1. tamar will use between $ \frac{1}{3} $ and $ \frac{3}{4} $ tablespoons of salt in a recipe. what fraction of a tablespoon might tamar use? choose the correct explanation.$ \frac{2}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{1}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{3}{12} $.$ \frac{1}{12}

Question

1. tamar will use between $ \frac{1}{3} $ and $ \frac{3}{4} $ tablespoons of salt in a recipe. what fraction of a tablespoon might tamar use? choose the correct explanation.$ \frac{2}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{1}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{3}{12} $.$ \frac{1}{12} < \frac{2}{12} < \frac{3}{12} $$ \frac{3}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{2}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{4}{12} $.$ \frac{2}{12} < \frac{3}{12} < \frac{4}{12} $$ \frac{5}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{4}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{9}{12} $.$ \frac{4}{12} < \frac{5}{12} < \frac{9}{12} $$ \frac{5}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{4}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{9}{12} $.$ \frac{4}{12} < \frac{5}{12} < \frac{9}{12} $$ \frac{4}{12} < \frac{5}{12} < \frac{9}{12} $$ \frac{9}{12} $ tablespoon because $ \frac{1}{3} $ is equivalent to $ \frac{6}{12} $ and $ \frac{3}{4} $ is equivalent to $ \frac{11}{12} $.$ \frac{6}{12} < \frac{9}{12} < \frac{11}{12} $

Accepted Answer

# Explanation:
## Step1: Convert fractions to twelfths
To compare $\frac{1}{3}$ and $\frac{3}{4}$ with other fractions, we find their equivalent fractions with denominator 12.
For $\frac{1}{3}$, multiply numerator and denominator by 4: $\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}$.
For $\frac{3}{4}$, multiply numerator and denominator by 3: $\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$.

## Step2: Analyze each option
We need a fraction $x$ such that $\frac{1}{3}<x<\frac{3}{4}$, or in twelfths, $\frac{4}{12}<x<\frac{9}{12}$.
- Option 1: $\frac{2}{12}<\frac{1}{12}<\frac{3}{12}$ is incorrect as $\frac{1}{12}<\frac{2}{12}$ and $\frac{1}{3}=\frac{4}{12}$, not $\frac{1}{12}$.
- Option 2: $\frac{1}{12}<\frac{2}{12}<\frac{3}{12}$ is incorrect as $\frac{1}{3}=\frac{4}{12}$, not $\frac{1}{12}$.
- Option 3: $\frac{2}{12}<\frac{3}{12}<\frac{4}{12}$ is incorrect as $\frac{1}{3}=\frac{4}{12}$, so $\frac{3}{12}=\frac{1}{4}<\frac{1}{3}$.
- Option 4: $\frac{2}{12}<\frac{3}{12}<\frac{4}{12}$ is incorrect as above.
- Option 5: $\frac{5}{12}$ is between $\frac{4}{12}$ ($\frac{1}{3}$) and $\frac{9}{12}$ ($\frac{3}{4}$)? Wait, no, let's re - check. Wait, the correct equivalent for $\frac{1}{3}$ is $\frac{4}{12}$ and $\frac{3}{4}$ is $\frac{9}{12}$. So we need a fraction between $\frac{4}{12}$ and $\frac{9}{12}$.
Looking at the option with $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$: $\frac{4}{12}=\frac{1}{3}$, $\frac{9}{12}=\frac{3}{4}$, and $\frac{5}{12}$ is between them. Wait, but let's check the options again. Wait, the option that says $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ (i.e., $\frac{4}{12}$ is $\frac{1}{3}$, $\frac{9}{12}$ is $\frac{3}{4}$): So the correct option is the one where the fraction is between $\frac{4}{12}$ and $\frac{9}{12}$. Looking at the options, the one with $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ (the option stating " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$"). Wait, let's check the original options again. The option: " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$". Wait, no, in the given options, there is an option: " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$". Wait, but let's check the fractions. $\frac{1}{3}=\frac{4}{12}$, $\frac{3}{4}=\frac{9}{12}$. So a fraction between them should be greater than $\frac{4}{12}$ and less than $\frac{9}{12}$. The option with $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ is correct because $\frac{4}{12}=\frac{1}{3}$, $\frac{9}{12}=\frac{3}{4}$, and $\frac{5}{12}$ is between $\frac{4}{12}$ and $\frac{9}{12}$. Wait, but let's check the options in the image. The option: " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$". So that's the correct one. Wait, but let's re - check the equivalent fractions.
$\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}$, $\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}$. So we need a fraction $x$ where $\frac{4}{12}<x<\frac{9}{12}$. The option with $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ (i.e., $\frac{4}{12}$ is $\frac{1}{3}$, $\frac{9}{12}$ is $\frac{3}{4}$) is correct. So the correct option is the one that says " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$". Wait, looking at the options in the image, the option: " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$". So that's the correct answer.

# Answer: The option with the explanation " $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ tablespoon because $\frac{1}{3}$ is equivalent to $\frac{4}{12}$ and $\frac{3}{4}$ is equivalent to $\frac{9}{12}$" (the one with $\frac{4}{12}<\frac{5}{12}<\frac{9}{12}$ as the inequality and the correct equivalent fractions explanation).

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QUESTION IMAGE

Question

Explanation:

Step1: Convert fractions to twelfths

Step2: Analyze each option

Answer: