## Key Concepts

- Use partial products
- Use the standard algorithm

## What are the 2-digit numbers?

10 to 99 numbers are the 2-digit numbers.

- The largest 2-digit number is
**99.** - The smallest 2-digit number is
**10.**

### Use partial products

#### What is meant by the partial products?

The partial product method **involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.**

For instance, 25 x 32 would become (20 x 30) + (20 x 2) + (5 x 30) + (5 x 2).

**Example 1:**

46 persons can sit in one compartment of the train. How many persons can sit in 52 such compartments?

**Solution:**

Use an area model to find the partial products for 46 x 52.

**2,392 persons can sit in 52 compartments. **

**Example 2:**

Ria bought a camera. A camera costs $32. Find the cost of 29 such cameras?

**Solution:**

Use an area model to find the partial products for 29 x 32.

**29 cameras costs $928. **

### Use the standard algorithm

#### Standard algorithm

The standard algorithm in math strategies is **where you line up the places and complete the problem starting on the right side with the ones, then the tens place adding in any number is carried.**

### 2 Digit Multiplication Steps

**Example 1: Multiply 45 x 36**

**Step 1: **Multiply the ones on the bottom by the ones on the top.

**Step 2:** Put the ones in the ones place and regroup the tens above the tens place.

**Step 3:** Multiply the bottom ones by the top tens.

**Step 4: **Add the tens you regrouped in step 2.

**Step 5: **Write down the answer to step 4 next to the ones.

**Step 6:** You now will be multiplying with the tens column. Write a 0 in the ones column.

**Step 7: **Multiply the tens on the bottom by the ones on the top.

**Step 8:** Put the tens next to the 0 from step 6 and regroup the hundreds by placing them above the tens column.

**Step 9:** Multiply the tens on the bottom by the tens on the top

**Step 10: **Add the regrouped amount from step 8

**Step 11:** Write down the answer to step 10

**Step 12:** Add the two numbers

**Example 2:**

**Example 3: **

**Example 4:**

Charmin took her 54 students to the aquarium. Admission for each student was $67. What was the total amount of money needed for the field trip?

**Solution:**

**Step 1:** Multiply by the ones.

**Step 2**: **Multiply** by the tens.

**Step 3: **Add the partial products.

** $3, 618 needed for the field trip. **

**Example 5:**

Kelvin has jewelry company. He ordered 63 boxes of glass beads. There were 47 beads in each box. How many glass beads did he order?

**Solution:**

**Step 1:** Multiply by the ones.

**Step 2: **Multiply by the tens.

**Step 3**: Add the partial products

**Kelvin ordered 2961 beads.**

## Exercise

- Use the partial products to find the product. Draw an area model as needed.
- 23 x 44
- 12 x 35
- Fill the missing numbers using an algorithm model.

- Fill the missing numbers.

- Use partial products to find the product.

- Use an algorithm to find the product.

- Use an algorithm to find the product. Estimate to check if your answer is reasonable.

- John sold 36 cookbooks. One book cost is $27 each. How much did he make?
- An adult human has 32 teeth. If there are 83 adults in a room, how many teeth is that in all?
- Each of the 15 people who visited a pop-up store bought 23 bars of handmade soap. How many bars of soap did they buy in all?
- 28 children can ride a carousel at a time. If the carousel made 19 trips and was filled to capacity each time, how many children did it carry in all?

### Concept Map

### What have we learned

- Understand 2 digit numbers.
- Understand partial products.
- Multiplying 2 digit number by 2 digit numbers through partial product model.
- Identify the partial products.
- Multiplying 2 digit number by 2 digit numbers through standard algorithm model.

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