Understanding Mixed Number Fractions

Oct 13, 2025 by magicalceylontours.com 104 views

Understanding Mixed Number Fractions

Mixed number fractions are a combination of a whole number and a fraction. They are used to represent a value that is part of a whole. In this quiz, we will be dealing with mixed number fractions to solve word problems.

Word Problem 1: Kai's Walk

Kai walked one and two-thirds of a mile on Saturday and four and one-sixth of a mile on Sunday. How many miles did Kai walk?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

One and two-thirds can be written as $\frac{5}{3}$ .
Four and one-sixth can be written as $\frac{25}{6}$ .

Now, we can add the two improper fractions together.

$\frac{5}{3} + \frac{25}{6}$

To add these fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6. So, we can rewrite the first fraction with a denominator of 6.

$\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

Now, we can add the two fractions together.

$\frac{10}{6} + \frac{25}{6} = \frac{35}{6}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{35}{6} = 5 \frac{5}{6}$

Therefore, Kai walked $5 \frac{5}{6}$ miles.

Answer: B. $5 \frac{5}{6}$

Word Problem 2: Tom's Run

Tom ran three and one-quarter of a mile on Monday and two and three-quarters of a mile on Tuesday. How many miles did Tom run?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

Three and one-quarter can be written as $\frac{13}{4}$ .
Two and three-quarters can be written as $\frac{11}{4}$ .

Now, we can add the two improper fractions together.

$\frac{13}{4} + \frac{11}{4}$

Since the denominators are the same, we can simply add the numerators.

$\frac{13 + 11}{4} = \frac{24}{4}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{24}{4} = 6$

Therefore, Tom ran 6 miles.

Answer: C. 6

Word Problem 3: Sarah's Hike

Sarah hiked two and one-half of a mile on Wednesday and three and one-half of a mile on Thursday. How many miles did Sarah hike?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

Two and one-half can be written as $\frac{5}{2}$ .
Three and one-half can be written as $\frac{7}{2}$ .

Now, we can add the two improper fractions together.

$\frac{5}{2} + \frac{7}{2}$

Since the denominators are the same, we can simply add the numerators.

$\frac{5 + 7}{2} = \frac{12}{2}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{12}{2} = 6$

Therefore, Sarah hiked 6 miles.

Answer: C. 6

Conclusion

In this quiz, we have seen how to solve word problems involving mixed number fractions. We have learned how to convert mixed numbers to improper fractions, add fractions with different denominators, and convert improper fractions back to mixed numbers. With practice and patience, you can become proficient in solving word problems involving mixed number fractions.

Practice Problems

Alex walked four and one-half of a mile on Monday and two and three-quarters of a mile on Tuesday. How many miles did Alex walk?
Ben ran three and one-quarter of a mile on Wednesday and two and one-half of a mile on Thursday. How many miles did Ben run?
Charlie hiked two and three-quarters of a mile on Friday and three and one-half of a mile on Saturday. How many miles did Charlie hike?

Answer Key

$6 \frac{3}{4}$
$5 \frac{3}{4}$
$6 \frac{1}{2}$
Quiz 3: Word Problems Involving Mixed Number Fractions ===========================================================

Understanding Mixed Number Fractions

Word Problem 1: Kai's Walk

Kai walked one and two-thirds of a mile on Saturday and four and one-sixth of a mile on Sunday. How many miles did Kai walk?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

One and two-thirds can be written as $\frac{5}{3}$ .
Four and one-sixth can be written as $\frac{25}{6}$ .

Now, we can add the two improper fractions together.

$\frac{5}{3} + \frac{25}{6}$

To add these fractions, we need to find a common denominator. The least common multiple of 3 and 6 is 6. So, we can rewrite the first fraction with a denominator of 6.

$\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

Now, we can add the two fractions together.

$\frac{10}{6} + \frac{25}{6} = \frac{35}{6}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{35}{6} = 5 \frac{5}{6}$

Therefore, Kai walked $5 \frac{5}{6}$ miles.

Answer: B. $5 \frac{5}{6}$

Word Problem 2: Tom's Run

Tom ran three and one-quarter of a mile on Monday and two and three-quarters of a mile on Tuesday. How many miles did Tom run?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

Three and one-quarter can be written as $\frac{13}{4}$ .
Two and three-quarters can be written as $\frac{11}{4}$ .

Now, we can add the two improper fractions together.

$\frac{13}{4} + \frac{11}{4}$

Since the denominators are the same, we can simply add the numerators.

$\frac{13 + 11}{4} = \frac{24}{4}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{24}{4} = 6$

Therefore, Tom ran 6 miles.

Answer: C. 6

Word Problem 3: Sarah's Hike

Sarah hiked two and one-half of a mile on Wednesday and three and one-half of a mile on Thursday. How many miles did Sarah hike?

To solve this problem, we need to add the two mixed numbers together. We can start by converting the mixed numbers to improper fractions.

Two and one-half can be written as $\frac{5}{2}$ .
Three and one-half can be written as $\frac{7}{2}$ .

Now, we can add the two improper fractions together.

$\frac{5}{2} + \frac{7}{2}$

Since the denominators are the same, we can simply add the numerators.

$\frac{5 + 7}{2} = \frac{12}{2}$

To convert this improper fraction back to a mixed number, we can divide the numerator by the denominator.

$\frac{12}{2} = 6$

Therefore, Sarah hiked 6 miles.

Answer: C. 6

Q&A

Q: What is a mixed number fraction?

A: A mixed number fraction is a combination of a whole number and a fraction. It is used to represent a value that is part of a whole.

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

A: To convert a mixed number to an improper fraction, you can multiply the whole number by the denominator and add the numerator. Then, write the result as an improper fraction.

Q: How do I add two mixed numbers together?

A: To add two mixed numbers together, you can convert them to improper fractions and then add them. Make sure to find a common denominator before adding the fractions.

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

A: To convert an improper fraction back to a mixed number, you can divide the numerator by the denominator. The result will be a whole number and a fraction.

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 both numbers can divide into evenly.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Practice Problems

Alex walked four and one-half of a mile on Monday and two and three-quarters of a mile on Tuesday. How many miles did Alex walk?
Ben ran three and one-quarter of a mile on Wednesday and two and one-half of a mile on Thursday. How many miles did Ben run?
Charlie hiked two and three-quarters of a mile on Friday and three and one-half of a mile on Saturday. How many miles did Charlie hike?

Answer Key

$6 \frac{3}{4}$
$5 \frac{3}{4}$
$6 \frac{1}{2}$