Question

7.3.ip-5
find the sum. use fraction strips to help.
\\(\frac{1}{12} + \frac{1}{6} + \frac{1}{12}\\)
click the icon to view the fraction strips.
select the correct choice below, and fill in the answer boxes to complete your choice
(type whole numbers. list the terms in the same order as they appear in the original list.)
a. \\(\frac{1}{12} + \frac{1}{6} + \frac{1}{12} = \frac{\square}{18} + \frac{\square}{18} + \frac{\square}{18} = \frac{\square}{18} = \frac{\square}{6}\\)
b. \\(\frac{1}{12} + \frac{1}{6} + \frac{1}{12} = \frac{\square}{13} + \frac{\square}{13} + \frac{\square}{13} = \frac{\square}{13} = \frac{\square}{7}\\)
c. \\(\frac{1}{12} + \frac{1}{6} + \frac{1}{12} = \frac{\square}{12} + \frac{\square}{12} + \frac{\square}{12} = \frac{\square}{12} = \frac{\square}{2}\\)
click to select and enter your answer(s) and then click check answer.
all parts showing

Explanation:

Step1: Find common denominator

The fractions are $\frac{1}{12}$, $\frac{1}{6}$, $\frac{1}{12}$. The least common denominator (LCD) of 12 and 6 is 12 (since 6 divides into 12). For option C, the denominator is 12, so we convert $\frac{1}{6}$ to twelfths: $\frac{1}{6}=\frac{2}{12}$.

Step2: Rewrite fractions

Rewrite each fraction with denominator 12: $\frac{1}{12}+\frac{2}{12}+\frac{1}{12}$.

Step3: Add numerators

Add the numerators: $1 + 2 + 1 = 4$, so we have $\frac{4}{12}$.

Step4: Simplify the fraction

Simplify $\frac{4}{12}$ by dividing numerator and denominator by 4: $\frac{4\div4}{12\div4}=\frac{1}{3}$? Wait, no, wait. Wait, 1 + 2 + 1 is 4? Wait, no: $\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{1 + 2 + 1}{12}=\frac{4}{12}=\frac{1}{3}$? But let's check the options. Wait, option C's last part is $\frac{\square}{3}$? Wait, maybe I misread. Wait, the original problem's option C (partially visible) has denominator 12 for the first three, then $\frac{\square}{12}=\frac{\square}{3}$. Let's recalculate:

$\frac{1}{12}+\frac{1}{6}+\frac{1}{12}$. Convert $\frac{1}{6}$ to $\frac{2}{12}$. So $\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{1 + 2 + 1}{12}=\frac{4}{12}=\frac{1}{3}$. Wait, but let's check the options. Option A uses denominator 18, which is not the LCD. Option B uses 13, which is wrong. Option C (the visible part) has denominators 12, then 12, then 3. So let's do it correctly:

$\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{1 + 2 + 1}{12}=\frac{4}{12}=\frac{1}{3}$. Wait, but maybe the option C is:

$\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{4}{12}=\frac{1}{3}$. But let's check the options again. Wait, the user's image shows option C as:

C. $\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{\square}{12}+\frac{\square}{12}+\frac{\square}{12}=\frac{\square}{12}=\frac{\square}{3}$

So converting $\frac{1}{6}$ to $\frac{2}{12}$, so:

$\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{1 + 2 + 1}{12}=\frac{4}{12}=\frac{1}{3}$. Wait, but 4 divided by 4 is 1, 12 divided by 4 is 3. So $\frac{4}{12}=\frac{1}{3}$. But let's check the options. Wait, maybe I made a mistake. Wait, the original problem:

Wait, the correct way is to find a common denominator. The denominators are 12, 6, 12. The LCD is 12. So:

$\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{1 + 2 + 1}{12}=\frac{4}{12}=\frac{1}{3}$. But let's check the options. Option A: denominator 18. Let's see, $\frac{1}{12}=\frac{1.5}{18}$? No, that's not a whole number. So option A is wrong. Option B: denominator 13, which is wrong. Option C: denominator 12, then 3. So the correct option is C. Let's fill in the boxes:

First box: 1 (for $\frac{1}{12}$), second box: 2 (for $\frac{1}{6}=\frac{2}{12}$), third box: 1 (for $\frac{1}{12}$), fourth box: 4 (1 + 2 + 1), fifth box: 1 (since $\frac{4}{12}=\frac{1}{3}$? Wait, no, 4 divided by 4 is 1, 12 divided by 4 is 3. Wait, $\frac{4}{12}=\frac{1}{3}$. So the fifth box is 1? Wait, no, 4/12 simplifies to 1/3. So:

$\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{4}{12}=\frac{1}{3}$. So the boxes for option C are: 1, 2, 1, 4, 1. But let's check the original problem's option C:

C. $\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{\square}{12}+\frac{\square}{12}+\frac{\square}{12}=\frac{\square}{12}=\frac{\square}{3}$

So first three boxes: 1, 2, 1. Fourth box: 4. Fifth box: 1 (since 4/12 = 1/3). Wait, but maybe the problem has a typo, or I miscalculated. Wait, no: 1/12 + 1/6 + 1/12. 1/6 is 2/12. So 1 + 2 + 1 = 4. 4/12 = 1/3. So option C is correct. So the answer is option C, with the boxes filled as 1, 2, 1, 4, 1. But let's confirm the options. Option A: denominators 18, which is incorrect. Option B: denominators 13, incorrect. So option C is correct.

Answer:

C. $\frac{1}{12}+\frac{1}{6}+\frac{1}{12}=\frac{1}{12}+\frac{2}{12}+\frac{1}{12}=\frac{4}{12}=\frac{1}{3}$ (filling the boxes: 1, 2, 1, 4, 1)