MULTIPLICATION |

**What is Multiplication?**

Multiplication is actually **repeated addition**.

So, ** 4 times 3** tells us to

*4 × 3 = 3 + 3 + 3 + 3*

*2 × 5 = 5 + 5*

**However, finding sums rather than products is not very efficient when we want 36 times 9. First of all we'd have to turn our paper sideways to write thirty-six 9's and all those plus signs, then it would take us a long time to find the sum. So, instead of making life difficult for ourselves, we learn the multiplication tables and we learn them well.
**

**Multiplier, Multiplicand and Product**

**The result** (answer) **of multiplication** is called the **product**. **The number** doing the **multiplying** is called the **multiplier** (what else?). **The number being multiplied** is called the **multiplicand**, but if we don't know our multiplication tables, it's called the **MULTIPLI-CAN'T**! If a word problem says "* the product of 2 numbers is 24 *", we know the

**Multiplying and Carrying**

Since **multiplication is addition**, and when we add, we often **have to carry** values **from one column to the next** -- we do the same when we multiply. If the product of any column is bigger than 10 times the value of the column, we carry to the neighboring place on the left.

Say we're multiplying 6 × 14.

We start with the one's column: 6 × 4 = **2**4

We put **4 in the 1's column** of the product, then **carry 2 tens** to the ten's place.

Then, we multiply 6 × 1 ten = 6 tens, add the 2 tens we carried to get 8 tens.

The product of 6 × 14 is 84.

**Watch for this OOPS!** A common **mistake** for beginners is **to multiply the carried number** instead of adding it. We must remember that we __ADDED__ THE CARRIED VALUE TO THE COLUMN -- so **first we multiply** and **then we add **what we carried.

When the **multiplier is only 1 digit**, we can **use** an approach like the Column Sum approach to addition called the **Column Product Method** in which we **write the product of** the multiplier and **each column** with the **columns aligned** and then we **add**.

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**Two-Digit Multipliers**

Let's do an example to explain the difference between 1-digit and 2-digit multipliers.

It's just a matter of lining up the **partial products** according to **place value**.

Notice the " **0** " in the **one's column** in the **2nd line** of the ** partial product**. In the third step, we're multiplying by

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**Estimating the Product: making an educated guess**

Often, if we're not sure our product is correct, or when we want to know approximately what the product will be, we can make an "educated guess" or **estimate**. We **round the numbers **up or down, then **multiply** them, to determine ** about how much** the answer should be.

In the last example, we had **19 × 15**.

**300** is a **good estimate** here because it is

**20 × 15**, and **20** is very **close to** **19**

Since **15** is exactly **half way between 10 and 20**, **rounding** it up to 20 or down to 10 **makes** our **estimate** much **less ****exact**. And since it's easy to multiply by 15, we didn't round it.

That was by choice, but if we **follow** the "**rounding rules**" precisely, our **estimate**

becomes 20 × 20 or **400**. Our first estimate -- **300** -- is **only 15 more** than the actual answer but

**400**, the estimate we get when we follow the rules, is **115 more** than 285, so in this case it is better not to round. If the 15 was 14 or 16, we would **round 14 down to 10** and **16 up to 20**.

Now get a pencil, an eraser and a note book, copy the questions,

do the practice exercise(s), then check your work with the solutions.

If you get stuck, review the examples in the lesson, then try again.

**Practice**

1) Round these numbers, estimate the product, then multiply to find the product:

a) | b) | c) | d) |

2) Use the **Column Product Method** to multiply:

a) | b) | c) | d) |

3) Find each product. Carry and put zeros in columns where needed.

a) | b) | c) |

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**Solutions**

1) Round these numbers, estimate the product, then multiply to find the product:

a) | estimate 30 × 10 = 300 multiply: 34 × 8 = 272 |
b) | estimate 600 × 10 = 6000 multiply: 576 × 7 = 4032 |

c) | estimate 50 × 100 = 5000 multiply: 97 × 52 = 5044 |
d) | estimate 700 × 50 = 35 000 multiply: 737 × 46 = 33 902 |

2) Use the **Column Product Method** to multiply:

a) |
b) |
c) |
d) |

3) Find each product. Carry and put zeros in columns where needed.

a) |
b) |
c) |