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Zorluk: OrtaFraction Operations

A machinist needs to drill a hole completely through a steel block that is 3343\frac{3}{4} inches thick. The drill bit advances through the steel at a constant rate of 316\frac{3}{16} of an inch per second. How many seconds will it take to drill completely through the block?

Cevap: 20 seconds

Cevap

It will take 20 seconds to drill completely through the block.
To find the time required, the total thickness of the block must be divided by the distance the drill advances per second. Converting 3343\frac{3}{4} to 154\frac{15}{4} and dividing by 316\frac{3}{16} is calculated by multiplying by the reciprocal: 154×163=20\frac{15}{4} \times \frac{16}{3} = 20.

Adım Adım Çözüm

1
Convert the mixed number to an improper fraction.
334=1543\frac{3}{4} = \frac{15}{4}
Fraction multiplication and division are performed using improper fractions rather than mixed numbers.
2
Set up the division equation to solve for time.
Time = Distance ÷\div Rate = 154÷316\frac{15}{4} \div \frac{3}{16}
The time required is equal to the total distance (thickness) divided by the rate of progress.
3
Rewrite the division problem as multiplication by the reciprocal.
154×163\frac{15}{4} \times \frac{16}{3}
Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.
4
Simplify the fractions by cross-canceling, then multiply.
5×4=205 \times 4 = 20
Cross-canceling common factors (15 and 3, 16 and 4) before multiplying makes the final calculation simpler.

Anahtar Kavram

Fraction Division and Applied Rates
Tahmini Süre:50s
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Fraction Operations

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