When multiplying a sum by a number, you can multiply each term separately by it and add the resulting results.
Calculate the values of the expressions.
Solution: 1. Replace the first factor with the sum of the bit terms. Let's multiply each term and add the resulting results.
2. Let's use the distribution property of multiplication.
Both of these methods use the distributive law for multiplication, but they differ in how partial products are calculated and written. The standard algorithm is generally a faster method, but unlike the domain method, it does not promote understanding or encourage the development of mathematical thinking. It is best to introduce long multiplication to your children using the area method before using the standard algorithm. The region method also supports the important ability to evaluate responses.
This hands-on practice with the materials greatly helps students develop an understanding of math concepts and provides a strong foundation for transitioning to paper-and-pencil methods. Work with children using examples, sketches, and explanations similar to the ones below.
3. Let's solve the first example with a column. To do this, write the second factor under the units. The bar means an equal sign.
4. Let's solve the second example in a column. When multiplying like this, you need to start with units.
Conclusion: when multiplying a three-digit number by single digit number The second factor should be written in a column under the units of the first factor. The dash replaces the equal sign. You need to start multiplying with units, then multiply tens and finally hundreds.
Multiplying single digit numbers
Be sure to discuss with them what you are doing. Start with 14, consisting of 10 and 4 rods. The same multiplication can be modeled using sketched boxes without any kitchen rods. Partial products are recorded in the fields. Review the examples below with your children. Discuss the steps and calculate, then add the partial products.
Practice method multiplication method
When introducing a new method, it is helpful to start with smaller numbers and multiplication facts that are easier to remember. This means the focus can be on method and also helps students who are struggling to memorize multiplication facts. In the examples above, only one factor was factored down to its base value of 10. When multiplying 2-digit by 2-digit numbers, both numbers are factored and we use four rectangles, as shown in the two examples below.
Calculate the values of the products.
Solution: 1. Let's use commutative property of multiplication- rearranging the factors does not change the product, so let’s swap the factors. We perform the multiplication in a column.
2. Let's solve the second example. Let's write four under the units of the first factor. Let's remember that when doing written multiplication, you need to start with units, then multiply tens, and finally hundreds. It is also necessary to take into account that the line under the numbers means the “equal” sign.
The example below shows how the method can be extended to multiply large numbers. Note that the area method becomes increasingly cumbersome as the number of digits increases. In such cases, where understanding has been established, the standard algorithm is probably better.
Comparison of the region method with the standard algorithm
Compare the 2 Methods Discuss the two methods with your children. Use the example below to show the correlation between the two methods.
More about matrix formulas
Why use array formulas. For example, you can calculate the total cost of a loan over a certain number of years.3. When solving the third example, we will do the same and also swap the factors.
If you multiply three digit numbers It is difficult to verbalize single-digit numbers, then you can multiply them in a column (Fig. 1).
1. Remember that when doing multiplication
column, you need to start multiplication with
units. Then the digit units are multiplied
Representation of arrays and table formulas
You can use array formulas to do complex tasks, such as. A table formula is a formula that can perform multiple calculations on one or more elements of an array. An array is a row of values, a column of values, or a combination of rows and columns of values. Table formulas can return one or more results. For example, you can place a table formula in a range of cells and use that formula to calculate a column or row of subtotals.
dozens. After that there are units in the hundreds place.
2. If you need to multiply a single-digit number by
three-digit number, then you can use
>> Lesson 13. Multiplying by a three-digit number
You can also put a table formula in one cell and then calculate one sum. A table formula that spans multiple cells is called a multi-element formula; A table formula that is in one cell is called a single cell formula.
Multicellular matrix formula
The first set of steps uses a multi-cell formula to calculate a set of subtotals. The second series uses a single cell formula to calculate the total. Here is a book built into the browser. Creating a multi-element array formula.
