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Fractions represent parts of a whole. They are composed of two main parts: the numerator and the denominator. The numerator, which is the top number, indicates how many parts are being considered. The denominator, the bottom number, shows into how many equal parts the whole is divided. For example, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. This fraction means that 3 out of 4 equal parts are being counted. Understanding fractions is crucial in various math problems and real-life scenarios, such as measuring ingredients or dividing items equally.

The denominator in a fraction is essential because it defines the division of the whole into equal parts. To change a fraction to an equivalent fraction with a different denominator, you often multiply or divide both the numerator and the denominator by the same number. In our exercise, we started with the fraction \(\frac{-20}{7}\). To convert it to a fraction with a denominator of 35, we had to find the factor to multiply 7 by to get 35. This factor is 5. Once we know the factor, we multiply both the numerator and the denominator by this factor, keeping the value of the fraction the same. This ensures the proportional relationship between the numerator and the denominator is maintained.

Multiplication plays a key role in converting fractions with different denominators. When determining the equivalent fraction, you find a factor that will convert the original denominator to the new one. In the provided exercise, we needed to find which number multiplied by 7 equals 35. This factor is 5. Next, we apply this factor to the numerator. For our fraction, it means multiplying -20 by 5, resulting in -100. Thus, the original fraction \(\frac{-20}{7}\) becomes \(\frac{-100}{35}\) when rewritten with a denominator of 35. Multiplying both parts of the fraction by the same number ensures the fraction's value remains unchanged while fitting the new denominator.