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# Strategy to Multiply ## Key Concepts

• Estimation, Standard algorithm, partial products, and word problems

## Estimation, standard algorithm, partial products, and word problems

### Estimation:

Estimation means finding a number that is close enough to the right answer.

### Example:

Estimate the product of 7 × 489 by rounding to the nearest hundred.

7 × 489

489 –>        500

Multiply 7 × 500 = 3500

Multiply 7 × 489 = 3,423

3,423 is close to 3,500. It is reasonable.

## What is meant by a standard algorithm?

A standard algorithm or method is a specific method of computation that is conventionally taught for solving particular mathematical problems.

Standard algorithm is a way of doing multiplication by using partial products or multiplying in parts.

### What is meant by partial products?

A model that breaks numbers down into their factors or place values to make multiplication easier.

### Example 1:

Multiply 215 × 9

Step1: Multiply 200 × 9 = 1800

Step2: Multiply 10 × 9 = 90

Step3: Multiply 5 × 9 = 45

Step4: Add 1800 + 90 + 45 =1935

### Example2:

Each T-Shirts’ cost is $485. Find the cost of 6 T-Shirts? Each frock’s cost is$4,480. Find the cost of 3 frocks?

Also, find the total cost for T-Shirts and Frocks.

Solution:

6 × 485 = c

Estimate: 6 × 485 is about 6 × 480= 2,880

Break apart 485 using place value and the distributive property.

6 × 485 = 6 × (400 + 85)

= 6 × 400 + 6 × 85

= 2400 + 510

= 2,910

The total cost of T-Shirts is $2,910. Find the cost of the dress 3 × 4,480 = y Estimate 3 × 4,480 is about 3 × 4,500 =13,440 Use an area model partial products. ### Example 2: Find the product of 3 × (7+4) using the distributive property Using the distributive law, we: • Multiply, or distribute, the outer term to the inner terms. • Combine like terms. • Solve the equation. 3(7+4) = 3(7) + 3(4) = 21 + 12 = 33 ### Example 3: Let us understand this concept with distributive property examples For example, 3(2 + 5) = 3 (7) = 21 Or By distributive law 3(2 + 5) = 3 × 2 + 3 × 5 = 6 + 15 = 21 Here we are distributing the process of multiplying 3 evenly between 2 and 5. We observe that whether we follow the order of the operation or distributive law or not, the result is the same. ### Example 4: Multiply 9 × 4860 using the standard algorithm model. Solution: Steps: 1. Multiply the ones 1. Multiply the tens 1. Multiply the hundreds, add any extra hundreds that we were carried over. 1. Multiply the thousands, add any extra thousands. ### Example 5: Use partial products to multiply 7 ×$332.

Solution:

Step 1: Estimate the product.

332 rounds to 300; 7 × $300 = 2100 Step 2: Multiply the 3 hundreds, or 300, by 7. 7 × 300=$2100

Step 3: Multiply the 3 tens, or 30, by 7.

7 × 30 =$210 Step 4: Multiply the 2 ones, or 2, by 7. 7 × 2=$14

Step 5: Add the partial products.

So, 7 × $332 =$2,324. Since $2,324 is close to the estimate of$2,100

### Example 6:

Use partial products to multiply 4 × $534. Step 1: Estimate the product. 4 ×$534 is about estimate 4 × $500 =$2000

Step 2: Multiply the 5 hundreds, or 500, by 4.

4 × 500 = 2000

Step 3: Multiply the 3 tens, or 30, by 4

4 × 30 =120

Step 4: Multiply the 4 ones, or 4, by 4.

4 × 4 = 16

Step 5: Add the partial products.

So, 4 × $534 =$2,136. Since $2,136 is close to the estimate of$2,000.

### Exercise:

1.       Solve the following using partial products:

(a) 78 × 8                                                 (b)  6 × 765                                     (c)   4 × 456

2.       Solve the following using distributive property:

(a)  4 × 564                                             (b)  2 × 465                                     (c)   3 × 590

3.       Find each product by choosing an appropriate strategy.

(a)  3 × 45                                                (b) 6 × 876                                      (c)   5 × 25

4.       Estimate the sum by rounding the number to the nearest thousand and then multiply.

(a)  3 x 3,953                                           (b)  5 × 5,458

5.       Solve the following using standard algorithm:

(a)  5 × 34                                                (b)  6 × 345                                     (c) 7 × 543

6.        A theatre can seat 460 people at one time. If a movie in the theatre fills every seat, every  day for 3 weeks, how many tickets were sold?

7.        A banana contains 105 calories. Last week, Nate and Haley ate a total of 14 bananas. How many calories did they eat?

An office needs to buy 20 new printers and 100 packages of paper. Each printer costs $300. Each package of paper costs$25. What is the cost of the printers and paper combined?

9.        A company sells jerseys for $50 each. In October, they see 32 jerseys. In April, they sold 55 jerseys. What is the total amount of money they earned by selling jerseys in October and April combined? 10. A toy shop sells 4 toys that cost$200 each. Find the cost of 4 toys?

### What have we learned:

• Understand estimation
• Understand  standard algorithm
• Understand  partial products
• Understand word problems

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