https://file.aiquickdraw.com/mathbot/file/1726370402812ay3d8g87.jpg

Make sure you use the correct fractions by looking at the dotted and solid lines in both a, b, and c.

Let's break down each model and analyze the multiplication facts represented:

### (a) First Model:
- The grid goes up to 5 on the vertical axis and 4 on the horizontal axis.
- The shaded portion stops at **3 on the vertical axis** and **4 on the horizontal axis**.
- This represents the multiplication fact:  
  \[
  3 \times 4 = 12
  \]

### (b) Second Model:
- The grid goes up to 1 on the vertical axis and 2 on the horizontal axis.
- The shaded portion stops at **1 on the vertical axis** and **1.5 on the horizontal axis** (3 halves).
- This represents the multiplication fact:  
  \[
  1 \times \frac{3}{2} = \frac{3}{2}
  \]

### (c) Third Model:
- The grid goes up to 1 on the vertical axis and 3 on the horizontal axis.
- The shaded portion stops at **0.5 on the vertical axis** and **1.5 on the horizontal axis** (3 halves).
- This represents the multiplication fact:  
  \[
  \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}
  \]

These rectangular models illustrate multiplication as an area, where the dimensions of the shaded portion represent the factors being multiplied.

---

Would you like more details or have any questions?

Here are some related questions you might explore:
1. How can you represent a fraction multiplied by a whole number using a rectangular area model?
2. What does it mean for one dimension to be a fraction in an area model?
3. How can an area model illustrate multiplication of decimals?
4. Can you explain why the area represents the product in multiplication?
5. How can we use these models to understand division problems?

**Tip:** When dealing with fractions in area models, think of each square as a part of the whole and consider how many parts fit into the dimensions of the shaded region.

What multiplication facts are illustrated by these rectangular area models?

Explore how multiplication facts involving whole numbers and fractions are represented using rectangular area models. Learn how the shaded portion of the model shows the product of two numbers, suitable for Grades 4-6.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation