Question

6 cm
4\\(\frac{1}{4}\\) cm
number sentence: ________
area: ________

Explanation:

Step1: Convert mixed number to improper fraction

The height is \(4\frac{1}{4}\) cm. To convert a mixed number \(a\frac{b}{c}\) to an improper fraction, we use the formula \(\frac{a\times c + b}{c}\). So for \(4\frac{1}{4}\), we have \(a = 4\), \(b = 1\), \(c = 4\). Then \(4\frac{1}{4}=\frac{4\times4 + 1}{4}=\frac{17}{4}\) cm.

Step2: Calculate the area of the rectangle

The area of a rectangle is given by the formula \(A=\text{length}\times\text{width}\). Here, the length is \(6\) cm and the width (height) is \(\frac{17}{4}\) cm. So we multiply \(6\) by \(\frac{17}{4}\). \(6\times\frac{17}{4}=\frac{6\times17}{4}=\frac{102}{4}\).

Step3: Simplify the fraction

Simplify \(\frac{102}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\). \(\frac{102\div2}{4\div2}=\frac{51}{2}\). Convert \(\frac{51}{2}\) back to a mixed number: \(51\div2 = 25\) with a remainder of \(1\), so \(\frac{51}{2}=25\frac{1}{2}\) (wait, there was a mistake in the original number sentence. Let's recalculate: \(6\times4\frac{1}{4}=6\times(4 + \frac{1}{4})=6\times4+6\times\frac{1}{4}=24+\frac{6}{4}=24 + 1\frac{2}{4}=25\frac{2}{4}=25\frac{1}{2}\)? Wait, no, \(6\times\frac{17}{4}=\frac{102}{4}=\frac{51}{2}=25.5 = 25\frac{1}{2}\), but the original had \(25\frac{2}{4}\) which simplifies to \(25\frac{1}{2}\) or \(\frac{51}{2}\) or \(25.5\). Wait, maybe the original mixed number was \(4\frac{1}{4}\), so \(6\times4\frac{1}{4}=6\times\frac{17}{4}=\frac{102}{4}=\frac{51}{2}=25\frac{1}{2}\) square centimeters. But let's check the steps again.

Wait, maybe the user made a typo, but let's follow the correct calculation:

Step1: Identify the formula for the area of a rectangle

The area \(A\) of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width. Here, \(l = 6\) cm and \(w = 4\frac{1}{4}\) cm.

Step2: Convert the mixed number to an improper fraction

\(4\frac{1}{4}=\frac{4\times4 + 1}{4}=\frac{17}{4}\)

Step3: Multiply the length and the width

\(A=6\times\frac{17}{4}=\frac{6\times17}{4}=\frac{102}{4}\)

Step4: Simplify the fraction

\(\frac{102}{4}=\frac{51}{2}=25\frac{1}{2}\) (or \(25.5\)) square centimeters. The original number sentence had \(25\frac{2}{4}\) which is equivalent to \(25\frac{1}{2}\) since \(\frac{2}{4}=\frac{1}{2}\).

Answer:

The area of the rectangle is \(\boldsymbol{25\frac{1}{2}}\) square centimeters (or \(\boldsymbol{\frac{51}{2}}\) \(cm^2\) or \(\boldsymbol{25.5}\) \(cm^2\)). The correct number sentence is \(6\times4\frac{1}{4}=25\frac{1}{2}\) (or \(6\times\frac{17}{4}=\frac{51}{2}\)).