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How are multiplication and division related?
Goal:
Goal:
Think About It!
Goal: Identify how multiplication and division relate using arrays.
Caleb loves The Treasure of the Secret Castle! He is reading about the jewels in the castle. Caleb wants to know how many jewels there are. There are four rooms in the castle that have the same number of jewels. Caleb wants to know how many jewels are in each room. We can use multiplication and division to help Caleb!
We can use multiplication to count the number of jewels there are. A multiplication sentence is what we write when we multiply. It has two factors, a multiplication symbol, an equal sign, and a product. We can use division to put the jewels into equal groups. We write a division sentence when we divide. It has a dividend, a division symbol, a divisor, an equal sign, and a quotient. Multiplication and division are related. When we multiply, we get a larger total. When we divide, our larger total gets broken down into smaller groups. The math sentences use the same numbers in different places. The product becomes the dividend. The first factor becomes the divisor. The second factor becomes the quotient.
number of groups times number in each group equals total number
total number divided by number of groups equals number in each group
factor times factor equals product
dividend divided by divisor equals quotient
Take a look at the math sentences below. Click on the product of the multiplication sentence. Click on the dividend of the division sentence.
3
🤔 No. This is a factor.
5
🤔 No. This is a factor.
15
😄 Yes! 15 is the product!
15
😄 Yes! 15 is the dividend!
3
🤔 No. This is the divisor.
5
🤔 No. This is the quotient.
We will use an array to multiply and divide. An array is a picture that puts an equal number of shapes into rows and columns. The number of rows is the number of groups. The number of shapes in each row (the number of columns) is the number in each group. Multiplication and division use the same numbers in different ways. That is why we can use an array to multiply and divide!
factor times factor equals product
dividend divided by divisor equals quotient
Arrow pointing to table. Left column labeled number of rows, top column labeled the number of shapes in each row, bottom column labeled total number of shapes
Click the math sentences and the array to learn more!
3 (arrow underneath labeled number of rows) times 5 (arrow underneath labeled number in each row) equals 15 (arrow underneath labeled total number of shapes). 15 (arrow underneath labeled total number of shapes) divided by 3 (arrow underneath labeled number of rows) equals 15 (arrow underneath labeled number in each row). Array of 2 by 5 -- left column labeled 1-3 and top column labeled 1-5.
Click to help Caleb count the jewels and then put them into equal groups!
___ \({ \times }\) ___ = ___
Caleb wants to know how many jewels there are in the castle. He says there are 4 groups of 6 jewels. What multiplication sentence can you use to show 4 groups of 6? The first factor is the number of groups. The second factor is the number in each group. Click the Show Me button to see the correct multiplication sentence!
4 \({ \times }\) 6 = ___
4 \({ \times }\) 6 = ___
4 and 6 are the factors. You can use the array to find the product. The first factor is the number of rows. The second factor is the number of shapes in each row. It is also the number of columns. Click the Show Me button to see the correct array!
This is a 4 by 6 array.
4 \({ \times }\) 6 = ___
The above array is a 4 by 6 array. The array is named after the number of rows and the number of columns! We can use the array we made to find the product. The product is the same number as the total number of shapes in the array. Count the dots or add the 4 groups of 6 to find the product.
Question:
What is 4 \({ \times }\) 6 equal to?
4 \({ \times }\) 6 = 24
Caleb has 24 jewels!
___ \({ \div }\) ___ = ___
Now Caleb knows that there are 24 jewels! He wants to keep them in the 4 equal groups of 6. That is because there are 4 rooms, with an equal number of jewels in each room. He wants to write a division sentence. He starts with the dividend. The dividend is the total number of jewels. The divisor is the number of equal groups. Click the Show Me button to see the correct division sentence!
24 \({ \div }\) 4 = ___
24 \({ \div }\) 4 = ___
24 is the dividend. It is also the total number of shapes in the array. 4 is the divisor. It is also the number of rows of the array. We will use 24 dots for the 24 jewels. We start with one column of 4 dots. That is because the array needs 4 rows. Then we will make another column of 4. We need to make columns of 4 until there are 24 dots in the array. Each row will have the same number of dots. Click the Show Me button to see the array!
This is a 4 by 6 array.
24 \({ \div }\) 4 = ___
The above array is a 4 by 6 array. We can use the array we made to find the quotient! The quotient is the number in each group. It is also the number of shapes in each row. Count the number of shapes in one row to find the quotient.
Question:
What is 24 \({ \div }\) 4 equal to?
24 \({ \div }\) 4 = 6
Each room has 6 jewels!
24 \({ \div }\) 4 = 6
4 \({ \times }\) 6 = 24
Do you see the same numbers in different places? We can use the same array in different ways too!
Multiplication and division are related. We can use the same array and numbers to do both!