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Answer :
Let's solve the problem step by step to find out how many teaspoons of toasted sesame seeds Omar needs for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes, and determine the rate in teaspoons of toasted sesame seeds per teaspoon of pepper flakes.
### Step-by-Step Solution
1. Understand the given ratio:
Omar's family recipe states that 4 teaspoons of toasted sesame seeds are used per [tex]\(\frac{1}{3}\)[/tex] teaspoon of pepper flakes.
2. Determine the rate:
To find out how many teaspoons of toasted sesame seeds are used per teaspoon of pepper flakes, we need to set up a ratio and make a note of the unit rate.
- The given ratio is 4 teaspoons of toasted sesame seeds per [tex]\(\frac{1}{3}\)[/tex] teaspoon of pepper flakes.
- To find the rate in terms of 1 teaspoon of pepper flakes, we calculate:
[tex]\[
\text{Rate} = \frac{4 \text{ tsp of toasted sesame seeds}}{\frac{1}{3} \text{ tsp of pepper flakes}}
\][/tex]
3. Simplify the rate:
To simplify the fraction:
[tex]\[
\text{Rate} = 4 \div \frac{1}{3} = 4 \times \frac{3}{1} = 12
\][/tex]
So, the rate is 12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes.
4. Calculate the amount needed for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes:
Now, we need to find out how many teaspoons of toasted sesame seeds are needed for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes.
- Using the rate we just found (12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes):
[tex]\[
\text{Sesame seeds needed} = 12 \times \frac{2}{3}
\][/tex]
- Perform the multiplication:
[tex]\[
\text{Sesame seeds needed} = 12 \times \frac{2}{3} = 12 \times 0.6667 = 8 \text{ teaspoons of toasted sesame seeds}
\][/tex]
### Final Answers:
- Omar needs 8 teaspoons of toasted sesame seeds for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes.
- The rate is 12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes.
### Step-by-Step Solution
1. Understand the given ratio:
Omar's family recipe states that 4 teaspoons of toasted sesame seeds are used per [tex]\(\frac{1}{3}\)[/tex] teaspoon of pepper flakes.
2. Determine the rate:
To find out how many teaspoons of toasted sesame seeds are used per teaspoon of pepper flakes, we need to set up a ratio and make a note of the unit rate.
- The given ratio is 4 teaspoons of toasted sesame seeds per [tex]\(\frac{1}{3}\)[/tex] teaspoon of pepper flakes.
- To find the rate in terms of 1 teaspoon of pepper flakes, we calculate:
[tex]\[
\text{Rate} = \frac{4 \text{ tsp of toasted sesame seeds}}{\frac{1}{3} \text{ tsp of pepper flakes}}
\][/tex]
3. Simplify the rate:
To simplify the fraction:
[tex]\[
\text{Rate} = 4 \div \frac{1}{3} = 4 \times \frac{3}{1} = 12
\][/tex]
So, the rate is 12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes.
4. Calculate the amount needed for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes:
Now, we need to find out how many teaspoons of toasted sesame seeds are needed for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes.
- Using the rate we just found (12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes):
[tex]\[
\text{Sesame seeds needed} = 12 \times \frac{2}{3}
\][/tex]
- Perform the multiplication:
[tex]\[
\text{Sesame seeds needed} = 12 \times \frac{2}{3} = 12 \times 0.6667 = 8 \text{ teaspoons of toasted sesame seeds}
\][/tex]
### Final Answers:
- Omar needs 8 teaspoons of toasted sesame seeds for [tex]\(\frac{2}{3}\)[/tex] teaspoon of pepper flakes.
- The rate is 12 teaspoons of toasted sesame seeds per 1 teaspoon of pepper flakes.
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