Subtrahend: 2/32
[tex]\implies \dfrac{2}{32} \implies \dfrac{1 \times 2}{16 \times 2} \implies \underlin\dfrac{1}{16}[/tex]
The LCM of the denominators in the subtraction problem (5/8 - 2/32) can be determined by writing the multiples of 16 (Simplified denominator) and 8.
Writing the multiples of the denominators (16 and 8):
Since we can see that 16 is a common multiple and is has the least value in both multiples, 16 is the common multiple of 8 and 16.
Multiply such number to the denominators such that the denominators are equivalent to the LCM. Keep in mind that the number we multiply in the denominator must be multiplied to the numerator.
[tex]\implies \dfrac{5}{8} - \dfrac{1}{16}[/tex]
[tex]\implies \dfrac{5 \times x}{8 \times x} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8x = \text{LCM}][/tex]
[tex]\implies \dfrac{5 \times 2}{8 \times 2} - \dfrac{1}{16} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [8 \times x = \text{LCM} \implies 8 \times x = 16 \implies x = 2][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1}{16}[/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{x}{16x} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16x = \text{LCM}][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1 \times 1}{16 \times 1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [16 \times x = \text{LCM} \implies 16 \times x = 16 \implies x = 1][/tex]
[tex]\implies \dfrac{10}{16} - \dfrac{1}{16}[/tex]
Finally, let's subtract the fractions as the fractions have like denominators.
[tex]\implies \dfrac{9}{16}[/tex]
Therefore, the simplified fraction is 9/16.
Parts of a subtraction problem:
Learn more about subtracting unlike fractions:
⇒ https://brainly.com/question/14641413
