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Chapter 1: Problem 505

Simplify. $$ 1-\frac{3}{5} \div \frac{1}{10} $$

Short Answer

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Step by step solution

01

Understand the division of fractions

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator. Here, the reciprocal of \(\frac{1}{10}\) is \(\frac{10}{1}\).
02

Rewrite the expression

Rewrite the original expression \(1 - \frac{3}{5} \div \frac{1}{10}\) using the reciprocal from Step 1: \(1 - \frac{3}{5} \times \frac{10}{1}\).
03

Multiply the fractions

Multiply \(\frac{3}{5}\) by \(\frac{10}{1}\): \(\frac{3 \times 10}{5 \times 1} = \frac{30}{5} = 6\).
04

Simplify the expression

Now subtract: \(1 - 6\).
05

Perform the subtraction

Calculate the result of \(1 - 6 = -5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

reciprocal
The concept of reciprocal is integral when dealing with fraction division. A reciprocal is essentially the

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