Question

One board is 6 feet long and the other is 5 1/2 feet long. The total area os 60 3/8 sq ft. What is the width?

Answer 1

Answer:

5 1/4 ft

Step-by-step explanation:

... Area = length × width

Dividing by length, we find width to be ...

... width = Area / length

... = (60 3/8 ft²)/(6 ft +5 1/2 ft) . . . . total length is the sum of the 2 board lengths

... = (483/8 ft²)/(92/8 ft) = 483/92 ft = 5 1/4 ft

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Math with Fractions

$60\dfrac{3}{8}=60+\dfrac{3}{8}=60\cdot\dfrac{8}{8}+\dfrac{3}{8}\\\\=\dfrac{60\cdot 8}{8}+\dfrac{3}{8}=\dfrac{480+3}{8}=\dfrac{483}{8}$

Division with fractions can be done a couple of different ways.

• "invert the denominator and multiply"
• make the denominators of the fractions be the same, so the quotient is the ratio of the numerators

We have used the second method here.

$11\dfrac{1}{2}=11+\dfrac{4}{8}=11\cdot\dfrac{8}{8}+\dfrac{4}{8}\\\\=\dfrac{11\cdot 8}{8}+\dfrac{4}{8}=\dfrac{88+4}{8}=\dfrac{92}{8}$

Now we have the two numbers as improper fractions, so the division looks like ...

$\displaystyle\frac{\left(\frac{483}{8}\right)}{\left(\frac{92}{8}\right)}=\frac{483}{92}=\frac{23\cdot 21}{23\cdot 4}\\\\=\frac{21}{4}=5\frac{1}{4}$