Which Of These Are Word Problems That Correctly Demonstrate The Following Equation: 2 3 ÷ 1 6 \frac{2}{3} \div \frac{1}{6} 3 2 ​ ÷ 6 1 ​ ?(You May Choose More Than One Correct Answer.)A. Mimi Has 2 3 \frac{2}{3} 3 2 ​ Of A Load Of Laundry. She Just Did

$$

Understanding the Equation

The given equation is $\frac{2}{3} \div \frac{1}{6}$. To solve this equation, we need to understand the concept of division of fractions. When we divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction. In this case, we can rewrite the equation as $\frac{2}{3} \times \frac{6}{1}$.

Solving the Equation

To solve the equation, we multiply the numerators and denominators of the two fractions. The numerator of the first fraction is 2, and the denominator is 3. The numerator of the second fraction is 6, and the denominator is 1. Multiplying the numerators gives us 2 x 6 = 12. Multiplying the denominators gives us 3 x 1 = 3. Therefore, the solution to the equation is $\frac{12}{3}$.

Simplifying the Solution

To simplify the solution, we can divide the numerator by the denominator. In this case, we can divide 12 by 3 to get 4. Therefore, the solution to the equation is 4.

Word Problems Demonstrating the Equation

Now that we have understood the equation and solved it, let's look at some word problems that demonstrate the equation. We will choose more than one correct answer.

Word Problem 1

Mimi has $\frac{2}{3}$ of a load of laundry. She just did a load of laundry that is $\frac{1}{6}$ of the total load. How many loads of laundry did Mimi do in total?

To solve this problem, we can multiply the fraction of the load that Mimi has by the fraction of the load that she just did. This gives us $\frac{2}{3} \times \frac{6}{1}$. We can simplify this expression to get $\frac{12}{3}$, which is equal to 4. Therefore, Mimi did 4 loads of laundry in total.

Word Problem 2

Tom has $\frac{2}{3}$ of a bag of apples. He wants to share them with his friend, who has $\frac{1}{6}$ of a bag of apples. How many bags of apples do Tom and his friend have in total?

To solve this problem, we can add the fractions of the bags of apples that Tom and his friend have. However, we need to find a common denominator first. The least common multiple of 3 and 6 is 6. Therefore, we can rewrite the fractions as $\frac{4}{6}$ and $\frac{1}{6}$. Adding these fractions gives us $\frac{5}{6}$. Therefore, Tom and his friend have $\frac{5}{6}$ of a bag of apples in total.

Word Problem 3

A recipe calls for $\frac{2}{3}$ of a cup of sugar. If you want to make half of the recipe, how much sugar will you need?

To solve this problem, we can multiply the fraction of the cup of sugar that the recipe calls for by $\frac{1}{2}$. This gives us $\frac{2}{3} \times \frac{1}{2}$. We can simplify this expression to get $\frac{2}{6}$, which is equal to $\frac{1}{3}$. Therefore, you will need $\frac{1}{3}$ of a cup of sugar to make half of the recipe.

Word Problem 4

A group of students have $\frac{2}{3}$ of a pizza to share. If they want to divide it equally among 6 students, how much pizza will each student get?

To solve this problem, we can divide the fraction of the pizza that the students have by the number of students. This gives us $\frac{2}{3} \div \frac{6}{1}$. We can rewrite this expression as $\frac{2}{3} \times \frac{1}{6}$. We can simplify this expression to get $\frac{2}{18}$, which is equal to $\frac{1}{9}$. Therefore, each student will get $\frac{1}{9}$ of a pizza.

Conclusion

In conclusion, the word problems that correctly demonstrate the equation $\frac{2}{3} \div \frac{1}{6}$ are:

• Mimi has $\frac{2}{3}$ of a load of laundry. She just did a load of laundry that is $\frac{1}{6}$ of the total load. How many loads of laundry did Mimi do in total?
• A recipe calls for $\frac{2}{3}$ of a cup of sugar. If you want to make half of the recipe, how much sugar will you need?

These word problems demonstrate the concept of division of fractions and can be used to help students understand the equation.

$$

Q: What is the equation $\frac{2}{3} \div \frac{1}{6}$ equal to?

A: The equation $\frac{2}{3} \div \frac{1}{6}$ is equal to 4. To solve this equation, we can multiply the first fraction by the reciprocal of the second fraction, which gives us $\frac{2}{3} \times \frac{6}{1}$. We can then simplify this expression to get $\frac{12}{3}$, which is equal to 4.

Q: How do I solve the equation $\frac{2}{3} \div \frac{1}{6}$?

A: To solve the equation $\frac{2}{3} \div \frac{1}{6}$, we can multiply the first fraction by the reciprocal of the second fraction. This gives us $\frac{2}{3} \times \frac{6}{1}$. We can then simplify this expression to get $\frac{12}{3}$, which is equal to 4.

Q: What is the concept of division of fractions?

A: The concept of division of fractions is that when we divide a fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction. This is because division is the same as multiplying by a reciprocal.

Q: How do I divide fractions with different denominators?

A: To divide fractions with different denominators, we need to find a common denominator first. We can then rewrite the fractions with the common denominator and divide them.

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 3 and 6 is 6.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, we need to find a common denominator first. We can then rewrite the fractions with the common denominator and add them.

Q: What is the concept of equivalent fractions?

A: Equivalent fractions are fractions that have the same value, but different numerators and denominators. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions.

Q: How do I simplify a fraction?

A: To simplify a fraction, we can divide the numerator by the denominator. If the numerator is a multiple of the denominator, we can simplify the fraction by dividing the numerator by the denominator.

Q: What is the concept of reciprocal fractions?

A: Reciprocal fractions are fractions that have the same numerator and denominator, but in reverse order. For example, the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Q: How do I multiply fractions?

A: To multiply fractions, we can multiply the numerators and denominators separately. This gives us a new fraction with the product of the numerators as the numerator and the product of the denominators as the denominator.

Q: What is the concept of division of fractions with zero?

A: Division of fractions with zero is undefined, because division by zero is undefined.

Q: How do I divide fractions with negative numbers?

A: To divide fractions with negative numbers, we can multiply the fractions by the reciprocal of the second fraction, and then change the sign of the result.

Q: What is the concept of equivalent ratios?

A: Equivalent ratios are ratios that have the same value, but different numerators and denominators. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent ratios.

Q: How do I simplify a ratio?

A: To simplify a ratio, we can divide the numerator by the denominator. If the numerator is a multiple of the denominator, we can simplify the ratio by dividing the numerator by the denominator.

Q: What is the concept of proportional relationships?

A: Proportional relationships are relationships between two or more quantities that are in the same ratio. For example, if a recipe calls for 2 cups of flour for 4 people, then it will call for 4 cups of flour for 8 people.

Q: How do I solve problems involving proportional relationships?

A: To solve problems involving proportional relationships, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of unit rates?

A: Unit rates are rates that have a denominator of 1. For example, if a recipe calls for 2 cups of flour for 4 people, then the unit rate is 2 cups of flour per person.

Q: How do I find the unit rate of a ratio?

A: To find the unit rate of a ratio, we can divide the numerator by the denominator. This gives us a new ratio with a denominator of 1.

Q: What is the concept of equivalent ratios with different units?

A: Equivalent ratios with different units are ratios that have the same value, but different units. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent ratios with different units.

Q: How do I convert between different units?

A: To convert between different units, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of proportional reasoning?

A: Proportional reasoning is the ability to understand and work with proportional relationships. It involves being able to set up and solve proportions, and to understand the concept of equivalent ratios.

Q: How do I develop proportional reasoning skills?

A: To develop proportional reasoning skills, we can practice solving problems involving proportional relationships. We can also use real-world examples to help us understand the concept of proportional relationships.

Q: What is the concept of ratio and proportion?

A: Ratio and proportion are concepts that involve comparing two or more quantities. A ratio is a comparison of two or more quantities, while a proportion is a statement that two ratios are equal.

Q: How do I solve problems involving ratio and proportion?

A: To solve problems involving ratio and proportion, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of equivalent ratios with different units?

A: Equivalent ratios with different units are ratios that have the same value, but different units. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent ratios with different units.

Q: How do I convert between different units?

A: To convert between different units, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of proportional reasoning?

A: Proportional reasoning is the ability to understand and work with proportional relationships. It involves being able to set up and solve proportions, and to understand the concept of equivalent ratios.

Q: How do I develop proportional reasoning skills?

A: To develop proportional reasoning skills, we can practice solving problems involving proportional relationships. We can also use real-world examples to help us understand the concept of proportional relationships.

Q: What is the concept of ratio and proportion?

A: Ratio and proportion are concepts that involve comparing two or more quantities. A ratio is a comparison of two or more quantities, while a proportion is a statement that two ratios are equal.

Q: How do I solve problems involving ratio and proportion?

A: To solve problems involving ratio and proportion, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of equivalent ratios with different units?

A: Equivalent ratios with different units are ratios that have the same value, but different units. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent ratios with different units.

Q: How do I convert between different units?

A: To convert between different units, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of proportional reasoning?

A: Proportional reasoning is the ability to understand and work with proportional relationships. It involves being able to set up and solve proportions, and to understand the concept of equivalent ratios.

Q: How do I develop proportional reasoning skills?

A: To develop proportional reasoning skills, we can practice solving problems involving proportional relationships. We can also use real-world examples to help us understand the concept of proportional relationships.

Q: What is the concept of ratio and proportion?

A: Ratio and proportion are concepts that involve comparing two or more quantities. A ratio is a comparison of two or more quantities, while a proportion is a statement that two ratios are equal.

Q: How do I solve problems involving ratio and proportion?

A: To solve problems involving ratio and proportion, we can use the concept of equivalent ratios. We can set up a proportion and solve for the unknown quantity.

Q: What is the concept of equivalent ratios with different units?

A: Equivalent ratios with different units are ratios that have the same value, but different units. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent ratios with different units.