Multiplication and Division word problems: 3 Easy ways to master
- Author: Noreen Niazi
- Last Updated on: September 30, 2023
You’re not alone if word problems make you want to tear your hair out.
But don’t worry; you’ve got this! You’ll quickly break through multiplication and division word problems with a few easy tricks.
Forget the confusion and frustration – it’s time to build your confidence from the ground up. Rather than seeing word problems as intimidating, consider them an exciting challenge to flex your mathematical muscles.
With regular practice, these brain teasers will become second nature. Stay positive, believe in yourself, and keep your eyes on the prize. Conquer each problem one step at a time, and before you know it, you’ll be the word problem whiz you were always meant to be!
Ready to get started? Let’s do this!
Multiplication and division word problems – they can seem tricky, but don’t worry, you’ve got this! These useful math skills are easier to master than you might think.
What Are Multiplication and Division Word Problems?
Multiplication and division word problems are just math problems described using words instead of numbers and symbols. They challenge you to take a wordy description of a situation, figure out what numbers are involved, and calculate the solution.
Solving them helps build valuable real-world skills. You’ll improve comprehension, critical thinking, and applying logic in new contexts. With regular practice, these word problems will become second nature!
Here are a few tips to get started:
- Read through the whole problem carefully. Identify what is being asked and what information you have been given.
- Look for keywords and phrases that indicate an operation like multiplication or division, such as ‘times,’ ‘product,’ ‘ratio,’ ‘per,’ or ‘shared equally.’ Underline or highlight them.
- Figure out what numbers correspond to what is being asked. You may need to substitute numbers for words or break longer phrases into shorter ones.
- Set up the problem using the numbers and indicated operation (x for multiplication or ÷ for division). Then solve!
- Check that your solution makes sense in the context of the original problem. Make sure all the details in the wording match your final answer.
You’ll solve multiplication and division word problems quickly with enthusiasm and practice! Stay positive, break big problems into small steps, and keep at it. You’ve got the skills – now put them to use! Before you know it, these will feel like a breeze.
Solving Word Problems Using Diagrams
Using diagrams makes solving word problems involving multiplication and division a breeze[1]. Why diagrams? Because they help you visualize what’s going on in the problem so you can figure out how to solve it.
Let’s walk through an example, shall we? Say you have this problem:
“24 students are going on a field trip. If each bus holds 8 students, how many busses are needed?”
- First, draw a box representing the total number of students, 24.
- Then, draw smaller boxes inside it to represent groups of 8 students for each bus.
- Keep adding boxes of 8 students until you’ve used up all 24 students.
- Count the number of small boxes – that’s how many buses you need!
- For this problem, you’ll end up with 3 boxes of 8 students, so the answer is 3 buses.
See how visualizing the problem made it so much easier to solve? Now you try one: “A bakery made 96 cupcakes. If they put 12 cupcakes in each box, how many boxes will they need?” Draw it out and you’ll get the answer in no time!
The key to mastering word problems is practicing. Try using diagrams to solve word problems involving multiplication and division each day. Start with simpler problems and work your way up to more complex ones. Before you know it, these problems will seem like a piece of cake! Stay enthusiastic – you’ve got this! With regular practice, you’ll be solving word problems in your sleep.
The Importance of Keywords
Multiplication and division word problems can seem tricky but don’t worry—with a few easy strategies, you’ll solve them quickly! The key is identifying important keywords that indicate what operation to use. Spotting these keywords is the first step to mastery.
Look for Multiplication Triggers
Keep an eye out for words like “times,” “product,” “twice,” “triple,” or “groups of.” These words signal that multiplication is needed to solve the problem. For example:
- “Sally has 3 times as many dolls as Jenny. Jenny has 12 dolls. How many dolls does Sally have?” 3 (times as many) = multiply
“The product of 7 and 8 is what number?” Product = multiply
Watch for Division Hints
Pay attention to words such as “divided by,” “split into,” “shared equally,” or “per.” These words indicate division is required. For example:
- “42 students were divided into 6 equal groups. How many students were in each group?” Divided into = divide
- “Tom earned $84 in tips which he shared equally among 7 coworkers. How much did each coworker receive?” Shared equally = divide
Look at the Question!
The question itself frequently contains clues about whether to multiply or divide. Questions with “How many in each group?” or “How much each?” usually involve division. Questions with “How many totals?” or “What is the product?” often require multiplication.
With practice, spotting these keywords will become second nature. Look for language that implies multiplying groups or dividing a whole into parts. Soon you’ll be solving multiplication and division word problems confidently and easily! Keep at it, and don’t get discouraged—you’ve got this!
Read the Problem Carefully
The most important step to mastering word problems is reading the problem carefully. Seriously, slow down and read each word problem thoroughly. You should dive right in and start solving, but take a deep breath and read it over a few times. Look for keywords that indicate what operation to use, like ‘times’, ‘product’, ‘divided by’ or ‘quotient’. Circle numbers and variables. Draw diagrams or models if it helps make the problem clearer.
Once you’ve read it over, ask yourself some questions. What are you trying to figure out? What information do you have? What additional info do you need? Solve word problems one step at a time instead of trying to do it all simultaneously. Think about what makes sense based on the context of the problem. How many are left if Sally has 8 apples and eats 3 of them? Well, Sally started with 8 apples, so if she ate 3 of them, there must be 8 – 3 = 5 apples left. See how thinking it through logically can help.
Make Educated Guesses
Don’t be afraid to make an educated guess. Use what you know to make an estimate and see if the answer choices make sense. Eliminate options that are clearly too large or too small. Guessing strategically can increase your odds of choosing the right answer.
Draw a Diagram or Act It Out
For tricky problems, drawing a diagram, picture, or model can be extremely helpful. You can also solve the problem with blocks, coins, or a number line. Manipulating concrete objects allows you to visually represent what’s happening in the word problem, and often the solution becomes clear as day.
Check Your Work
Double-check that your solution makes sense within the context of the original problem. Do all the numbers add up? Did you use the correct operation? Plug your solution back into the problem to ensure it’s the logical answer. Carefully checking your solution will allow you to catch any silly mistakes before moving on.
With practice, these word problems will become second nature. Stay enthusiastic and remember to read carefully, think it through step-by-step, make educated guesses when needed, and always double-check your work. You’ve got this! Keep at it, and word problems will no longer seem so problematic.
Identify What the Problem Is Asking
You’ve got this! Word problems involving multiplication and division can seem tricky, but you’ll solve them quickly with some practice. The most important first step is to determine exactly what the problem is asking. Read the problem carefully and look for keywords and phrases to determine the question.
Once you know what is being asked, you can work through the problem step-by-step. The key is not to feel overwhelmed – take it slowly and be methodical. Look for numbers, quantities, and values in the problem to determine what needs to be multiplied or divided. Pay close attention to units of measurement as well, like feet, pounds, etc.
Some common keywords to look out for include:
- Times (x): Indicates multiplication, e.g. “Bob had 3 times as many apples as Jenny.”
- Product: The multiplication result, e.g., “What is the product of 4 and 6?”
- Divided by (/): Indicates division, e.g. “The class was divided into 6 groups.”
- Quotient: The result of division, e.g. “What is the quotient of 12 divided by 3?”
- Per: Can indicate either multiplication or division, e.g. “Bob earns $10 per hour” or “There are 3 boxes per crate.”
Once you’ve determined the operation, write out the numbers, values, and units of measurement given in the problem. Set up the multiplication or division problem and solve it! Double-check your work to make sure the answer makes sense. If it seems off, re-read the original problem to set it up properly.
With regular practice, these word problems will become second nature. Stay enthusiastic and remember to go slowly. You’ve got the skills – now put them to work! Keep at it; before you know it, you’ll be a word problem-solving master!
Read more about decimal and fractions
Converting Mixed Numbers to Improper Fractions: A Step-by-Step Guide
Choose the Correct Operation: Multiplication or Division
Choosing between multiplication and division can be tricky in word problems, but you’ll solve them quickly with some practice! Here are a few tips to help determine which operation you need:
Think about the question
Read the word problem carefully. Is it asking you to find a total amount, like the number of apples if you have 3 bags with 4 apples each? That’s multiplication – you need to calculate 3 x 4 = 12 apples total. Or is it asking you to find how many groups, like figuring out how many 4-apple bags you can fill if you have 12 apples? That would be 12 / 4 = 3 bags.
Look for keywords
Certain words indicate you should multiply, like ‘each’, ‘every’, ‘altogether,’ ‘total’, or ‘product’. Words like ‘share’, ‘divide’, ‘distribute’, or ‘per’ usually mean you should divide. Underline or highlight these keywords to help determine the right operation.
Figure out the unknown.
Decide what the question asks you to find – the total, number of groups, and amount in each group. Set up the problem by writing what you know, leaving the unknown blank. For example, if you have 3 bags with 4 apples in each, you know:
3 bags
4 apples in each bag
? total apples
So you fill in the blank with 3 x 4 = 12. For division, do the opposite:
12 apples
? bags
4 apples in each bag
Then solve: 12 / 4 = 3 bags
Check your work
Make sure the answer makes sense in the context of the original problem. If you calculated 12 total apples but the question asked how many apples were in each bag, go back and try again – you used the wrong operation! With regular practice, these word problems will become second nature. Keep at it, and don’t get discouraged if you make a mistake. You’ve got this!
Show Your Work
Showing your work is one of the best ways to master multiplication and division word problems. Why? Because it helps you organize your thoughts and break down the problem into easy-to-understand steps. When you write out each step, you’ll gain confidence in solving these tricky problems.
So grab your pencil and some scrap paper – it’s time to show your work! Follow these three simple techniques:
1. Read the entire problem.
This problem has gone viral on YouTube due to two versions of the order of operations. There needs to be more clarity in which the multiplication sign is omitted. There are two different ways to approach this.
2. Identify what needs to be found.
What exactly are you trying to figure out? Circle or underline key phrases in the problem that indicate what needs to be calculated or solved. This could be a total amount, difference, product, or quotient. Knowing what you need to find will guide setting up your work.
3. Set up the problem visually.
Use addition, subtraction, multiplication, or division to represent the relationships described in the word problem. For example, if the problem refers to “groups of 6,” you would likely use multiplication (6 x ? = ?). If it refers to “sharing 12 apples among 3 friends,” you would set up 12 / 3 = ?. Setting up the mathematical operations visually is the key to solving word problems confidently!
By reading carefully, identifying what needs to be found, and setting up the problem visually with the appropriate operations, you’ll be solving multiplication and division word problems in no time. Showing your work in an organized way builds understanding and mastery. Keep practicing and stay enthusiastic – you’ve got this! Before you know it, word problems will be a breeze.
Check Your Answer
You’ve set up the problem, worked through all the steps, and now comes the moment of truth—check your answer! This is a crucial final step to build confidence in your math skills. Here are three ways to verify you nailed that multiplication or division word problem.
Double Check Your Work
Go back through each work step to ensure you made no silly mistakes. Check that numbers are in the right place value, signs are correct, and units are properly labeled. One small error could throw off your final answer, so take the time to double-check. You’ll be glad you did!
Plug In Your Answer
Pull your answer into the original problem to ensure it works out. For example, if the problem stated, “35 students are going on a field trip. Busses hold 8 students each. How many busses are needed?” and you answered 5 busses, plug that back in: 35 students / 5 busses = 7 students per bus. Perfect, your answer checks out! This strategy works for most multiplication and division word problems.
Estimate First
Before starting the problem, guess what the answer might be. Then, once you’ve worked through all the steps, compare your estimate to your actual answer. If they’re close, that’s a good sign you’re on the right track! Estimating builds number sense and helps detect unreasonable answers.
Keep practicing these useful techniques, stay enthusiastic, and you’ll be a word problem whiz before you know it! Multiplication and division problems won’t stand a chance against your math mastery. You’ve got this! Keep up the good work.
Conclusion: Mastering the art of graphing piecewise functions
You’ve got this! Armed with these three simple strategies, you’ll solve multiplication and division word problems in no time. Practice makes perfect, so keep at it. Before you know it, you’ll be breezing through these problems and impressing everyone with your math skills. Remember, take it step by step, visualize what’s happening, and check your work. With consistency and persistence, you’ll build up your confidence and competence. Soon, you’ll realize you’ve gained a valuable life skill that will serve you well for years. Stay positive, believe in yourself, and keep working at it. You’ve got this! Now get out there and show the world what you can do.
FAQs About Multiplication and Division Word Problems
You’ve got this! Multiplication and division word problems may seem tricky initially, but with some practice, you’ll solve them in no time. Here are some of the most frequently asked questions to help boost your confidence.
The secret is translating the words into an equation. Circle key numbers and determine what operation to use—multiplication or division. Arrange the numbers in the correct order, then solve! The more you practice, the better you’ll learn how to translate word problems into equations.
Don’t panic! Re-read the problem slowly and look for clues. Ask yourself some questions:
- What are the numbers in the problem?
- What is the question asking you to find?
- Do keywords indicate multiplication (times, product) or division (share, split)?
Work through the problem step-by-step. You can do this! Even if you make a mistake, you’ll learn from it and be better equipped for the next problem.
Here are a few tips to keep in mind:
- Pay attention to units like feet, pounds, dollars, etc. They determine what number goes where in the equation.
- If the problem involves groups or sets, think of multiplication. If it involves splitting or sharing, think division.
- Draw a diagram or model to represent the problem. This can help make the relationships between the numbers clearer.
- Check that your answer makes sense in the context of the original problem. Make sure the units match, and the numbers are reasonable.
- Practice regularly! The more word problems you solve, the more natural the process feels.
Believe in yourself and keep at it. You have all the skills to master multiplication and division word problems. Stay positive, translate each problem carefully, and check your work. You’ve got this! Keep practicing, and don’t hesitate to ask a teacher or parent if you have any other questions. Happy problem-solving!