15 Math Problem Solvers with Steps

This can also make math more rewarding. Instead of relying on calculators, students learn strategies that can improve their concentration and estimation skills while building number sense. And, while there are educators who oppose math “tricks” for valid reasons, proponents point to benefits such as increased confidence to handle difficult problems.

15 Math Problem Solvers with Steps

Here are 15 techniques to solve math problems faster:

Many students struggle to learn the addition of integers of three digits or higher together, but changing the process’s steps can make it easier.

The first step is to add the easy part. The second step is to add the rest.

For example, students must find the sum of 393 and 89. They should quickly see that adding 7 onto 393 will equal 400 — an easier number to work with. To balance the equation, they can then subtract 7 from 89.

The process when broken down appears:

• 393 + 89
• (393 + 7) + (89 – 7)
• 400 + 82
• 482

With this quick technique, big numbers won’t look as scary now.

2. Two-Step Subtraction

There’s a similar method for subtraction.

This method involves removing what’s easy. Then remove what’s left.

For example, suppose students would have to find the difference of 567 and 153. Most will feel that 500 is a simpler number than 567. So, they have to take away 67 from the minuend — 567 — and the subtrahend — 153 — before solving the equation.

Here’s the process:

• 567 – 153
• (567 – 67) – (153 – 67)
• 500 – 86
• 414

Now, instead of two complex numbers, students will only have to solve one.

3. Subtracting from 1,000

Students can gain confidence in handling four-digit integers with this quick technique.

To subtract a number from 1,000, this technique involves subtracting that number’s first two digits from 9. Then, subtract the final digit from 10.

Now, let’s give you an example; let’s say students would have to solve 1,000 – 438. 

Here are the steps:

• 9 – 4 = 5
• 9 – 3 = 6
• 10 – 8 = 2
• 562

This also applies to 10,000, 100,000, and other integers that follow this pattern.

When students have to multiply two integers, they can be quick with the process when one is an even number. All they have to do is just to halve the even number and double the other number.

Students can stop the process when they can no longer halve the even integer, or when the equation becomes manageable.

Let’s use 33 x 48 as an example.

The process follows:

• 66 x 24
• 132 x 12
• 264 x 6
• 528 x 3
• 1,584

The only prerequisite to get it right with this fourth math problem solver with steps is to understand the 2 times table.

5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

It simplifies multiplication if a number in the equation is a power of 2, meaning it works for 2, 4, 8, 16, and so on.

Here’s what to do: For each power of 2 that makes up that number, double the other number.

For example, 9 x 16 is the same thing as 9 x (2 x 2 x 2 x 2) or 9 x 24. Students can therefore double 9 four times to reach the answer:

• 9 x 24
• 18 x 23
• 36 x 22
• 72 x 2
• 144

Unlike doubling and halving, this technique demands an understanding of exponents and a strong command of the 2 times table.

6. Multiplying by 9

For most students, multiplying by 9 — or 99, 999 and any number that follows this pattern — is difficult compared with multiplying by a power of 10.

But there’s an easy tactic to solve this issue, divided into two parts.

Firstly, students round up the 9  to 10. Secondly, after solving the new equation, the students subtract the number they just multiplied by 10 from the answer.

For example, 67 x 9 will lead to the same answer as 67 x 10 – 67. Following the order of operations will give a result of 603. Similarly, 67 x 99 is the same as 67 x 100 – 67.

Despite more steps, altering the equation this way is usually faster as it saves time.

There’s an easier way of multiplying two-digit integers by 11. This way is one of the 15 Math problem solvers with steps.

Let’s go into an example quickly. Let’s say students must find the product of 11 x 34.

The idea is to put a space between the digits, making it 3_4. Then, add the two digits together and put the sum in the space.

The answer is 374.

What happens if the sum is two digits? Students would put the second digit in the space and add 1 to the digit to the left of the space. For example:

• 11 x 77
• 7_(7+7)_7
• 7_(14)_7
• (7+1)_4_7
• 847

It’s multiplication without having to multiply. Hope you understand.

8. Multiplying Even Numbers by 5

Another math problem solver with steps is this technique. It only requires basic division skills.

There are two steps to go about this. We’ll use 5 x 6 as an example. Firstly, divide the number being multiplied by 5 — which is 6 — in half. Second, add 0 to the right of the number.

The result is 30, which is the correct answer.

This is an ideal, easy technique for students mastering the 5 times table.

9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well and is also part of the 15 Math problem solvers with steps. This technique can be taught when the students are learning the 5 times table.

There are 3 steps to solving this problem. We’ll give an example below; 5 x 7

First, you will have to subtract 1 from the number being multiplied by 5, making it an even number. The second step is to cut that number in half — from 6 to 3 in this instance. The third and final step is to add 5 to the right of the number.

The answer is 35.

Who needs a calculator? Absolutely no one.

10. Squaring a Two-Digit Number that Ends with 1

Now, squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

Here are the four steps to this shortcut. Let’s use 812 as an example:

• Subtract 1 from the integer: 81 – 1 = 80
• Next, you square the integer, which is now an easier number: 80 x 80 = 6,400
• Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560
• Add 1: 6,560 + 1 = 6,561

This step eliminates the difficulty surrounding the second digit, allowing students to work with multiples of 10.

11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier when you follow this process that has two parts.

First, students will always make 25 of the product’s last digits.

The next step is to determine the product’s first digits. Students must multiply the number’s first digit, let’s use 9, for example — by the integer that’s one higher — 10, in this case.

So, students would solve 952 by designating 25 as the last two digits. They would then multiply 9 x 10 to receive 90. Putting these numbers together, the result is 9,025.

As you’ve seen, a hard problem becomes an easy multiplication for many students.

12. Calculating Percentages

Cross-multiplication is an important skill to develop, but there’s an easier way to calculate percentages.

For instance, if students want to know what 65% of 175 is, they can multiply the numbers together and move the decimal place two digits to the left.

The result is 113.75, which is indeed the correct answer. You can use your conventional calculator to try this out.

This shortcut is a useful timesaver on tests and quizzes. It is also among the math problem solvers with steps.

13. Balancing Averages

To determine the average among a set of numbers, students can balance them instead of using a complex formula.

Now, suppose a student wants to volunteer for an average of 10 hours a week over four weeks. In the first three weeks, the student worked for 10, 12, and 14 hours.

To determine the number of hours required in the fourth week, the student would have to add how much he or she surpassed or missed the target average in the other weeks:

• 14 hours – 10 hours = 4 hours
• 12 – 10 = 2
• 10 – 10 = 0
• 4 hours + 2 hours + 0 hours = 6 hours

To learn the number of hours for the final week, the student must subtract the sum from the target average:

• 10 hours – 6 hours = 4 hours

When you practice more often, this method may not even require pencil and paper. That’s how easy it is.

14. Identifying Buzzwords

Students who struggle to translate word problems into equations will benefit from learning how to spot buzzwords — phrases that indicate specific actions.

This isn’t a trick. It’s a technique.

The students should learn to look for these buzzwords, and what skill they align with in most contexts:

Be sure to include buzzwords that typically appear in their textbooks (or other classroom math books), as well as ones you use on tests and assignments.

As a result, they should have an easier time processing word problems.

15. Creating Sub-Questions

For complex word problems, the students need to know how to dissect the question by answering three specific sub-questions.

Each student should ask him or herself:

• What am I looking for? — Students should read the question over and over, looking for buzzwords and identifying important details.
• What information do I need? — Students should determine which facts, figures, and variables they need to solve the question. For example, if they determine the question is rooted in subtraction, they need the minuend and subtrahend.
• What information do I have? — Students should be able to create the core equation using the information in the word problem, after determining which details are important.

These sub-questions help students avoid overload.

Instead of writing and analyzing each detail of the question, they’ll be able to identify key information. If you identify students who are struggling with these, you can use peer learning as needed.

For more fresh approaches to teaching math in your classroom, consider treating your students to a range of fun math activities.

Showing these 15 techniques to students can give them the confidence to tackle tough questions.

They’re also mental math exercises, helping them build skills related to focus, logic, and critical thinking.

A rewarding class equals an engaging class. That’s an easy equation to remember.

Frequently Asked Questions on Maths Problem Solvers with Steps

1. Are these steps easy?

Of course, they are. The steps listed above are easy to understand and easy to apply. You just have to take your time and practice more often

2. How does one solve a math problem?

Firstly, you have to understand the question given to you. Understanding the question is the first step in fully solving the math problem. When you are done understanding, apply the steps you’ve learned in class. You need to take your time and be very careful when applying these steps to come to the correct answer.

3. Do the steps listed above always work?

Yes, it does. The steps are verified by professional mathematicians and they have proven there is no failure to any math problem once you follow the steps.

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Conclusion

We believe that you’ve been amazed by the easy steps listed above and how you can solve those maths problems faster once you apply the steps. We wish you good luck in your academic pursuit.