} = \frac{-1}{2}, \quad \frac{8}{7}, \quad \frac{-1.2}{1.5} = \frac{-4}{5}, \quad 7.65 = \frac{153}{20}, \quad 2\frac{2}{5} = \frac{12}{5}, \quad -4.2 = -\frac{21}{5} \]

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Bonus Knowledge

Let’s break down each of these numbers into their decimal forms, as it makes comparisons or calculations much simpler! The first number, \(-\frac{2}{4}\), simplifies to \(-0.5\). The second, \(\frac{8}{7}\), is approximately \(1.14\). Next up, \(-\frac{1.2}{1.5}\) becomes \(-0.8\). Meanwhile, \(7.65\) is already in decimal form. The mixed number \(2 \frac{2}{5}\) can be converted to \(2.4\) since \( \frac{2}{5} = 0.4\). Finally, \(-4.2\) remains as is. Putting it all together, we’ve got: - \(-0.5\) - \(1.14\) - \(-0.8\) - \(7.65\) - \(2.4\) - \(-4.2\) Now onwards to comparing these numbers with a fun twist! The numbers tell a tale of highs and lows, with \(7.65\) reigning as the champion of positivity, while \(-4.2\) hangs out at the party's less cheerful end. Who knew fractions could embody such drama? Oh, but wait, was that mixed number \(2 \frac{2}{5}\) trying to sneak a peak at the winning score? It’s quite the underdog story! So grab a scorecard, because it’s a wild ride from the deepest dungeons of negativity to the shining peaks of positivity!

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