Which One Of The Following Pairs Of Numbers Contains Like Fractions?A. \[$\frac{6}{7}\$\] And \[$\frac{60}{70}\$\]B. \[$\frac{5}{4}\$\] And \[$\frac{4}{5}\$\]C. \[$\frac{1}{2}\$\] And \[$\frac{3}{2}\$\]D.
Understanding Like Fractions
In mathematics, like fractions are fractions that have the same denominator. They are also known as equivalent fractions. When two fractions have the same denominator, they can be compared directly to determine which one is larger or smaller. In this article, we will explore which pair of numbers contains like fractions.
What are Like Fractions?
Like fractions are fractions that have the same denominator. For example, {\frac{1}{2}$}$ and {\frac{2}{4}$}$ are like fractions because they have the same denominator, which is 2. Similarly, {\frac{3}{4}$}$ and {\frac{6}{8}$}$ are like fractions because they have the same denominator, which is 4.
How to Identify Like Fractions
To identify like fractions, we need to look at the denominators of the fractions. If the denominators are the same, then the fractions are like fractions. For example, in the pair {\frac{1}{2}$}$ and {\frac{2}{4}$}$, the denominators are the same, which is 2. Therefore, these fractions are like fractions.
Analyzing the Options
Now, let's analyze the options given in the problem.
Option A: {\frac{6}{7}$}$ and {\frac{60}{70}$}$
In this option, the denominators are not the same. The first fraction has a denominator of 7, while the second fraction has a denominator of 70. Therefore, these fractions are not like fractions.
Option B: {\frac{5}{4}$}$ and {\frac{4}{5}$}$
In this option, the denominators are not the same. The first fraction has a denominator of 4, while the second fraction has a denominator of 5. Therefore, these fractions are not like fractions.
Option C: {\frac{1}{2}$}$ and {\frac{3}{2}$}$
In this option, the denominators are the same, which is 2. Therefore, these fractions are like fractions.
Option D: {\frac{2}{3}$}$ and {\frac{3}{4}$}$
In this option, the denominators are not the same. The first fraction has a denominator of 3, while the second fraction has a denominator of 4. Therefore, these fractions are not like fractions.
Conclusion
In conclusion, the pair of numbers that contains like fractions is Option C: {\frac{1}{2}$}$ and {\frac{3}{2}$}$. These fractions have the same denominator, which is 2. Therefore, they are like fractions.
Why is it Important to Understand Like Fractions?
Understanding like fractions is important because it helps us to compare fractions directly. When we have like fractions, we can compare them by looking at the numerators. For example, if we have two like fractions, {\frac{1}{2}$}$ and {\frac{2}{2}$}$, we can see that the second fraction is larger because its numerator is larger.
Real-World Applications of Like Fractions
Like fractions have many real-world applications. For example, in cooking, we often need to measure ingredients in fractions. If we have a recipe that calls for {\frac{1}{2}$}$ cup of sugar, and we want to make a larger batch, we can multiply the fraction by a whole number to get the new amount. For example, if we want to make a batch that is twice as large, we can multiply the fraction by 2 to get {\frac{1}{2}$}$ x 2 = {\frac{1}{1}$}$ cup of sugar.
Common Mistakes to Avoid When Working with Like Fractions
When working with like fractions, there are several common mistakes to avoid. One mistake is to assume that the fractions are not like fractions just because the numerators are different. For example, if we have two fractions, {\frac{1}{2}$}$ and {\frac{3}{2}$}$, we might assume that they are not like fractions because the numerators are different. However, the denominators are the same, which means that the fractions are like fractions.
Tips for Working with Like Fractions
When working with like fractions, there are several tips to keep in mind. One tip is to always look at the denominators first. If the denominators are the same, then the fractions are like fractions. Another tip is to use a common denominator to compare fractions. For example, if we have two fractions, {\frac{1}{2}$}$ and {\frac{3}{4}$}$, we can use a common denominator of 4 to compare them. We can rewrite the first fraction as {\frac{2}{4}$}$ to make it easier to compare.
Conclusion
In conclusion, like fractions are fractions that have the same denominator. They are also known as equivalent fractions. When two fractions have the same denominator, they can be compared directly to determine which one is larger or smaller. In this article, we analyzed the options given in the problem and determined that the pair of numbers that contains like fractions is Option C: {\frac{1}{2}$}$ and {\frac{3}{2}$}$. We also discussed the importance of understanding like fractions and provided tips for working with them.
Frequently Asked Questions (FAQs) About Like Fractions
Q: What are like fractions?
A: Like fractions are fractions that have the same denominator. They are also known as equivalent fractions.
Q: Why is it important to understand like fractions?
A: Understanding like fractions is important because it helps us to compare fractions directly. When we have like fractions, we can compare them by looking at the numerators.
Q: How do I identify like fractions?
A: To identify like fractions, we need to look at the denominators of the fractions. If the denominators are the same, then the fractions are like fractions.
Q: Can I compare fractions that have different denominators?
A: Yes, you can compare fractions that have different denominators by using a common denominator. For example, if you have two fractions, {\frac{1}{2}$}$ and {\frac{3}{4}$}$, you can use a common denominator of 4 to compare them.
Q: What is a common denominator?
A: A common denominator is a number that is the same for two or more fractions. For example, if you have two fractions, {\frac{1}{2}$}$ and {\frac{3}{4}$}$, a common denominator is 4.
Q: How do I find a common denominator?
A: To find a common denominator, you can list the multiples of each denominator and find the smallest multiple that is common to both. For example, if you have two fractions, {\frac{1}{2}$}$ and {\frac{3}{4}$}$, the multiples of 2 are 2, 4, 6, 8, ... and the multiples of 4 are 4, 8, 12, 16, .... The smallest multiple that is common to both is 4.
Q: Can I simplify like fractions?
A: Yes, you can simplify like fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, if you have a fraction {\frac{6}{8}$}$, you can simplify it by dividing both the numerator and the denominator by their GCD, which is 2, to get {\frac{3}{4}$}$.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction. For example, if you have a fraction {\frac{6}{8}$}$, the GCD is 2.
Q: Can I add or subtract like fractions?
A: Yes, you can add or subtract like fractions by adding or subtracting the numerators and keeping the denominator the same. For example, if you have two fractions, {\frac{1}{2}$}$ and {\frac{3}{2}$}$, you can add them by adding the numerators to get {\frac{4}{2}$}$, which simplifies to {\frac{2}{1}$}$.
Q: Can I multiply or divide like fractions?
A: Yes, you can multiply or divide like fractions by multiplying or dividing the numerators and denominators separately. For example, if you have two fractions, {\frac{1}{2}$}$ and {\frac{3}{2}$}$, you can multiply them by multiplying the numerators to get 1 x 3 = 3 and multiplying the denominators to get 2 x 2 = 4, resulting in {\frac{3}{4}$}$.
Q: What are some real-world applications of like fractions?
A: Like fractions have many real-world applications, such as in cooking, where we often need to measure ingredients in fractions, and in science, where we need to compare quantities in fractions.
Q: Can I use like fractions to solve word problems?
A: Yes, you can use like fractions to solve word problems by comparing quantities in fractions. For example, if you have a recipe that calls for {\frac{1}{2}$}$ cup of sugar and you want to make a larger batch, you can multiply the fraction by a whole number to get the new amount.
Q: Can I use like fractions to solve algebraic equations?
A: Yes, you can use like fractions to solve algebraic equations by comparing quantities in fractions. For example, if you have an equation {\frac{x}{2}$}$ = {\frac{3}{4}$}$, you can solve for x by multiplying both sides of the equation by 2 to get x = {\frac{3}{4}$}$ x 2, which simplifies to x = {\frac{3}{2}$}$.
Conclusion
In conclusion, like fractions are fractions that have the same denominator. They are also known as equivalent fractions. Understanding like fractions is important because it helps us to compare fractions directly. We can identify like fractions by looking at the denominators, and we can compare them by using a common denominator. We can also simplify like fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD). Like fractions have many real-world applications, such as in cooking and science, and we can use them to solve word problems and algebraic equations.