How to Solve Multiplication Problems Using Pictures Step by Step
Students of third grade are well known with the concept of Multiplication as repetitive addition. Multiplication using pictures is a fun element in contrast to the regular worksheets and thus is essential to help students understand the concepts effectively and quickly. Multiplication with pictures makes the learning process fun, and thus, students are more focused on the concepts. Students get to see the specified number of copies of the group of items or some people, and they can either count the actual objects or multiply the groups by the number of items in each group. This makes the entire process more visualized. This article contains a brief understanding of the concept of Multiplication and problems to multiply using pictures.
A Brief on Multiplication
Multiplication is one of the elementary arithmetic operations of mathematics and is very useful in various mathematical and real-life problems and scenarios. We represent the multiplication operator using ‘x’ or ‘*’ based on various instances and our needs. Multiplication has three major properties, which are as follows:
Multiplication satisfies the commutative property, meaning a * b = b * a.
Multiplication satisfies the associative property, meaning a * (b * c) = (a * b) * c.
Multiplication is distributive over addition and subtraction, meaning a * (b + c) = (a * b) + (a * c) or a * (bc) = (a * b) - (a * c)
Solved Examples For Multiplication Using Pictures
1: Which Multiplication Sentence Does the Given Array of Stars Indicate?
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Ans. Since there are 25 stars, thus we need to find the multiplication sentence giving 10 as the answer. Therefore, starting with every sentence:
5 x 5 = 25 => This sentence is the correct representation for the array of stars.
4 x 4 = 16 => Not the array representation.
4 x 5 = 20 => Not the array representation
5 x 6 = 30 => Not the array representation
Therefore, the first multiplication sentence, i.e., 5 x 5, is the correct representation for the stars' array.
2: Complete the Multiplication Equations With the Help of the Given Arrays:
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Ans. Here are the solutions for both the problems:
Since the result is 9, and one of the numbers is 3, we find the other number using the diagram. The figure represents three arrays. Thus, the number to be included in the equation is 3, which will give 3 x 3 = 9.
In this problem equation, the result is ten, and one of the numbers is 5, and we find the other number using the figure, which represents two arrays of stars. Thus the number to be included in the equation is 2, which will give 5 x 2 = 10.
3: Multiply the Numbers and Find the Missing Digit Out of the Given Fish Images.
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Ans. Here, the problem is 632 x 4, and the solution is 2_28. We must fill the blank with the appropriate answer. Now, 632 x 4 = 2528. Therefore, the second fish from the left represents the answer to fill the blank for the correct product.
4: Solve the Following Using the Given Grid:
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5 x 5
4 x 8
9 x 7
Ans. Here, using the grid,
For the 5th row and 5th column, the answer is 25. Therefore, 5 x 5 =25.
For the 4th row and 8th column, the answer is 32. Therefore, 4 x 8 = 32.
For the 9th row and 7th column, the answer is 63. Therefore, 9 x 7 = 63.
5: Solve 3 x 5 Using a Number Line.
Ans. Using the number line, as it is given 3 x 5, we will take three jumps of five numbers each,
Thus:
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The answer is 3 x 5 = 15.
Fun Facts:
William Oughtred, an Anglican Clergyman and an English Mathematician introduced the symbol ‘x’ for Multiplication.
Multiple came from two Latin words, ‘multus’, meaning ‘multi’ and ‘plex’, meaning ‘fold’.
Multiplying any number of arrays by 1 gives the number or the array itself.
Multiplying a number by zero gives a 0.
If we multiply any number by 10, we need to add a 0 in the result after the given number.
FAQs on Multiply Using Pictures with Visual Models
1. What does multiply using pictures mean in maths?
Multiplying using pictures means representing multiplication as equal groups or arrays using drawings or objects. Instead of just writing numbers, you draw groups to show how multiplication works.
- Multiplication means adding equal groups.
- For example, 3 × 4 means 3 groups of 4.
- You can draw 3 circles, each containing 4 dots.
- Total dots = 4 + 4 + 4 = 12.
2. How do you multiply using pictures step by step?
To multiply using pictures, draw equal groups or an array that matches the multiplication sentence. Follow these steps:
- Step 1: Write the multiplication fact (for example, 4 × 3).
- Step 2: Draw 4 equal groups.
- Step 3: Put 3 objects in each group.
- Step 4: Count all objects to find the total.
3. How do you show multiplication using an array model?
An array model shows multiplication as rows and columns arranged in a rectangle. In an array, one number represents rows and the other represents columns.
- Example: 3 × 5
- Draw 3 rows.
- Place 5 dots in each row.
- Total dots = 3 × 5 = 15.
4. What is an example of multiplying using pictures?
An example of multiplying using pictures is drawing equal groups to represent the multiplication fact. For example, 2 × 6 means 2 groups of 6.
- Draw 2 circles.
- Place 6 stars in each circle.
- Add them: 6 + 6 = 12.
5. Why is multiplying using pictures important for learning maths?
Multiplying using pictures is important because it builds a strong understanding of equal groups, repeated addition, and arrays. Visual models help learners see how numbers combine.
- Improves conceptual understanding.
- Connects addition and multiplication.
- Supports early learners and visual learners.
- Prepares students for area models and algebra.
6. What is the difference between repeated addition and multiplication using pictures?
The difference is that repeated addition adds the same number several times, while multiplication using pictures shows those equal groups visually. Both represent the same idea.
- Repeated addition: 5 + 5 + 5 = 15.
- Multiplication sentence: 3 × 5 = 15.
- Picture model: 3 groups with 5 objects in each group.
7. How do you multiply larger numbers using pictures?
To multiply larger numbers using pictures, use an array or area model to organize rows and columns neatly. This keeps the drawing clear and structured.
- Example: 6 × 8
- Draw 6 rows.
- Place 8 dots in each row.
- Count or use repeated addition: 6 × 8 = 48.
8. What is the commutative property in multiplying using pictures?
The commutative property of multiplication means changing the order of numbers does not change the product. In pictures, the array just rotates.
- Example: 3 × 4 = 12.
- Also, 4 × 3 = 12.
- A 3-by-4 array and a 4-by-3 array have the same total squares.
9. Can you use pictures to explain word problems in multiplication?
Yes, pictures can help solve multiplication word problems by drawing equal groups or arrays to represent the situation. Visual models make the problem easier to understand.
- Example: There are 5 bags with 3 apples each.
- Draw 5 groups.
- Put 3 apples in each group.
- Total apples = 5 × 3 = 15.
10. What are common mistakes when multiplying using pictures?
Common mistakes in multiplying using pictures include drawing unequal groups or miscounting the total objects. Accuracy in grouping and counting is important.
- Drawing different numbers in each group.
- Confusing rows and columns in arrays.
- Counting one object twice.
- Skipping objects while counting.
