Morgan is designing a rectangular quilt. The quilt will be 1(3)/(5)m wide and will have an area of 6m^(2). How long is the quilt? m

Convert to Improper Fraction: Convert the mixed number for the width of the quilt to an improper fraction. 1(3/5) can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and placing the result over the original denominator. 1(3/5) = (1 * 5 + 3)/5 = (5 + 3)/5 = 8/5 The width of the quilt is 8/5 meters.Use Area Formula: Use the area formula for a rectangle to find the length. The area (A) of a rectangle is given by the formula A = width * length. We know the area is 6 square meters (6m^2) and the width is 8/5 meters. Let's denote the length of the quilt as 'L'. So, the equation is 6 = (8/5) * L.Solve for Length: Solve for the length 'L'. To find 'L', divide both sides of the equation by 8/5. L = 6 / (8/5) To divide by a fraction, multiply by its reciprocal. L = 6 * (5/8) L = 30/8 L = 3.75 The length of the quilt is 3.75 meters.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Morgan is designing a rectangular quilt. The quilt will be
1(3)/(5)m wide and will have an area of
6m^(2).
How long is the quilt?
m

Morgan is designing a rectangular quilt. The quilt will be $1 \frac{3}{5} \mathrm{~m}$ wide and will have an area of $6 \mathrm{~m}^{2}$ . $\newline$ How long is the quilt? $\newline$ m

View step-by-step help

Home

Math Problems

Grade 7

Scale drawings: word problems

Full solution

Q. Morgan is designing a rectangular quilt. The quilt will be

1 \frac{3}{5} \mathrm{~m}

wide and will have an area of

6 \mathrm{~m}^{2}

\newline

How long is the quilt?

\newline

Convert to Improper Fraction: Convert the mixed number for the width of the quilt to an improper fraction. $\newline$ $1\frac{3}{5}$ can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and placing the result over the original denominator. $\newline$ $1\frac{3}{5} = (1 \times 5 + 3)/5 = (5 + 3)/5 = \frac{8}{5}$ $\newline$ The width of the quilt is $\frac{8}{5}$ meters.
Use Area Formula: Use the area formula for a rectangle to find the length. $\newline$ The area $A$ of a rectangle is given by the formula $A = \text{width} \times \text{length}$ . $\newline$ We know the area is $6$ square meters $(6\,\text{m}^2)$ and the width is $\frac{8}{5}$ meters. $\newline$ Let's denote the length of the quilt as ' $L$ '. $\newline$ So, the equation is $6 = \left(\frac{8}{5}\right) \times L$ .
Solve for Length: Solve for the length $L$ . To find $L$ , divide both sides of the equation by $\frac{8}{5}$ . $L = \frac{6}{(\frac{8}{5})}$ To divide by a fraction, multiply by its reciprocal. $L = 6 \times (\frac{5}{8})$ $L = \frac{30}{8}$ $L = 3.75$ The length of the quilt is $3.75$ meters.