A Bag Contains 3 Cups Of Flour. Noah Removes $\frac{1}{3}$ Cup Of Flour For Baking. How Much Flour Is Left In The Bag? Write Your Answer As A Mixed Number.Noah Removes Another $\frac{4}{3}$ Cups Of Flour From The Bag. How Much

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Introduction

In this article, we will delve into the world of fractions and mixed numbers, exploring how to calculate the remaining amount of flour in a bag after Noah removes a portion for baking. We will start with a simple scenario and then move on to a more complex one, demonstrating the application of fractions and mixed numbers in real-life situations.

Initial Amount of Flour

A bag contains 3 cups of flour. This is our initial amount, which we will use as a reference point for our calculations.

Noah Removes $\frac{1}{3}$ Cup of Flour

Noah decides to remove $\frac{1}{3}$ cup of flour from the bag for baking. To find out how much flour is left, we need to subtract $\frac{1}{3}$ from the initial amount of 3 cups.

To perform this subtraction, we can use a number line or a visual representation of the fractions. However, in this case, we will use a more straightforward approach by converting the mixed number to an improper fraction.

First, let's convert the initial amount of 3 cups to an improper fraction:

3=3×31×3=933 = \frac{3 \times 3}{1 \times 3} = \frac{9}{3}

Now, we can subtract $\frac{1}{3}$ from $\frac{9}{3}$:

93−13=9−13=83\frac{9}{3} - \frac{1}{3} = \frac{9 - 1}{3} = \frac{8}{3}

So, after Noah removes $\frac{1}{3}$ cup of flour, there are $\frac{8}{3}$ cups of flour left in the bag.

Converting $\frac{8}{3}$ to a Mixed Number

To express $\frac{8}{3}$ as a mixed number, we need to divide the numerator (8) by the denominator (3) and find the quotient and remainder.

8÷3=2 with a remainder of 28 \div 3 = 2 \text{ with a remainder of } 2

Therefore, $\frac{8}{3}$ can be written as a mixed number:

2232\frac{2}{3}

So, after Noah removes $\frac{1}{3}$ cup of flour, there are $2\frac{2}{3}$ cups of flour left in the bag.

Noah Removes Another $\frac{4}{3}$ Cups of Flour

Noah decides to remove another $\frac{4}{3}$ cups of flour from the bag. To find out how much flour is left, we need to subtract $\frac{4}{3}$ from the remaining amount of $2\frac{2}{3}$ cups.

First, let's convert the mixed number $2\frac{2}{3}$ to an improper fraction:

223=2×3+23=832\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}

Now, we can subtract $\frac{4}{3}$ from $\frac{8}{3}$:

83−43=8−43=43\frac{8}{3} - \frac{4}{3} = \frac{8 - 4}{3} = \frac{4}{3}

So, after Noah removes another $\frac{4}{3}$ cups of flour, there are $\frac{4}{3}$ cups of flour left in the bag.

Converting $\frac{4}{3}$ to a Mixed Number

To express $\frac{4}{3}$ as a mixed number, we need to divide the numerator (4) by the denominator (3) and find the quotient and remainder.

4÷3=1 with a remainder of 14 \div 3 = 1 \text{ with a remainder of } 1

Therefore, $\frac{4}{3}$ can be written as a mixed number:

1131\frac{1}{3}

So, after Noah removes another $\frac{4}{3}$ cups of flour, there are $1\frac{1}{3}$ cups of flour left in the bag.

Conclusion

In this article, we have explored how to calculate the remaining amount of flour in a bag after Noah removes a portion for baking. We have used fractions and mixed numbers to represent the initial and remaining amounts of flour, demonstrating the application of these mathematical concepts in real-life situations.

By following the steps outlined in this article, you can easily calculate the remaining amount of flour in a bag after a portion has been removed. Whether you are a student, a baker, or simply someone who enjoys working with fractions and mixed numbers, this article has provided you with the tools and techniques you need to tackle these types of problems with confidence.

References

Additional Resources

Introduction

In our previous article, "A Bag of Flour: Understanding Fractions and Mixed Numbers," we explored how to calculate the remaining amount of flour in a bag after Noah removes a portion for baking. We used fractions and mixed numbers to represent the initial and remaining amounts of flour, demonstrating the application of these mathematical concepts in real-life situations.

In this article, we will continue to explore the world of fractions and mixed numbers, answering some of the most frequently asked questions related to this topic.

Q&A

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of two parts: a numerator (the top number) and a denominator (the bottom number). For example, the fraction $\frac{1}{2}$ represents one half of a whole.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, the mixed number $2\frac{1}{2}$ represents two whole units and one half of a unit.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert $2\frac{1}{2}$ to an improper fraction, you would multiply 2 by 2 and add 1:

2×2=42 \times 2 = 4

4+1=54 + 1 = 5

So, $2\frac{1}{2}$ is equal to $\frac{5}{2}$.

Q: How do I subtract fractions?

A: To subtract fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and then convert both fractions to have the LCM as the denominator. For example, to subtract $\frac{1}{2}$ from $\frac{3}{4}$, you would first find the LCM of 2 and 4, which is 4. Then, you would convert both fractions to have 4 as the denominator:

12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

34=3×14×1=34\frac{3}{4} = \frac{3 \times 1}{4 \times 1} = \frac{3}{4}

Now, you can subtract the fractions:

34−24=3−24=14\frac{3}{4} - \frac{2}{4} = \frac{3 - 2}{4} = \frac{1}{4}

Q: How do I add fractions?

A: To add fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the two denominators and then convert both fractions to have the LCM as the denominator. For example, to add $\frac{1}{2}$ and $\frac{3}{4}$, you would first find the LCM of 2 and 4, which is 4. Then, you would convert both fractions to have 4 as the denominator:

12=1×22×2=24\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

34=3×14×1=34\frac{3}{4} = \frac{3 \times 1}{4 \times 1} = \frac{3}{4}

Now, you can add the fractions:

24+34=2+34=54\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way to represent a part of a whole, while a decimal is a way to represent a number as a sum of powers of 10. For example, the fraction $\frac{1}{2}$ is equal to the decimal 0.5.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, you would divide 1 by 2:

1÷2=0.51 \div 2 = 0.5

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to find the greatest common divisor (GCD) of the decimal and the denominator 1. Then, you can express the decimal as a fraction. For example, to convert 0.5 to a fraction, you would find the GCD of 0.5 and 1, which is 0.5. Then, you can express 0.5 as a fraction:

0.5=0.5×21×2=120.5 = \frac{0.5 \times 2}{1 \times 2} = \frac{1}{2}

Conclusion

In this article, we have answered some of the most frequently asked questions related to fractions and mixed numbers. We have explored the concepts of fractions, mixed numbers, and decimals, and have provided examples of how to convert between these different forms.

By following the steps outlined in this article, you can easily convert between fractions, mixed numbers, and decimals, and can apply these mathematical concepts to real-life situations.

References

Additional Resources