# Look for a Pattern: One & Two Operation Problems with Positive Decimals

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• 0:01 Looking For A Pattern
• 1:45 Finding A Pattern - Example 1
• 2:45 Finding And Using The Formula
• 3:55 Finding A Pattern - Example 2

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn how finding a pattern can help you solve one- and two-operation problems involving decimal numbers. Learn what it takes to find a pattern and then to use the pattern to find the answer.

## Looking for a Pattern

Problems come in all types. In this video lesson, we look at problems that involve decimal numbers and patterns. Decimal numbers are those numbers that have a decimal point, and a pattern is simply a set of numbers ordered by a specific rule. Because patterns follow rules, we can write a formula to describe a pattern. Once we have the formula, we can find any number in the pattern.

For example, the pattern 2, 3, 4, 5, â€¦ can be represented by the formula x + 1. When our x equals 1, we get 1 + 1 = 2. When x = 2, we get 2 + 1 = 3. The pattern here is that each number is its position plus 1. The first number is 1 + 1. The second is 2 + 1, and so on.

In this formula, our x stands for where our answer is in the pattern sequence. If x is 1, our answer is the first number in our pattern sequence. If x is 2, our answer is the second number in our pattern sequence. We can also get specific. If we have the equation x + 1 = 5 with a pattern of 2, 3, 4, 5, then the equation is specifically looking for the fourth number in our pattern sequence. We know this because the fourth number in our sequence is 5, which is the same as what our equation equals.

We can replace our x + 1 with the 5. Does 5 = 5? Yes. We know this is the fourth number in our sequence because the x equals 4 when x + 1 equals 5. In this example, we used whole numbers, but our problems can have decimal numbers in them too.

Let's take a look at this problem.

## Selling Susan's Pies

Susan is trying to find a pattern at her local bakery. She sees that if one person comes, then a pie and a half is sold. If two people come, then three pies are sold. If three people come, then four and a half pies are sold. If four people come, then six pies are sold. Find the formula for this pattern and use the formula to find how many pies are sold if 10 people come.

For this problem, the number of people can represent the position of our number in the pattern sequence. The first number is 1.5 for one person. The second number is 3 for two people. The third number is 4.5 for three people. And the fourth number is 6 for four people. Our pattern begins with the numbers 1.5, 3, 4.5, and 6. Of course the pattern continues, but right now it is our job to find the formula for this pattern so we know how to continue it.

## Finding and Using the Formula

What we need to do now is to find what the pattern is so we can write a formula. Looking at these numbers, what do you see going on? Do you see how each number is the number of people multiplied by 1.5? That's right. It seems that at this local bakery, each customer purchases 1.5 pies. To write our formula, we can use x to represent the number of people coming in. Our pattern then tells us to multiply it by 1.5. So our formula is 1.5x.

Now that we have our formula, we can use it to answer the rest of the problem. The rest of the problem wants us to figure out how many pies are sold if 10 people come. To find this answer, we will use our formula, 1.5x, and plug in 10 for x to find the number of pies that are sold. We get 1.5 * 10 = 15. So, 15 pies are sold when 10 people come. Our complete answer then is the formula 1.5x along with 15 for the number of pies sold to 10 people.

Let's look at another example.

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