Question

name:_______________________ period:_____
homework #20 regular
day 1
1 which of the following points on the number line best represents \\(\frac{5}{8}\\)?
number line with points a, b, c, d between 0 and 1
2 marcy lives 1.15 miles away from her grandmother. what fraction represents the distance between marcy’s house and her grandmother’s? don’t forget to simplify
3 a student receives a 95% on their math test. which of the following values are equivalent to 95%? select all that apply
a. 95 b. 0.95 c. \\(\frac{19}{20}\\) d. \\(\frac{95}{100}\\)
4 nineteen of the 20 students in mr gonzalez’s science class are attending the field trip. what decimal best represents the portion of the class that is attending the field trip?

Explanation:

Question 1

Step1: Understand the fraction

$\frac{5}{8}$ is a fraction between 0 and 1. Let's convert it to a decimal: $\frac{5}{8}=0.625$.

Step2: Analyze the number line

The number line has points between 0 and 1. Let's assume the intervals. Since 0.625 is more than 0.5 (which is $\frac{1}{2}$) and less than 1. Looking at the points A, B, C, D. Let's see the positions. $\frac{5}{8}=0.625$, so we need to find which point is around 0.625. Let's assume the number line is divided such that from 0 to 1, the points are placed. Let's check the order: A is closer to 0.5, B maybe a bit more, C around 0.6 - 0.7, D closer to 1. So 0.625 is likely point C (assuming the labels, but since we need to find the point, let's confirm: $\frac{5}{8}=0.625$, so on the number line, the point that is 0.625 from 0. So if the number line has marks, and 0.625 is between 0.5 and 1, so the point that is at 0.625. Let's say the points are A (maybe 0.55), B (0.6), C (0.625), D (0.9). So the best representation is point C (assuming the labels, but since the problem has points A, B, C, D, and $\frac{5}{8}=0.625$, so the point that is 0.625. So the answer would be the point corresponding to 0.625, which is likely C (depending on the number line's marking, but since we need to answer, let's proceed).

Step1: Convert decimal to fraction

Marcy lives 1.15 miles away. 1.15 can be written as $\frac{115}{100}$.

Step2: Simplify the fraction

Simplify $\frac{115}{100}$ by dividing numerator and denominator by 5: $\frac{115\div5}{100\div5}=\frac{23}{20}$. Or as a mixed number, but the problem says fraction, so $\frac{23}{20}$ (or $1\frac{3}{20}$, but since 1.15 is 1 + 0.15, 0.15 is $\frac{3}{20}$, so total is $\frac{23}{20}$).

Step1: Convert percentage to decimal

95% as a decimal is $95\div100 = 0.95$, so option B is correct.

Step2: Convert percentage to fraction

95% as a fraction is $\frac{95}{100}$, which simplifies to $\frac{19}{20}$ (dividing numerator and denominator by 5: $95\div5 = 19$, $100\div5 = 20$), so option C is correct. Option D is $\frac{95}{100}$, which is the unsimplified fraction, so D is also correct. Option A is 95, which is not equivalent to 95% (since 95% is 0.95, not 95).

Answer:

C (assuming the number line's points, the point representing $\frac{5}{8}=0.625$ is C)

Question 2