Select The Correct Answer From The Drop-down Menu.Dave Is Helping His Grandmother Make Trail Mix. His Grandmother Asks Him To Add $\frac{1}{5}$ Cup Of Fruit For Every $\frac{1}{3}$ Cup Of Nuts.To Satisfy His Grandmother's Request,
Introduction
Mathematics is an essential part of our daily lives, and it can be found in various aspects, including cooking and baking. In this article, we will explore a math problem related to making trail mix, a popular snack that combines nuts and dried fruits. The problem involves fractions, which are a fundamental concept in mathematics. We will guide you through the steps to solve the problem and provide you with a deeper understanding of fractions.
The Problem
Dave is helping his grandmother make trail mix. His grandmother asks him to add $\frac{1}{5}$ cup of fruit for every $\frac{1}{3}$ cup of nuts. To satisfy his grandmother's request, Dave needs to determine the correct ratio of fruit to nuts.
Understanding Fractions
Fractions are a way to represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). In this problem, we have two fractions: $\frac{1}{5}$ and $\frac{1}{3}$. The first fraction represents the amount of fruit, and the second fraction represents the amount of nuts.
Step 1: Determine the Ratio of Fruit to Nuts
To determine the correct ratio of fruit to nuts, we need to find a common denominator for the two fractions. The least common multiple (LCM) of 5 and 3 is 15. We can rewrite the fractions with a common denominator:
Now that we have a common denominator, we can compare the two fractions. The ratio of fruit to nuts is 3:5.
Step 2: Calculate the Amount of Fruit and Nuts
To calculate the amount of fruit and nuts, we need to multiply the ratio by a common multiplier. Let's say we want to make 15 cups of trail mix. We can multiply the ratio by 15:
\frac{3}{5} \times 15 = 9$ cups of fruit
\frac{5}{5} \times 15 = 15$ cups of nuts
So, Dave needs to add 9 cups of fruit and 15 cups of nuts to make 15 cups of trail mix.
**Conclusion**
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In this article, we solved a math problem related to making trail mix. We used fractions to determine the correct ratio of fruit to nuts and calculated the amount of fruit and nuts needed to make a certain amount of trail mix. This problem demonstrates the importance of fractions in mathematics and how they can be applied to real-world problems.
**Key Takeaways**
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* Fractions are a way to represent a part of a whole.
* The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly.
* To determine the correct ratio of two fractions, we need to find a common denominator.
* To calculate the amount of fruit and nuts, we need to multiply the ratio by a common multiplier.
**Practice Problems**
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1. A recipe calls for $\frac{2}{3}$ cup of sugar for every $\frac{1}{4}$ cup of flour. If we want to make 12 cups of the recipe, how much sugar and flour do we need?
2. A bakery sells $\frac{3}{5}$ loaf of bread for every $\frac{2}{3}$ loaf of bread. If we want to buy 15 loaves of bread, how many loaves of each type do we need?
**Answer Key**
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1. $\frac{2}{3} \times 12 = 8$ cups of sugar and $\frac{1}{4} \times 12 = 3$ cups of flour.
2. $\frac{3}{5} \times 15 = 9$ loaves of bread and $\frac{2}{3} \times 15 = 10$ loaves of bread.<br/>
**Trail Mix Math: A Q&A Guide**
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**Introduction**
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In our previous article, we explored a math problem related to making trail mix. We used fractions to determine the correct ratio of fruit to nuts and calculated the amount of fruit and nuts needed to make a certain amount of trail mix. In this article, we will provide a Q&A guide to help you better understand the concepts and solve similar problems.
**Q: What is the difference between a numerator and a denominator?**
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A: A numerator is the top number in a fraction, and a denominator is the bottom number. For example, in the fraction $\frac{1}{5}$, 1 is the numerator and 5 is the denominator.
**Q: How do I find the least common multiple (LCM) of two numbers?**
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A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the following formula:
LCM(a, b) = (a × b) / GCD(a, b)
where GCD(a, b) is the greatest common divisor of a and b.
**Q: How do I determine the correct ratio of two fractions?**
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A: To determine the correct ratio of two fractions, you need to find a common denominator. You can do this by listing the multiples of each denominator and finding the smallest number that appears in both lists. Alternatively, you can use the following formula:
Common denominator = LCM(denominator 1, denominator 2)
**Q: How do I calculate the amount of fruit and nuts needed to make a certain amount of trail mix?**
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A: To calculate the amount of fruit and nuts needed, you need to multiply the ratio by a common multiplier. Let's say you want to make 15 cups of trail mix. You can multiply the ratio by 15:
$\frac{3}{5} \times 15 = 9$ cups of fruit
$\frac{5}{5} \times 15 = 15$ cups of nuts
**Q: What is the difference between a ratio and a proportion?**
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A: A ratio is a comparison of two numbers, while a proportion is a statement that two ratios are equal. For example, the ratio of fruit to nuts is 3:5, while the proportion is $\frac{3}{5} = \frac{x}{y}$.
**Q: How do I solve a proportion problem?**
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A: To solve a proportion problem, you need to cross-multiply and solve for the unknown variable. Let's say you have the proportion $\frac{3}{5} = \frac{x}{y}$. You can cross-multiply and solve for x:
3y = 5x
**Q: What are some real-world applications of fractions and proportions?**
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A: Fractions and proportions are used in many real-world applications, including cooking, baking, and science. For example, a recipe may call for a certain ratio of ingredients, while a scientist may use proportions to calculate the concentration of a solution.
**Conclusion**
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In this article, we provided a Q&A guide to help you better understand the concepts of fractions and proportions. We covered topics such as numerators and denominators, least common multiples, and proportions. We also provided examples and formulas to help you solve similar problems.
**Practice Problems**
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1. A recipe calls for $\frac{2}{3}$ cup of sugar for every $\frac{1}{4}$ cup of flour. If we want to make 12 cups of the recipe, how much sugar and flour do we need?
2. A bakery sells $\frac{3}{5}$ loaf of bread for every $\frac{2}{3}$ loaf of bread. If we want to buy 15 loaves of bread, how many loaves of each type do we need?
3. A scientist needs to calculate the concentration of a solution. The solution contains $\frac{3}{5}$ grams of salt for every $\frac{2}{3}$ grams of water. If the scientist wants to make 15 grams of the solution, how much salt and water do they need?
**Answer Key**
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1. $\frac{2}{3} \times 12 = 8$ cups of sugar and $\frac{1}{4} \times 12 = 3$ cups of flour.
2. $\frac{3}{5} \times 15 = 9$ loaves of bread and $\frac{2}{3} \times 15 = 10$ loaves of bread.
3. $\frac{3}{5} \times 15 = 9$ grams of salt and $\frac{2}{3} \times 15 = 10$ grams of water.</span></p>