Jordan Biked 4 3 10 4 \frac{3}{10} 4 10 3 ​ Miles. Sarah Biked 5 3 4 5 \frac{3}{4} 5 4 3 ​ Miles.How Many More Miles Did Sarah Bike Than Jordan?Enter Your Answer As A Mixed Number In Simplest Form.

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Comparing Mixed Numbers: A Math Problem

When dealing with mixed numbers, it's essential to understand how to compare and subtract them. In this article, we will explore how to find the difference between two mixed numbers, specifically in the context of a problem involving Jordan and Sarah's biking distances.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It's written in the form of a whole number followed by a fraction, such as 43104 \frac{3}{10} or 5345 \frac{3}{4}. To compare mixed numbers, we need to convert them into improper fractions, which are fractions with a larger numerator than denominator.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

For example, let's convert 43104 \frac{3}{10} to an improper fraction:

  1. Multiply the whole number by the denominator: 4×10=404 \times 10 = 40
  2. Add the numerator: 40+3=4340 + 3 = 43
  3. Write the result as an improper fraction: 4310\frac{43}{10}

Similarly, let's convert 5345 \frac{3}{4} to an improper fraction:

  1. Multiply the whole number by the denominator: 5×4=205 \times 4 = 20
  2. Add the numerator: 20+3=2320 + 3 = 23
  3. Write the result as an improper fraction: 234\frac{23}{4}

Comparing and Subtracting Mixed Numbers

Now that we have converted both mixed numbers to improper fractions, we can compare and subtract them.

To compare two improper fractions, we can compare their numerators. If the numerators are equal, we can compare the denominators. If the denominators are equal, the fractions are equal.

In this case, we want to find the difference between 4310\frac{43}{10} and 234\frac{23}{4}. To do this, we need to find a common denominator. The least common multiple (LCM) of 10 and 4 is 20.

We can rewrite both fractions with a denominator of 20:

4310=43×210×2=8620\frac{43}{10} = \frac{43 \times 2}{10 \times 2} = \frac{86}{20}

234=23×54×5=11520\frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20}

Now that we have a common denominator, we can subtract the fractions:

8620−11520=86−11520=−2920\frac{86}{20} - \frac{115}{20} = \frac{86 - 115}{20} = \frac{-29}{20}

Simplifying the Result

The result is a negative fraction, which means that Sarah biked fewer miles than Jordan. To simplify the result, we can convert the fraction to a mixed number:

−2920=−1920\frac{-29}{20} = -1 \frac{9}{20}

Conclusion

In this article, we learned how to compare and subtract mixed numbers. We converted the mixed numbers to improper fractions, found a common denominator, and subtracted the fractions. The result was a negative fraction, which we simplified to a mixed number. This problem demonstrates the importance of understanding mixed numbers and how to work with them in math.

Key Takeaways

  • Mixed numbers are combinations of whole numbers and fractions.
  • To compare mixed numbers, convert them to improper fractions.
  • To subtract mixed numbers, find a common denominator and subtract the fractions.
  • Negative fractions can be simplified to mixed numbers.

Practice Problems

  1. Convert the mixed number 3253 \frac{2}{5} to an improper fraction.
  2. Compare the mixed numbers 2342 \frac{3}{4} and 1561 \frac{5}{6}.
  3. Subtract the mixed numbers 4124 \frac{1}{2} and 2342 \frac{3}{4}.

Answer Key

  1. 175\frac{17}{5}
  2. 234>1562 \frac{3}{4} > 1 \frac{5}{6}
  3. 2142 \frac{1}{4}
    Mixed Number Q&A: Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about mixed numbers. Whether you're a student, teacher, or simply someone looking to brush up on their math skills, this Q&A section will provide you with the answers you need.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It's written in the form of a whole number followed by a fraction, such as 43104 \frac{3}{10} or 5345 \frac{3}{4}.

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

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. The result becomes the new numerator, while the denominator remains the same.

For example, let's convert 43104 \frac{3}{10} to an improper fraction:

  1. Multiply the whole number by the denominator: 4×10=404 \times 10 = 40
  2. Add the numerator: 40+3=4340 + 3 = 43
  3. Write the result as an improper fraction: 4310\frac{43}{10}

Q: How do I compare mixed numbers?

A: To compare mixed numbers, you need to convert them to improper fractions. Then, you can compare the numerators. If the numerators are equal, you can compare the denominators. If the denominators are equal, the fractions are equal.

For example, let's compare 43104 \frac{3}{10} and 5345 \frac{3}{4}:

  1. Convert both mixed numbers to improper fractions: 4310\frac{43}{10} and 234\frac{23}{4}
  2. Compare the numerators: 43>2343 > 23
  3. Since the numerators are not equal, we can compare the denominators: 10<410 < 4
  4. Since the denominator of 4310\frac{43}{10} is smaller, 4310\frac{43}{10} is greater than 234\frac{23}{4}

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to find a common denominator. Then, you can subtract the fractions.

For example, let's subtract 43104 \frac{3}{10} and 5345 \frac{3}{4}:

  1. Convert both mixed numbers to improper fractions: 4310\frac{43}{10} and 234\frac{23}{4}
  2. Find a common denominator: 20
  3. Rewrite both fractions with a denominator of 20: 8620\frac{86}{20} and 11520\frac{115}{20}
  4. Subtract the fractions: 8620−11520=−2920\frac{86}{20} - \frac{115}{20} = \frac{-29}{20}

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a larger numerator than denominator. While both can be used to represent the same value, they are written differently.

For example, the mixed number 43104 \frac{3}{10} is equivalent to the improper fraction 4310\frac{43}{10}.

Q: Can I simplify a mixed number?

A: Yes, you can simplify a mixed number by converting it to an improper fraction and then simplifying the fraction.

For example, let's simplify 43104 \frac{3}{10}:

  1. Convert the mixed number to an improper fraction: 4310\frac{43}{10}
  2. Simplify the fraction: 4310=43÷110÷1=4310\frac{43}{10} = \frac{43 \div 1}{10 \div 1} = \frac{43}{10}

Since the numerator and denominator have no common factors, the fraction cannot be simplified further.

Q: Can I add mixed numbers?

A: Yes, you can add mixed numbers by converting them to improper fractions, finding a common denominator, and then adding the fractions.

For example, let's add 43104 \frac{3}{10} and 5345 \frac{3}{4}:

  1. Convert both mixed numbers to improper fractions: 4310\frac{43}{10} and 234\frac{23}{4}
  2. Find a common denominator: 20
  3. Rewrite both fractions with a denominator of 20: 8620\frac{86}{20} and 11520\frac{115}{20}
  4. Add the fractions: 8620+11520=20120\frac{86}{20} + \frac{115}{20} = \frac{201}{20}

Conclusion

In this Q&A article, we addressed some of the most frequently asked questions about mixed numbers. Whether you're a student, teacher, or simply someone looking to brush up on their math skills, this article should provide you with the answers you need.

Key Takeaways

  • Mixed numbers are combinations of whole numbers and fractions.
  • To compare mixed numbers, convert them to improper fractions.
  • To subtract mixed numbers, find a common denominator and subtract the fractions.
  • Mixed numbers can be simplified by converting them to improper fractions and then simplifying the fraction.
  • Mixed numbers can be added by converting them to improper fractions, finding a common denominator, and then adding the fractions.

Practice Problems

  1. Convert the mixed number 3253 \frac{2}{5} to an improper fraction.
  2. Compare the mixed numbers 2342 \frac{3}{4} and 1561 \frac{5}{6}.
  3. Subtract the mixed numbers 4124 \frac{1}{2} and 2342 \frac{3}{4}.
  4. Simplify the mixed number 43104 \frac{3}{10}.
  5. Add the mixed numbers 43104 \frac{3}{10} and 5345 \frac{3}{4}.

Answer Key

  1. 175\frac{17}{5}
  2. 234>1562 \frac{3}{4} > 1 \frac{5}{6}
  3. 2142 \frac{1}{4}
  4. 4310\frac{43}{10}
  5. 97209 \frac{7}{20}