Math+Chapter+2

**__Math Chapter 2: Multiplication__** Multiplying with Zeroes | Estimating Products | Multiplying 2 and 3 Digit Numbers | Lattice Multiplication | Make an Organized List | Decimal Patterns | Estimating Decimal Products | Multiplying Whole Numbers and Decimals | Multiplying Two Decimals | Variables and Expressions | Translating Words to Expressions | Find a Rule | Solving Equations | Problem Solving: Weight **__Multiplying with Zeroes__**

Multiplying two numbers together that end in zeroes is easy.

Why? Because any number times 0 always equals 0! It doesn't matter if it's 3x0 or 8764829x0, it still gives the same answer: 0! That's because if you have zero groups of a number you have zero.

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When you multiply two numbers together ending in zeroes, count the number of zeroes and write it as your answer, then multiply the remaining digits.

Example: 300x2000=600000 because there are 5 zeroes in the question and 3x2=6.

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**__Estimating Products__**

Estimating products is very similar to estimating sums and differences, which we did in chapter 1.

Let's use 87x27x4 as an example. There are different ways we can estimate this product.

Method 1: Step 1. Round 87 to 100. You can round any number greater than 80 to 100. Step 2. Round 27 to 30. Step 3. Multiply 100x30 to get 3000. Step 4. Multiply 3000 by 4 to get 12000.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">This is an overestimate because we rounded two numbers up.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Method 2: <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Step 1. Round 87 to 100. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Step 2. Round 27 to 25. If one of my factors is either 4 or 8, and another is between 20-30, I can round to 25. This is because 25x4=100 and 8x4=200. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Step 3. Multiply 25x4=100 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Step 4. Multiply 100x100 to get 10000

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Even though I rounded 27 down to 25, this is still an overestimate because I rounded 87 to 100. Underestimates come when you round more than one number down.

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Multiplying 2 and 3 Digit Numbers__**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Games

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">This is the traditional way to multiply a three digit number by a two digit number. Click Here to go to lattice multiplication.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">We will use the example 689x15.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">When you multiply a 2 digit number by a 2 or 3 digit number, we have to think of the second number as being written in expanded form. Think of 15 as 10+5. The first thing you do is multiply the number in the ones place of the second number by each digit in the first number and regroup as necessary.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> 689 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> __x 5__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">3445

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Next, you have to multiply the digit in the tens column of the second number by the first number. To do this, start by placing a zero under the first product.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> 689 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> __x 5__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">3445 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> 0

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">We have to do this because we are actually multiplying by 10, not 1. Remember, we are thinking of the second number as if it is in expanded form. Now multiply 1 by 689.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> 689 __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">x 5 __ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">3445 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">6890

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Now, add the two products together.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> 689

__<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">x 5 __

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;"> 3445

__<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">+6890 __ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">10335

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Games__**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Number Monster Choose hard mode <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Drag and Drop math Choose multiplication then 3 and 2 digits

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Lattice Multiplication__**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">This is the method for lattice multiplication. For the traditional method, click here.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Lattice multiplication is an easy way to multiply without having to keep your rows lined up or worry about adding in the extra zero on the second row. There are no partial products to worry about. You just multiply and add.

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Make an Organized List__**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">The ice cream parlor has 3 flavors of ice cream: vanilla, chocolate, and strawberry <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">There are 3 toppings: hot fudge, carmel, and strawberry

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">How many different combinations are there?

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Making an organized list can help you answer this question by showing all of the possible combinations. Pair each ice cream flavor with each topping.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">v-f ch-f s-f <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">v-c ch-c s-c <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">v-s ch-s s-s

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">There are 9 possible combinations.

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__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Decimal Patterns **__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">When we multiply whole numbers, we know to count the number of zeroes in the factors and add them to the end of our answer.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">When we multiply decimals by numbers ending in "0" we count the number of 0's and move the decimal point that many places to the right.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Examples:

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.31x10=3.1 because there is one 0 in 10, so we move the decimal point one place to the right.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.02x1,000=20 because there are 3 0's in 1,000 so we move the decimal point three places to the right.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">4.32x100=432 because there are 2 0's in 100 so we move the decimal point two places to the right.

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 * __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Estimating Decimal Products __**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Estimating decimal products is just like estimating sums and differences of decimals. Just round each decimal to the nearest whole number then multiply regularly.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Examples:

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">1.6x8.99 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Round 1.6 to 2 and 8.99 to 9 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">2x9=18

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">43x2.1 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Round 2.1 to 2 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">43x2=86

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">2.23x15.9 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Round 2.23 to 2 and 15.9 to 16 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">2x16=32

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__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Multiplying Whole Numbers and Decimals **__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">To multiply a whole number by a decimal, the easiest thing to do is ignore the decimal point and multiply as usual. When you have your product, count the number of digits after the decimal point in the factor and place your decimal point in the same place.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Examples:

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">2.56x25 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Multiply 256x25 to get 6400 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">There are 2 digits after the decimal point in 2.56, so count two places from the right in 6400 and put a decimal. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">2.56x25=64

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">5.4x3 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Multiply 54x3 to get 162 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">There is one digit after the decimal point in 5.4, so count one place from the right and put a decimal. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">5.4x3=16.2

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.55x8 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Multiply 55x8 to get 440 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">There are two digits after the decimal point in 0.55, so count two places from the right and put a decimal. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.55x8=4.40

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Multiplying Two Decimals**__

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">When we multiply two decimals we can use the same rules as multiplying a decimal by a whole number. Ignore the decimal point and multiply as usual. Then count the number of places after the decimal in each factor and place the decimal point that many places from the right in your product.

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Games**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Hoop Shot**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Power Football**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**AAA Math**__

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 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Variables and Expressions **
 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Translating Words to Expressions **
 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Finding a Rule **
 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Solving Equations **
 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Problem Solving: Weight **