Determine If Each Expression Is Less Than, Equal To, Or Greater Than $1 \frac{1}{4}$.$\[ \begin{array}{|c|c|c|c|} \hline & \text{Less Than } 1 \frac{1}{4} & \text{Equal To } 1 \frac{1}{4} & \text{Greater Than } 1 \frac{1}{4} \\ \hline 1

Determine if Each Expression is Less than, Equal to, or Greater than $1 \frac{1}{4}$

In this article, we will explore the concept of comparing fractions and mixed numbers to determine if they are less than, equal to, or greater than a given value, specifically $1 \frac{1}{4}$. We will examine various expressions and use mathematical operations to determine their relationships to $1 \frac{1}{4}$.

Understanding $1 \frac{1}{4}$

Before we begin, let's understand the value of $1 \frac{1}{4}$. This mixed number can be converted to an improper fraction by multiplying the whole number part (1) by the denominator (4) and then adding the numerator (1). This gives us:

$$1 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4}$$

Comparing Fractions

To compare fractions, we need to have the same denominator. If the denominators are different, we can find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator.

Example 1: Comparing $\frac{1}{2}$ and $\frac{3}{4}$

To compare $\frac{1}{2}$ and $\frac{3}{4}$, we need to find the LCM of 2 and 4, which is 4. We can convert $\frac{1}{2}$ to have a denominator of 4 by multiplying the numerator and denominator by 2:

$$\frac{1}{2} = \frac{(1 \times 2)}{2 \times 2} = \frac{2}{4}$$

Now we can compare the two fractions:

$$\frac{2}{4} < \frac{3}{4}$$

Therefore, $\frac{1}{2}$ is less than $\frac{3}{4}$.

Example 2: Comparing $\frac{2}{3}$ and $\frac{3}{4}$

To compare $\frac{2}{3}$ and $\frac{3}{4}$, we need to find the LCM of 3 and 4, which is 12. We can convert both fractions to have a denominator of 12:

$$\frac{2}{3} = \frac{(2 \times 4)}{3 \times 4} = \frac{8}{12}$$

$$\frac{3}{4} = \frac{(3 \times 3)}{4 \times 3} = \frac{9}{12}$$

Now we can compare the two fractions:

$$\frac{8}{12} < \frac{9}{12}$$

Therefore, $\frac{2}{3}$ is less than $\frac{3}{4}$.

Comparing Mixed Numbers

To compare mixed numbers, we need to convert them to improper fractions and then compare the fractions.

Example 1: Comparing $1 \frac{1}{2}$ and $1 \frac{3}{4}$

To compare $1 \frac{1}{2}$ and $1 \frac{3}{4}$, we need to convert both mixed numbers to improper fractions:

$$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$$

$$1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{7}{4}$$

Now we can compare the two fractions:

$$\frac{3}{2} < \frac{7}{4}$$

Therefore, $1 \frac{1}{2}$ is less than $1 \frac{3}{4}$.

Example 2: Comparing $2 \frac{1}{3}$ and $2 \frac{2}{3}$

To compare $2 \frac{1}{3}$ and $2 \frac{2}{3}$, we need to convert both mixed numbers to improper fractions:

$$2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$$

$$2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{8}{3}$$

Now we can compare the two fractions:

$$\frac{7}{3} < \frac{8}{3}$$

Therefore, $2 \frac{1}{3}$ is less than $2 \frac{2}{3}$.

In this article, we have explored the concept of comparing fractions and mixed numbers to determine if they are less than, equal to, or greater than a given value, specifically $1 \frac{1}{4}$. We have examined various expressions and used mathematical operations to determine their relationships to $1 \frac{1}{4}$. By converting fractions and mixed numbers to improper fractions and comparing the fractions, we can determine if one expression is less than, equal to, or greater than another expression.

Comparing fractions and mixed numbers is an essential skill in mathematics, and it has many real-world applications. By understanding how to compare fractions and mixed numbers, we can make informed decisions and solve problems in various fields, such as science, engineering, and finance. In conclusion, the ability to compare fractions and mixed numbers is a valuable skill that can be applied in many areas of life.

• [1] "Fractions and Mixed Numbers" by Math Open Reference
• [2] "Comparing Fractions" by Khan Academy
• [3] "Mixed Numbers" by Purplemath

• [1] "Fractions and Mixed Numbers" by IXL
• [2] "Comparing Fractions" by Mathway
• [3] "Mixed Numbers" by Math Goodies
  Determine if Each Expression is Less than, Equal to, or Greater than $1 \frac{1}{4}$: Q&A

In our previous article, we explored the concept of comparing fractions and mixed numbers to determine if they are less than, equal to, or greater than a given value, specifically $1 \frac{1}{4}$. We examined various expressions and used mathematical operations to determine their relationships to $1 \frac{1}{4}$. In this article, we will answer some frequently asked questions (FAQs) related to comparing fractions and mixed numbers.

Q: How do I compare two fractions with different denominators?

A: To compare two fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator.

Q: What is the LCM of two numbers?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 2 and 4 is 4, because 4 is a multiple of both 2 and 4.

Q: How do I convert a fraction to have a denominator of 12?

A: To convert a fraction to have a denominator of 12, you need to multiply the numerator and denominator by the same number that will make the denominator equal to 12. For example, to convert $\frac{1}{2}$ to have a denominator of 12, you would multiply the numerator and denominator by 6:

$$\frac{1}{2} = \frac{(1 \times 6)}{2 \times 6} = \frac{6}{12}$$

Q: How do I compare two mixed numbers?

A: To compare two mixed numbers, you need to convert them to improper fractions and then compare the fractions. For example, to compare $1 \frac{1}{2}$ and $1 \frac{3}{4}$, you would convert both mixed numbers to improper fractions:

$$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$$

$$1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{7}{4}$$

Then, you can compare the two fractions:

$$\frac{3}{2} < \frac{7}{4}$$

Therefore, $1 \frac{1}{2}$ is less than $1 \frac{3}{4}$.

Q: How do I determine if a fraction is less than, equal to, or greater than $1 \frac{1}{4}$?

A: To determine if a fraction is less than, equal to, or greater than $1 \frac{1}{4}$, you need to convert the fraction to have a denominator of 4 and then compare it to $\frac{5}{4}$, which is the equivalent of $1 \frac{1}{4}$. If the fraction is less than $\frac{5}{4}$, it is less than $1 \frac{1}{4}$. If the fraction is equal to $\frac{5}{4}$, it is equal to $1 \frac{1}{4}$. If the fraction is greater than $\frac{5}{4}$, it is greater than $1 \frac{1}{4}$.

Q: Can I use a calculator to compare fractions?

A: Yes, you can use a calculator to compare fractions. However, it is always a good idea to understand the concept of comparing fractions and to be able to do it manually.

In this article, we have answered some frequently asked questions related to comparing fractions and mixed numbers. We have provided examples and explanations to help you understand the concept of comparing fractions and mixed numbers. By following the steps outlined in this article, you should be able to compare fractions and mixed numbers with confidence.

Comparing fractions and mixed numbers is an essential skill in mathematics, and it has many real-world applications. By understanding how to compare fractions and mixed numbers, you can make informed decisions and solve problems in various fields, such as science, engineering, and finance. In conclusion, the ability to compare fractions and mixed numbers is a valuable skill that can be applied in many areas of life.

• [1] "Fractions and Mixed Numbers" by Math Open Reference
• [2] "Comparing Fractions" by Khan Academy
• [3] "Mixed Numbers" by Purplemath

• [1] "Fractions and Mixed Numbers" by IXL
• [2] "Comparing Fractions" by Mathway
• [3] "Mixed Numbers" by Math Goodies