When the fraction 56/32 is written first in its simplest fractional form and then expressed as a decimal value, what is the resulting decimal number?

Introduction / Context: This question combines two basic arithmetic skills: simplifying a fraction and converting a fraction to its decimal representation. Such tasks help examiners see whether candidates can move comfortably between different numerical forms. Here, we start with the fraction 56/32, simplify it fully, and then write the result as a decimal number.

Given Data / Assumptions: - Original fraction = 56/32. - We must first reduce it to simplest form. - Then we convert the simplified fraction into a decimal. - Usual decimal notation with a point is assumed, for example 1.75.

Concept / Approach: To simplify 56/32, we divide numerator and denominator by their greatest common divisor. Once in simplest form, we convert the resulting fraction to a decimal either by performing division or by using known fraction–decimal equivalents. The result must match exactly one of the given options.

Step-by-Step Solution: Start with 56/32. Both numbers are divisible by 8, a common factor. 56 / 8 = 7, 32 / 8 = 4, so 56/32 simplifies to 7/4. Now convert 7/4 to decimal by performing 7 ÷ 4. 7 ÷ 4 = 1.75. Therefore, the required decimal value is 1.75.

Verification / Alternative check: We can also use mixed number conversion. 7/4 is 1 whole and 3/4, written as 1 3/4. The fraction 3/4 equals 0.75. Therefore 1 + 0.75 = 1.75. This again confirms the decimal value 1.75 as consistent.

Why Other Options Are Wrong: Option 1.705 does not equal 7/4 and seems unrelated to the true division result. Option 1.450 is also different from 1.75 and does not correspond to any standard simplification of 56/32. Option 7.50 represents a much larger number and would correspond to 15/2 rather than 7/4. It is far from the correct value.

Common Pitfalls: A typical mistake is to simplify incorrectly, for example dividing 56 and 32 by 4 only once and not checking whether further simplification is possible. Another error is mis-dividing 7 by 4 and producing an incorrect decimal. Carefully performing the division or using the known value of 3/4 helps avoid such errors.

Final Answer: The required decimal value obtained from 56/32 is 1.75.