Question

math day 3 ng fractions b. write any fraction that is less than \\(\frac{1}{8}\\). answer: d. color and compare. \\(\frac{1}{2}\\) \\(\frac{1}{2}\\) \\(\frac{1}{3}\\) \\(\frac{1}{3}\\) \\(\frac{1}{3}\\) \\(\frac{1}{2}\\) \\(\frac{2}{3}\\) use the number line to compare the fractions below. \\(\frac{3}{4}\\) \\(\frac{3}{8}\\)

Explanation:

Part b

Step 1: Understand fraction comparison

To find a fraction less than $\frac{1}{8}$, we can use a fraction with a smaller numerator (when denominator is same) or a larger denominator (when numerator is same). For example, with same denominator 8, a numerator less than 1 (but since we use positive fractions, we can take $\frac{1}{9}$ (larger denominator) or $\frac{0}{8}$ (but 0/8 is 0, we can take $\frac{1}{9}$ or $\frac{1}{10}$, or with same denominator, $\frac{0}{8}$ is 0, but a simple one is $\frac{1}{9}$ or $\frac{1}{10}$, or $\frac{0}{8}$ (but usually positive non - zero, so $\frac{1}{9}$). But a simpler one with denominator 8: $\frac{0}{8}$ is 0, but if we take numerator less than 1, but for positive fractions, a fraction like $\frac{1}{9}$ is less than $\frac{1}{8}$ because when comparing $\frac{1}{8}$ and $\frac{1}{9}$, cross - multiply: $1\times9 = 9$ and $1\times8 = 8$, since $9>8$, $\frac{1}{8}>\frac{1}{9}$. But also, with denominator 8, a fraction like $\frac{0}{8}=0$ which is less than $\frac{1}{8}$, or $\frac{1}{10}$, etc. A common one is $\frac{1}{9}$ or $\frac{0}{8}$ (but 0/8 is 0). Let's take $\frac{1}{9}$ or $\frac{1}{10}$, or $\frac{0}{8}$. But a simple answer is $\frac{1}{9}$ (or any fraction with numerator 1 and denominator greater than 8, or numerator less than 1 with denominator 8). Let's take $\frac{1}{9}$ or $\frac{1}{10}$, or $\frac{0}{8}$. But for the purpose of this, let's take $\frac{1}{9}$ (or $\frac{1}{10}$, etc.). But also, with denominator 8, a fraction like $\frac{0}{8}=0$ which is less than $\frac{1}{8}$. But a more straightforward one is $\frac{1}{9}$.

Step 2: Write the fraction

We can choose $\frac{1}{9}$ (or $\frac{1}{10}$, $\frac{0}{8}$, etc.). Let's take $\frac{1}{9}$ as an example.

Step 1: Find a common denominator

To compare $\frac{1}{2}$ and $\frac{2}{3}$, we find the least common denominator (LCD) of 2 and 3, which is 6.

Step 2: Convert the fractions

Convert $\frac{1}{2}$ to sixths: $\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}$
Convert $\frac{2}{3}$ to sixths: $\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}$

Step 3: Compare the fractions

Since $\frac{3}{6}<\frac{4}{6}$,[SSE onError error]

Answer:

(for part b):
$\frac{1}{9}$ (or any fraction less than $\frac{1}{8}$, e.g., $\frac{1}{10}$, $\frac{0}{8}$)

Part d (comparing $\frac{1}{2}$ and $\frac{2}{3}$)