Claire is making a frame to display a drawing she made. The frame is 11(1)/(5)cm wide. The frame has a rectangular shape and an area of 560cm^(2). How tall is the frame? cm

Convert to improper fraction: Convert the mixed number for the width of the frame to an improper fraction. 11(1/5) cm can be written as (11 * 5 + 1)/5 cm, which is (55 + 1)/5 cm. So, 11(1/5) cm = 56/5 cm.Use area formula: Use the area formula for a rectangle, which is Area = Width * Height. We know the area (560 cm^2) and the width (56/5 cm), and we need to find the height. Let's denote the height as H. So, the equation is 560 = (56/5) * H.Solve for H: Solve for H by dividing both sides of the equation by the width (56/5 cm). H = 560 / (56/5) H = 560 * (5/56)Simplify the fraction: Simplify the fraction by canceling out common factors. Both 560 and 56 have a common factor of 56. H = (560/56) * (5/1) H = 10 * 5 H = 50Check the calculation: Check the calculation for any mathematical errors. We started with an area of 560 cm^2 and a width of 56/5 cm. After dividing the area by the width, we got a height of 50 cm. Multiplying the width (56/5 cm) by the height (50 cm) should give us the original area. (56/5) * 50 = 560 11.2 * 50 = 560 560 = 560 The calculation checks out, so there are no mathematical errors.

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Q. Claire is making a frame to display a drawing she made. The frame is

11 \frac{1}{5} \mathrm{~cm}

wide. The frame has a rectangular shape and an area of

560 \mathrm{~cm}^{2}

\newline

How tall is the frame?

\newline

\mathrm{cm}

Convert to improper fraction: Convert the mixed number for the width of the frame to an improper fraction. $\newline$ $11\left(\frac{1}{5}\right)$ cm can be written as $\frac{11 \times 5 + 1}{5}$ cm, which is $\frac{55 + 1}{5}$ cm. $\newline$ So, $11\left(\frac{1}{5}\right)$ cm = $\frac{56}{5}$ cm.
Use area formula: Use the area formula for a rectangle, which is $\text{Area} = \text{Width} \times \text{Height}$ . $\newline$ We know the area ( $560 \, \text{cm}^2$ ) and the width ( $\frac{56}{5} \, \text{cm}$ ), and we need to find the height. $\newline$ Let's denote the height as $H$ . $\newline$ So, the equation is $560 = \left(\frac{56}{5}\right) \times H$ .
Solve for $H$ : Solve for $H$ by dividing both sides of the equation by the width ( $\frac{56}{5}\,\text{cm}$ ). $\newline$ $H = 560 ÷ \frac{56}{5}$ $\newline$ $H = 560 \times \frac{5}{56}$
Simplify the fraction: Simplify the fraction by canceling out common factors. $\newline$ Both $560$ and $56$ have a common factor of $56$ . $\newline$ $H = \frac{560}{56} \times \frac{5}{1}$ $\newline$ $H = 10 \times 5$ $\newline$ $H = 50$
Check the calculation: Check the calculation for any mathematical errors. $\newline$ We started with an area of $560\,\text{cm}^2$ and a width of $\frac{56}{5}\,\text{cm}$ . After dividing the area by the width, we got a height of $50\,\text{cm}$ . $\newline$ Multiplying the width $(\frac{56}{5}\,\text{cm})$ by the height $(50\,\text{cm})$ should give us the original area. $\newline$ $(\frac{56}{5}) \times 50 = 560$ $\newline$ $11.2 \times 50 = 560$ $\newline$ $560 = 560$ $\newline$ The calculation checks out, so there are no mathematical errors.