Yasmin Purchased 6 Heads Of Cabbage, Each Weighing $2 \frac{3}{8}$ Pounds. How Much Did The Cabbage Weigh In Total?A. $9 \frac{3}{4}$ Pounds B. $ 12 3 8 12 \frac{3}{8} 12 8 3 ​ [/tex] Pounds C. $13 \frac{1}{8}$ Pounds

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Introduction

In this article, we will delve into the world of mathematics and tackle a problem that has puzzled many a student: Yasmin's cabbage conundrum. With six heads of cabbage, each weighing a whopping $2 \frac{3}{8}$ pounds, we must calculate the total weight of the cabbage. This problem requires a combination of fractions, multiplication, and addition, making it an excellent exercise in mathematical problem-solving.

Understanding the Problem

Yasmin has purchased six heads of cabbage, each with a weight of $2 \frac{3}{8}$ pounds. To find the total weight of the cabbage, we need to multiply the weight of one head by the number of heads. However, we must first convert the mixed number $2 \frac{3}{8}$ to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. In this case, we have:

238=(2×8)+38=16+38=1982 \frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}

Multiplying the Weight of One Head by the Number of Heads

Now that we have the weight of one head in improper fraction form, we can multiply it by the number of heads to find the total weight of the cabbage:

198×6=19×68=1148\frac{19}{8} \times 6 = \frac{19 \times 6}{8} = \frac{114}{8}

Simplifying the Fraction

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 114 and 8 is 2. Therefore, we can simplify the fraction as follows:

1148=114÷28÷2=574\frac{114}{8} = \frac{114 \div 2}{8 \div 2} = \frac{57}{4}

Converting the Improper Fraction to a Mixed Number

To make the answer more understandable, we can convert the improper fraction to a mixed number. To do this, we divide the numerator by the denominator and find the remainder:

574=1414\frac{57}{4} = 14 \frac{1}{4}

Conclusion

In conclusion, Yasmin's six heads of cabbage weigh a total of $14 \frac{1}{4}$ pounds. This problem required us to convert a mixed number to an improper fraction, multiply the weight of one head by the number of heads, and simplify the resulting fraction. By following these steps, we can solve even the most complex math problems.

Answer

The correct answer is:

Let's compare our answer to the options provided:

A. $9 \frac{3}{4}$ pounds B. $12 \frac{3}{8}$ pounds C. $13 \frac{1}{8}$ pounds

Introduction

In our previous article, we solved the cabbage conundrum by calculating the total weight of Yasmin's six heads of cabbage. However, we received many questions from readers who wanted to know more about the problem and its solution. In this article, we will address some of the most frequently asked questions and provide additional insights into the world of mathematics.

Q&A

Q: What is the weight of one head of cabbage?

A: The weight of one head of cabbage is $2 \frac{3}{8}$ pounds.

Q: Why do we need to convert the mixed number to an improper fraction?

A: We need to convert the mixed number to an improper fraction because it makes it easier to multiply the weight of one head by the number of heads.

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

A: To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. In this case, we have:

2 \frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8} </span></p> <h3>Q: Why do we multiply the weight of one head by the number of heads?</h3> <p>A: We multiply the weight of one head by the number of heads to find the total weight of the cabbage.</p> <h3>Q: How do we simplify the fraction?</h3> <p>A: To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 114 and 8 is 2. Therefore, we can simplify the fraction as follows:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>114</mn><mn>8</mn></mfrac><mo>=</mo><mfrac><mrow><mn>114</mn><mo>÷</mo><mn>2</mn></mrow><mrow><mn>8</mn><mo>÷</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>57</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{114}{8} = \frac{114 \div 2}{8 \div 2} = \frac{57}{4} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">114</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0908em;vertical-align:-0.7693em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">2</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">114</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">÷</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7693em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">57</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p> <h3>Q: Why do we convert the improper fraction to a mixed number?</h3> <p>A: We convert the improper fraction to a mixed number to make the answer more understandable.</p> <h3>Q: How do we convert an improper fraction to a mixed number?</h3> <p>A: To convert an improper fraction to a mixed number, we divide the numerator by the denominator and find the remainder:</p> <p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>57</mn><mn>4</mn></mfrac><mo>=</mo><mn>14</mn><mfrac><mn>1</mn><mn>4</mn></mfrac></mrow><annotation encoding="application/x-tex">\frac{57}{4} = 14 \frac{1}{4} </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">57</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord">14</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p> <h3>Q: What is the total weight of Yasmin's six heads of cabbage?</h3> <p>A: The total weight of Yasmin's six heads of cabbage is $14 \frac{1}{4}$ pounds.</p> <h3>Q: Why is this problem important?</h3> <p>A: This problem is important because it requires us to apply mathematical concepts such as fractions, multiplication, and addition to solve a real-world problem.</p> <h3>Q: How can I apply this problem to my everyday life?</h3> <p>A: You can apply this problem to your everyday life by using mathematical concepts to solve problems that involve fractions, multiplication, and addition.</p> <h2><strong>Conclusion</strong></h2> <p>In conclusion, Yasmin's cabbage conundrum is a math problem that requires us to apply mathematical concepts such as fractions, multiplication, and addition to solve a real-world problem. By following the steps outlined in this article, we can solve even the most complex math problems.</p> <h2><strong>Additional Resources</strong></h2> <p>If you want to learn more about fractions, multiplication, and addition, we recommend the following resources:</p> <ul> <li>Khan Academy: Fractions</li> <li>Mathway: Multiplication and Addition</li> <li>IXL: Fractions and Decimals</li> </ul> <h2><strong>Final Thoughts</strong></h2> <p>We hope this article has been helpful in answering your questions about Yasmin's cabbage conundrum. Remember, math is all around us, and by applying mathematical concepts to real-world problems, we can solve even the most complex challenges.</p>