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There are several different types of word **problems** that kids may encounter, and solving these problems will demonstrate a full understanding of the meaning of the **four operations**: addition, subtraction, multiplication, and division. It also relies on and develops reading and language skills.

**See the fact file below for more information on the problems involving the four operations and patterns in arithmetic or alternatively, you can download our 34-page Problems Involving the Four Operations and Patterns in Arithmetic worksheet pack to utilise within the classroom or home environment.**

## Key Facts & Information

### REVIEW OF TERMS

- Terms are the names of the different parts of an equation.
- Addends are the numbers that are added together.
- The sum is the answer you get when you add numbers together.
- We write a plus sign (+) in between two addends, and an equal sign (=) before the sum.
- The minuend is the number that’s being subtracted from. It’s the larger number. It always comes before the subtrahend.
- The subtrahend is the number that’s being taken away from the minuend. It’s the smaller number.
- The difference is the answer we get in a subtraction equation.
- We use a minus sign (-) in between the minuend and the subtrahend.
- We write an equals sign (=) before the difference.
- The multiplicand is the number to be multiplied.
- The multiplier is the number that tells how many times a multiplicand should be multiplied.
- The multiplicand and multiplier are also called factors.
- The multiplier is often written first, but the position of these numbers does not matter. This is called the Commutative Property of Multiplication.
- The answer in a multiplication equation is called the product. A multiplication sign (x) is written between two factors.
- The dividend is the number that’s being divided.
- The divisor is the number that tells how many times a dividend should be divided.
- The answer we get in a division equation is called the quotient.
- A division sign (÷) is placed between the dividend and the divisor. It’s a short horizontal line with dots above and below it. You may also see the slash (/) used as a division sign.

### VARIABLES IN ADDITION AND SUBTRACTION EQUATIONS

- Variables are letters used to represent a number you don’t know yet.
- You can use any letter in the alphabet to represent a variable.
- Solving for the value of the variable is similar to finding what number goes into the box. All you need to do is “undo” whatever has been done with the variable. Here’s an example:
- x + 6 = 9

- The number 6 was added to the variable x. To undo this, we have to subtract 6. To undo addition, you must subtract.
- To keep an equation balanced, whatever we do on one side, we must also do on the other side. So if we subtract 6 from the left, we have to subtract 6 from the right side too.
- x + 6 = 9
- x + 6 – 6 = 9 – 6
- x = 3

- We can add or subtract any number to one side of an equation, and as long as we do it to the other side too, the equation remains balanced!
- Once we get something like “variable = some number”, that is the value of the variable that makes the equation true.
- The value of the variable that will make the equation true is called the solution to the equation.
- That means the value of x is 3, and x = 3 is the solution to the equation.
- Here’s another example.
- 10 – y = 2

- The variable y was subtracted from 10. Since y was subtracted from 10, let’s try adding y and see what happens. Just remember to do the same thing on both sides.
- -y + y = 0, because anything minus itself equals 0.
- 10 – y + y = 2 + y
- 10 = 2 + y
- 8 = y

- That means the value of y is 9, and y = 8 is the solution to the equation.

### VARIABLES IN MULTIPLICATION AND DIVISION EQUATIONS

- Just like addition and subtraction, we could also do the same “undo” technique for multiplication and division.
- What if we have a multiplication equation with a variable like this?
- y x 2 = 10

- To solve, we can try using coefficients.
- 2y = 10
- 2y ÷ 2 = 10 ÷ 2
- y = 5

- The coefficient of a variable is the number used to multiply the variable. In the expression 2y, 2 is the coefficient of the variable y.
- That means the solution to the equation is y = 5.
- Let’s try solving division equations. Here is an example.
- p ÷ 7 = 12
- p ÷ 7 x 7 = 12 x 7
- p = 84

- The variable p was divided by 7. You can undo this by multiplying both sides by 7.
- This means the solution to the equation is p = 84.

### SOLVING MULTI-STEP WORD PROBLEMS

- Whenever solving word problems, you have to:
- Figure out what the problem is asking;
- Decide what operation to use.
- Keywords can help you figure out which operation to use.

- Some word problems only take one operation to solve. Others, however, ask you to perform two or more operations. You must solve them in the correct order to arrive at the correct answer. These are called multi-step word problems.
- Robert had 16 marbles. His brother gave him 3 more bags of marbles. If each bag contained 5 marbles, how many marbles does Robert have now?
- What are the information given?
- Robert had 16 marbles. His brother gave him 3 more bags with 5 marbles in each bag.

- What is being asked?
- Let m be the total number of marbles

- What operation should be used?
- Addition, Multiplication

- You need to add the number of marbles Robert has and the number of marbles his brother gave him.
- However, notice that we do not know how many marbles his brother gave him. All we know is that his brother gave him 3 bags of marbles with 5 marbles in each bag.
- To find the total number of marbles in the 3 bags, you can use addition or multiplication.
- Using addition, if there are 3 bags of marbles, and each bag had 5 marbles, then you have 3 groups of 5s.
- Total number of marbles = 5 + 5 + + 5 = 15 marbles
- Using multiplication, if there are 3 bags of marbles, and each bag had 5 marbles, then you have 3 groups of 5s.
- Total number of marbles = 3 x 5 = 15 marbles
- Now that we know how many marbles Robert’s brother gave him, we can now solve the problem. Let’s use m as a variable for the total number of marbles.
- When we add 16 and 15, m will be 31. So, Robert has 31 marbles now.
- Let’s try another example.
- Sylvia needed to read a book that has 120 pages. She read 26 pages on Friday night, 25 pages on Saturday night, and 18 pages on Sunday night. How many pages did she have left to read?
- What are the information given?
- 120 pages Sylvia has to read; 26 pages were read on Friday; 25 pages on Saturday; 18 pages on Sunday

- What is being asked?
- Let p be the number of pages left

- What operation should be used?
- Subtraction, Addition

- You need to subtract the number of pages Sylvia has read from the total number of pages of the book.
- However, we do not know the total number of pages Sylvia has already read.
- To find the total number of pages Sylvia has read, we need to add all the pages she has read.
- Total number of pages read = 26 + 25 + 18 = 69 pages
- Now that we know how many pages Sylvia has already read, we can now solve the problem. Let’s use p as a variable for the number of pages left for Sylvia to read.
- 120 pages – 69 pages = p

- Subtracting 120 and 69, p will be 51. Therefore, Sylvia has 51 pages left to read.

### ARITHMETIC PATTERNS

- The arithmetic pattern is one of the simplest sequences to learn about. It involves adding or subtracting from a common difference, d, to create a string of numbers that are related to one another.
- For example, in the sequence:
- 3, 5, 7, 9

- Their common difference is 2, and the sequence progresses by adding the common difference.
- It may be difficult to determine the common difference and identify the arithmetic pattern in the sequence just by looking at the string of numbers. Therefore, there are a few tools you can use to ease the process of finding the common difference and the entire sequence.
- For example, you are asked to look for the next number in the sequence:
- 8, 18, 28

- Looking at the chart, you could make the assumption that the common difference for this sequence is 10 and the next number to appear in the sequence should be 38.
- It is important to note that the order of the addends has no effect on the resulting sum. You can use the addition chart to predict the outcome of the sum.
- There are three principles you should keep in mind to ease the process of addition.
- When you add two even numbers together, the resulting sum is always even.
- When you add two odd numbers together, the resulting sum is always even.
- When you add an odd number and an even number, the resulting sum is always odd.

**Problems Involving the Four Operations and Patterns in Arithmetic Worksheets**

This is a fantastic bundle which includes everything you need to know about the problems involving the four operations and patterns in arithmetic across 34 in-depth pages. These are** ready-to-use Problems Involving the Four Operations and Patterns in Arithmetic worksheets that are perfect for teaching students about the several different types of word problems that they may encounter, and solving these problems will demonstrate a full understanding of the meaning of the four operations: addition, subtraction, multiplication, and division. It also relies on and develops reading and language skills. **

### Complete List Of Included Worksheets

- Lesson Plan
- Problems Involving the Four Operations and Patterns in Arithmetic
- Cookie Problems
- More Word Problems
- Multi-Step Addition
- Missing Subtraction Patterns
- Multiples of 10
- Multiplication Patterns
- Missing Subtraction
- Reverse Operation
- Two-Step Word Problems
- Real Wor(l)d Problems

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