Question

1. write 0.375 as an equivalent fraction (in simplest form).
2. solve for s.

( s cdot 2\frac{3}{4} = 14\frac{1}{5} )
word problem

1. iodine and xenon are beside each other on the periodic table of elements. however, their melting points are very different. iodine’s melting point is ( 113.7^circ \text{c} ), while xenon’s melting point is ( -111.74^circ \text{c} ). what is the difference between these two melting points? how could you use a number line to see if your answer is reasonable?

Explanation:

Question 9

Step1: Identify decimal place

0.375 has three decimal places, so write as $\frac{375}{1000}$.

Step2: Simplify the fraction

Find GCD of 375 and 1000. GCD(375,1000)=125. Divide numerator and denominator by 125: $\frac{375\div125}{1000\div125}=\frac{3}{8}$.

Step1: Convert mixed numbers to improper fractions

$2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$, $14\frac{1}{5}=\frac{14\times5+1}{5}=\frac{71}{5}$.

Step2: Solve for \( s \)

The equation is \( s\times\frac{11}{4}=\frac{71}{5} \). Multiply both sides by \( \frac{4}{11} \): \( s=\frac{71}{5}\times\frac{4}{11}=\frac{284}{55} \). Convert to mixed number: \( \frac{284}{55}=5\frac{9}{55} \).

Step1: Calculate the difference

To find the difference between \( 113.7^\circ\text{C} \) and \( - 111.74^\circ\text{C} \), use the formula \( \text{Difference}=113.7-(-111.74) \). Subtracting a negative is adding the positive: \( 113.7 + 111.74 = 225.44^\circ\text{C} \).

Step2: Use number line for reasonableness

• Locate \( -111.74 \) on the number line (left of 0).
• Locate \( 113.7 \) on the number line (right of 0).
• The distance between them should be the sum of the distance from \( -111.74 \) to 0 (111.74) and from 0 to 113.7 (113.7). Adding these: \( 111.74+113.7 = 225.44 \), which matches our calculation, so the answer is reasonable.

Answer:

$\frac{3}{8}$

Question 10