Comparing the Lengths of the Sandwiches

Oct 13, 2025 by talynt.org 10 views

A Medium Sandwich at Heidi's Heroes: A Math Problem

Understanding the Problem

When it comes to comparing the lengths of sandwiches, we need to consider the units of measurement. In this problem, we have a medium sandwich that is $\frac{5}{8}$ foot long, and a small sandwich that is $4 \frac{7}{8}$ inches long. Our goal is to determine how many inches longer the medium sandwich is than the small sandwich.

Converting Feet to Inches

To compare the lengths of the two sandwiches, we need to convert the length of the medium sandwich from feet to inches. Since there are 12 inches in a foot, we can multiply the length of the medium sandwich by 12 to get its length in inches.

$\frac{5}{8} \text{ foot} \times 12 \text{ inches/foot} = \frac{5}{8} \times 12 = 7.5 \text{ inches}$

Comparing the Lengths of the Sandwiches

Now that we have the length of the medium sandwich in inches, we can compare it to the length of the small sandwich. The small sandwich is $4 \frac{7}{8}$ inches long, which is equal to $4.875$ inches.

To find the difference in length between the two sandwiches, we can subtract the length of the small sandwich from the length of the medium sandwich.

$7.5 \text{ inches} - 4.875 \text{ inches} = 2.625 \text{ inches}$

Simplifying the Answer

We can simplify the answer by converting the decimal to a fraction. Since $2.625$ is equal to $\frac{21}{8}$ , we can write the answer as a fraction.

$\frac{21}{8} \text{ inches}$

Converting the Fraction to a Mixed Number

To make the answer more understandable, we can convert the fraction to a mixed number. Since $\frac{21}{8}$ is equal to $2 \frac{5}{8}$ , we can write the answer as a mixed number.

$2 \frac{5}{8} \text{ inches}$

Conclusion

In conclusion, the medium sandwich at Heidi's Heroes is $2 \frac{5}{8}$ inches longer than the small sandwich.

Key Takeaways

To compare the lengths of sandwiches, we need to consider the units of measurement.
We can convert feet to inches by multiplying the length by 12.
To find the difference in length between two sandwiches, we can subtract the length of the smaller sandwich from the length of the larger sandwich.
We can simplify the answer by converting the decimal to a fraction or by converting the fraction to a mixed number.

Additional Practice Problems

If you want to practice solving similar problems, here are a few additional practice problems:

A large sandwich is $3 \frac{1}{4}$ feet long. How many inches longer is the large sandwich than a small sandwich that is $2 \frac{3}{4}$ inches long?
A medium sandwich is $5 \frac{1}{2}$ inches long. How many inches longer is the medium sandwich than a small sandwich that is $3 \frac{1}{4}$ inches long?

Answer Key

A. $2 \frac{5}{8}$ inches

Discussion Questions

What are some common units of measurement for lengths?
How can we convert feet to inches?
What is the difference between a fraction and a mixed number?
How can we simplify a fraction or a mixed number?

References

[1] "Converting Feet to Inches." Math Open Reference, mathopenref.com/converting-feet-to-inches.html.
[2] "Fractions and Mixed Numbers." Math Is Fun, mathisfun.com/fractions/mixed-numbers.html.
A Medium Sandwich at Heidi's Heroes: A Math Problem Q&A

Q: What is the length of the medium sandwich at Heidi's Heroes?

A: The length of the medium sandwich at Heidi's Heroes is $\frac{5}{8}$ foot long.

Q: How many inches is the medium sandwich long?

A: To find the length of the medium sandwich in inches, we need to convert the length from feet to inches. Since there are 12 inches in a foot, we can multiply the length of the medium sandwich by 12 to get its length in inches.

$\frac{5}{8} \text{ foot} \times 12 \text{ inches/foot} = \frac{5}{8} \times 12 = 7.5 \text{ inches}$

Q: What is the length of the small sandwich?

A: The length of the small sandwich is $4 \frac{7}{8}$ inches long.

Q: How many inches longer is the medium sandwich than the small sandwich?

A: To find the difference in length between the two sandwiches, we can subtract the length of the small sandwich from the length of the medium sandwich.

$7.5 \text{ inches} - 4.875 \text{ inches} = 2.625 \text{ inches}$

Q: Can we simplify the answer?

A: Yes, we can simplify the answer by converting the decimal to a fraction. Since $2.625$ is equal to $\frac{21}{8}$ , we can write the answer as a fraction.

$\frac{21}{8} \text{ inches}$

Q: Can we convert the fraction to a mixed number?

A: Yes, we can convert the fraction to a mixed number. Since $\frac{21}{8}$ is equal to $2 \frac{5}{8}$ , we can write the answer as a mixed number.

$2 \frac{5}{8} \text{ inches}$

Q: What are some common units of measurement for lengths?

A: Some common units of measurement for lengths include inches, feet, yards, and miles.

Q: How can we convert feet to inches?

A: To convert feet to inches, we can multiply the length in feet by 12.

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A mixed number is a way of expressing a fraction as a combination of a whole number and a fraction.

Q: How can we simplify a fraction or a mixed number?

A: We can simplify a fraction or a mixed number by converting the decimal to a fraction or by converting the fraction to a mixed number.

Q: What are some real-world applications of converting units of measurement?

A: Converting units of measurement is an important skill in many real-world applications, such as:

Building construction: Architects and builders need to convert units of measurement to ensure that buildings are constructed to the correct specifications.
Cooking: Recipes often require converting units of measurement to ensure that the correct amount of ingredients is used.
Science: Scientists need to convert units of measurement to ensure that their experiments are conducted accurately.

Q: How can we practice converting units of measurement?

A: We can practice converting units of measurement by:

Using online resources, such as conversion calculators or worksheets.
Practicing with real-world examples, such as building construction or cooking recipes.
Creating our own conversion problems and solving them.

Q: What are some common mistakes to avoid when converting units of measurement?

A: Some common mistakes to avoid when converting units of measurement include:

Forgetting to convert units of measurement.
Converting units of measurement incorrectly.
Not checking the units of measurement before performing a calculation.

Q: How can we ensure that we are converting units of measurement correctly?

A: We can ensure that we are converting units of measurement correctly by:

Double-checking our calculations.
Using conversion calculators or worksheets.
Practicing with real-world examples.