How to Solve 2 Digit By 2 Digit Multiplication Multi Step Word Problems with Steps and Examples
As we know, in Mathematics, multiplication is one of the four basic operations; the others are addition, subtraction and division. Multiplication is known as the repeated addition of the same number. Likewise, double-digit multiplication is simply single-digit multiplication which is done twice. It is done by arranging the numbers so that the provided numbers are placed one below the other.
A 2-digit number can be multiplied with a single digit, with another 2-digit number or a 3-digit number and so on. Therefore, in this chapter, we will learn about 2-digit by 2-digit multiplication, multi-step word problems, and word problems on addition and subtraction.
What is 2-Digit Multiplication?
2-digit multiplication is the method or process of multiplying 2-digit numbers arranged in two place values, i.e., ones and tens. The process of multiplying numbers is the same as multiplying single digits. However, in 2-digit multiplication, we multiply each digit by one by the multiplier. It means the multiplier is first multiplied with the one digit of the multiplicand and then multiplied with the tens digit of the multiplicand.
An example of 2-digit multiplication
2-Digit by 2-Digit Multiplication Multi-Step Word Problems
2-digit by 2-digit multiplication multi-step word problems are mathematical problems that involve multiple steps and require the use of 2-digit by 2-digit multiplication. These problems can be challenging because they require students to not only perform mathematical calculations but also to understand and interpret the problem and to use that information to determine the correct solution. In this, we need to convert the statements into a mathematical form, and then we can multiply them.
Here, we will have the question in the statement form. Let us understand it with the help of an example:
Example: 24 folders each has 56 sheets of paper inside them. How many sheets of paper are there altogether?
Ans: The multiplication starts with the ones place first and then moves on to the tens place. The numbers are placed one below the other.
We can add 56 sheets 24 times
Or
Since multiplication is repeated addition, we can multiply 56 and 24 to get the answer.
Multiplication of 56 and 24
Solved Examples of Multi-Step Word Problems
Q1. A baker has 57 loaves of bread. He wants to sell each loaf for $35. How much money will the baker make from selling all the loaves of bread?
Ans: To solve this problem, students would need to perform the 2-digit by 2-digit multiplication of 57 x 35, which is 1995. They would then need to understand that the problem is asking for the total amount of money the baker will make from selling all the loaves of bread and that the answer is $1995.
Multiplication
Thus the product of 57 and 35 is 1995.
Q2. At a party, Sam ate 25 chocolates, each containing 33 calories. At the party, how many calories does Sam consume?
Ans: Write the given numbers in column form. First, multiply the one digit of the multiplier with the multiplicand and then multiply the tens digit with the multiplicand. Add the partial products to obtain the required result.
Multiplication
Thus Sam ate a total of 825 calories at the party.
Practice Problems
Q 1. A teacher has 41 students in her class. Each student needs 32 pages of notebook paper for the school year. How many pages of notebook paper will the teacher need to provide for the class?
Ans: 1312
Q 2. A construction company has 35 workers on its payroll. Each worker needs 16 sets of safety equipment for the construction season. How many sets of safety equipment will the company need to provide for its workers?
Ans: 560
Word Problems on Addition and Subtraction
Word problems on addition and subtraction are very important to build upon the basic skills among the students. In math, word problems mean that the information is presented through storytelling, and students have to understand it and then transform it into math equations. The worksheets help students to practice and make their basic skills stronger.
Q1. 49 fourth graders, 35 fifth graders and 76 sixth graders showed up for soccer practice. How many students were there in total?
Ans: 160 Students
Q2. A large tank truck can hold up to 11,256 gallons of oil. If the truck already contains 9,365 gallons of oil, how many more gallons will be required to fill the tanker?
Ans: 1891 Gallons
Addition Subtraction Multiplication Division Worksheets
An addition, subtraction, multiplication, and division worksheet is given below:
Q 1. A store has 45 apples, and they received 12 more apples. How many apples do they have now?
Ans: 57
Q 2. A boy had 89 candies, and he ate 12 candies. How many candies he has now?
Ans:
Q 3. A store has 6 shelves of books, and each shelf has 9 books. How many books are there in total?
Ans: 54
Q 4. A shop has 96 chocolates and wants to divide them into boxes of 8 chocolates each. How many boxes will be needed?
Ans: 12
Summary
So, in this chapter, we have learned and discussed what 2-digit multiplication is and how 2-digit is multiplied by 2-digit in a stepwise process to understand and learn it better. We have solved a few multi-step word problems related to 2-digit by 2-digit multiplication.
We also solved addition subtraction multiplication division worksheets PDF to enhance the skills of the students and make the concept very clear. Apart from that, under this chapter, we will practice worksheets based on the word problems on addition and subtraction so that they can be understood better.
FAQs on Mastering 2 Digit By 2 Digit Multiplication in Multi Step Word Problems
1. What is a 2 digit by 2 digit multiplication multi step word problem?
A 2 digit by 2 digit multiplication multi step word problem is a maths problem that requires multiplying two two-digit numbers and completing additional steps like addition or subtraction to find the final answer.
- It involves numbers from 10 to 99.
- You must identify more than one operation.
- It often represents real-life situations like cost, area, or total items.
- You solve it step by step in the correct order.
2. How do you solve a 2 digit by 2 digit multiplication word problem step by step?
To solve a 2 digit by 2 digit multiplication word problem, first multiply the two numbers, then complete any additional required operations.
- Read the problem carefully.
- Identify the two-digit numbers to multiply.
- Use the standard multiplication method.
- Complete extra steps like addition or subtraction.
- Write the final answer with units.
3. What is the standard method for multiplying two 2 digit numbers?
The standard algorithm multiplies each digit of one number by each digit of the other and then adds the partial products. Example:
- Multiply ones: 4 × 6 = 24
- Multiply tens and cross multiply.
- Add partial products.
- 23 × 5 = 115
- 23 × 40 = 920
- Add: 115 + 920 = 1035
4. Can you give an example of a multi step multiplication word problem?
A multi step multiplication word problem requires multiplication plus another operation. Example: A school buys 28 packs of pencils with 34 pencils in each pack and gives away 150 pencils.
- Total pencils bought: 28 × 34 = 952
- Pencils left: 952 − 150 = 802
5. How do you know when a word problem requires 2 digit by 2 digit multiplication?
A word problem requires 2 digit by 2 digit multiplication when it involves equal groups with two-digit numbers in both quantities. Look for keywords such as:
- “each”
- “every”
- “per”
- “groups of”
6. What are common mistakes in 2 digit by 2 digit multiplication word problems?
Common mistakes include place value errors and forgetting extra steps in multi step problems.
- Not adding a zero when multiplying by the tens digit.
- Adding partial products incorrectly.
- Stopping after multiplication without finishing the final step.
- Ignoring units in the final answer.
7. How do you multiply 2 digit numbers using the area model?
The area model multiplies two-digit numbers by breaking them into tens and ones. Example: 34 × 27.
- (30 + 4)(20 + 7)
- 30 × 20 = 600
- 30 × 7 = 210
- 4 × 20 = 80
- 4 × 7 = 28
- Add: 600 + 210 + 80 + 28 = 918
8. Why are multi step word problems important in multiplication?
Multi step word problems are important because they develop problem-solving skills and real-life application of multiplication. They help students:
- Understand order of operations.
- Interpret real-world scenarios.
- Apply multiplication with addition or subtraction.
- Build logical reasoning skills.
9. What is a real life example of 2 digit by 2 digit multiplication?
A real-life example is calculating total cost when buying multiple items. If 46 tickets cost 32 dollars each, total cost = 46 × 32.
- 46 × 32 = 1472
10. How can I check my answer in a 2 digit by 2 digit multiplication problem?
You can check your answer by using estimation or the inverse operation.
- Round numbers to estimate: 48 × 29 ≈ 50 × 30 = 1500.
- Compare with exact answer: 48 × 29 = 1392 (reasonable).
- Redo multiplication carefully.
- Use a calculator to verify.
