Finding the Smallest Number of Pieces

Oct 13, 2025 by leolavanderia.com.br 136 views

You are going to plot $\frac{2}{3}$ and $\frac{3}{4}$ on the number line below. What is the smallest number of pieces you need to partition, or break, the segment from 0 to 1 into, to plot both fractions on the number line?

Introduction

When dealing with fractions, it's often helpful to visualize them on a number line. This can make it easier to compare and understand the relative positions of different fractions. However, in order to plot fractions on a number line, we need to be able to break down the segment from 0 to 1 into smaller pieces. In this article, we'll explore the smallest number of pieces needed to plot the fractions $\frac{2}{3}$ and $\frac{3}{4}$ on the number line.

Understanding the Problem

To plot a fraction on a number line, we need to be able to identify the point that corresponds to that fraction. For example, to plot the fraction $\frac{1}{2}$ , we need to find the point that is halfway between 0 and 1. This can be done by dividing the segment from 0 to 1 into two equal pieces.

Breaking Down the Segment

To plot the fractions $\frac{2}{3}$ and $\frac{3}{4}$ , we need to break down the segment from 0 to 1 into smaller pieces. Let's start by considering the fraction $\frac{2}{3}$ . This fraction can be broken down into three equal pieces, with the point corresponding to $\frac{2}{3}$ being two of those pieces.

Finding the Smallest Number of Pieces

To find the smallest number of pieces needed to plot both fractions, we need to consider the least common multiple (LCM) of the denominators of the two fractions. The LCM of 3 and 4 is 12. This means that we can break down the segment from 0 to 1 into 12 equal pieces.

Plotting the Fractions

Now that we have broken down the segment from 0 to 1 into 12 equal pieces, we can plot the fractions $\frac{2}{3}$ and $\frac{3}{4}$ . The point corresponding to $\frac{2}{3}$ is 8 of the 12 pieces, and the point corresponding to $\frac{3}{4}$ is 9 of the 12 pieces.

Conclusion

In conclusion, to plot the fractions $\frac{2}{3}$ and $\frac{3}{4}$ on the number line, we need to break down the segment from 0 to 1 into 12 equal pieces. This is the smallest number of pieces needed to plot both fractions on the number line.

Frequently Asked Questions

What is the least common multiple (LCM) of 3 and 4? The LCM of 3 and 4 is 12.
How many pieces do we need to break down the segment from 0 to 1 into? We need to break down the segment from 0 to 1 into 12 equal pieces.
What is the point corresponding to $\frac{2}{3}$ ? The point corresponding to $\frac{2}{3}$ is 8 of the 12 pieces.
What is the point corresponding to $\frac{3}{4}$ ? The point corresponding to $\frac{3}{4}$ is 9 of the 12 pieces.

Step-by-Step Solution

Find the least common multiple (LCM) of 3 and 4. The LCM of 3 and 4 is 12.
Break down the segment from 0 to 1 into 12 equal pieces. We can break down the segment from 0 to 1 into 12 equal pieces.
Plot the fractions $\frac{2}{3}$ and $\frac{3}{4}$ on the number line. The point corresponding to $\frac{2}{3}$ is 8 of the 12 pieces, and the point corresponding to $\frac{3}{4}$ is 9 of the 12 pieces.

Example Problems

Plot the fractions $\frac{1}{2}$ and $\frac{3}{4}$ on the number line. To plot the fractions $\frac{1}{2}$ and $\frac{3}{4}$ , we need to break down the segment from 0 to 1 into 4 equal pieces. The point corresponding to $\frac{1}{2}$ is 2 of the 4 pieces, and the point corresponding to $\frac{3}{4}$ is 3 of the 4 pieces.
Plot the fractions $\frac{2}{3}$ and $\frac{5}{6}$ on the number line. To plot the fractions $\frac{2}{3}$ and $\frac{5}{6}$ , we need to break down the segment from 0 to 1 into 6 equal pieces. The point corresponding to $\frac{2}{3}$ is 4 of the 6 pieces, and the point corresponding to $\frac{5}{6}$ is 5 of the 6 pieces.

Real-World Applications

Plotting fractions on a number line has many real-world applications. For example, in architecture, fractions are used to describe the proportions of different parts of a building. In engineering, fractions are used to describe the proportions of different parts of a machine. In finance, fractions are used to describe the proportions of different parts of a portfolio.

Conclusion

In conclusion, plotting fractions on a number line is an important skill that has many real-world applications. By breaking down the segment from 0 to 1 into smaller pieces, we can plot fractions on the number line and understand their relative positions. The smallest number of pieces needed to plot both fractions on the number line is 12.