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

5 1/4 ft

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(3)/(8)=60+(3)/(8)=60\cdot(8)/(8)+(3)/(8)\\\\=(60\cdot 8)/(8)+(3)/(8)=(480+3)/(8)=(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(1)/(2)=11+(4)/(8)=11\cdot(8)/(8)+(4)/(8)\\\\=(11\cdot 8)/(8)+(4)/(8)=(88+4)/(8)=(92)/(8)`

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

`\displaystyle(\left((483)/(8)\right))/(\left((92)/(8)\right))=(483)/(92)=(23\cdot 21)/(23\cdot 4)\\\\=(21)/(4)=5(1)/(4)`