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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

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Linear Algebra Solutions

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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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What are 'multiplication facts'? Why are they essential to your child's success in math?

by Bronwyn Reid O'Connor and Benjamin Zunica, The Conversation

multiplication

One of the essential skills students need to master in primary school mathematics are "multiplication facts."

What are they? What are they so important? And how can you help your child master them?

What are multiplication facts?

Multiplication facts typically describe the answers to multiplication sums up to 10x10. Sums up to 10x10 are called "facts" as it is expected they can be easily and quickly recalled. You may recall learning multiplication facts in school from a list of times tables.

The shift from "times tables" to "multiplication facts" is not just about language. It stems from teachers wanting children to see how multiplication facts can be used to solve a variety of problems beyond the finite times table format.

For example, if you learned your times tables in school (which typically went up to 12x12 and no further), you might be stumped by being asked to solve 15x8 off the top of your head. In contrast, we hope today's students can use their multiplication facts knowledge to quickly see how 15x8 is equivalent to 10x8 plus 5x8.

The shift in terminology also means we are encouraging students to think about the connections between facts. For example, when presented only in separate tables, it is tricky to see how 4x3 and 3x4 are directly connected.

Math education has changed

In a previous piece, we talked about how mathematics education has changed over the past 30 years.

In today's mathematics classrooms, teachers still focus on developing students' mathematical accuracy and fast recall of essential facts, including multiplication facts.

But we also focus on developing essential problem-solving skills. This helps students form connections between concepts, and learn how to reason through a variety of real-world mathematical tasks.

Why are multiplication facts so important?

By the end of primary school, it is expected students will know multiplication facts up to 10x10 and can recall the related division fact (for example, 10x9=90, therefore 90÷10=9).

Learning multiplication facts is also essential for developing "multiplicative thinking." This is an understanding of the relationships between quantities, and is something we need to know how to do on a daily basis.

When we are deciding whether it is better to purchase a 100g product for $3 or a 200g product for $4.50, we use multiplicative thinking to consider that 100g for $3 is equivalent to 200g for $6—not the best deal!

Multiplicative thinking is needed in nearly all math topics in high school and beyond. It is used in many topics across algebra, geometry, statistics and probability.

This kind of thinking is profoundly important. Research shows students who are more proficient in multiplicative thinking perform significantly better in mathematics overall.

In 2001, an extensive RMIT study found there can be as much as a seven-year difference in student ability within one mathematics class due to differences in students' ability to access multiplicative thinking.

These findings have been confirmed in more recent studies, including a 2021 paper .

So, supporting your child to develop their confidence and proficiency with multiplication is key to their success in high school mathematics. How can you help?

Below are three research-based tips to help support children from Year 2 and beyond to learn their multiplication facts.

1. Discuss strategies

One way to help your child's confidence is to discuss strategies for when they encounter new multiplication facts.

Prompt them to think of facts they already and how they can be used for the new fact.

For example, once your child has mastered the x2 multiplication facts, you can discuss how 3x6 (3 sixes) can be calculated by doubling 6 (2x6) and adding one more 6. We've now realized that x3 facts are just x2 facts "and one more"!

What are 'multiplication facts'? Why are they essential to your child's success in maths?

Strategies can be individual: students should be using the strategy that makes the most sense to them. So you could ask a questions such as "if you've forgotten 6x7, how could you work it out?" (we might personally think of 6x6=36 and add one more 6, but your child might do something different and equally valid).

This is a great activity for any quiet car trip. It can also be a great drawing activity where you both have a go at drawing your strategy and then compare. Identifying multiple strategies develops flexible thinking.

2. Help them practice

Practicing recalling facts under a friendly time crunch can be helpful in achieving what teachers call "fluency" (that is, answering quickly and easily).

A great game you could play with your children is " multiplication heads up " . Using a deck of cards, your child places a card to their forehead where you can see but they cannot. You then flip over the top card on the deck and reveal it to your child. Using the revealed card and the card on your child's head you tell them the result of the multiplication (for example, if you flip a 2 and they have a 3 card, then you tell them "6!").

Based on knowing the result, your child then guesses what their card was.

If it is challenging to organize time to pull out cards, you can make an easier game by simply quizzing your child. Try to mix it up and ask questions that include a range of things they know well with and ones they are learning.

Repetition and rehearsal will mean things become stored in long-term memory.

3. Find patterns

Another great activity to do at home is print some multiplication grids and explore patterns with your child.

What are 'multiplication facts'? Why are they essential to your child's success in maths?

A first start might be to give your child a blank or partially blank multiplication grid which they can practice completing.

Then, using colored pencils, they can color in patterns they notice. For example, the x6 column is always double the answer in the x3 column. Another pattern they might see is all the even answers are products of 2, 4, 6, 8, 10. They can also notice half of the grid is repeated along the diagonal.

This also helps your child become a mathematical thinker, not just a calculator.

The importance of multiplication for developing your child's success and confidence in mathematics cannot be understated. We believe these ideas will give you the tools you need to help your child develop these essential skills.

Provided by The Conversation

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11 Helpful Math Tricks You Need to Know

I magine being able to slowly rewire your brain to become more logical and more efficient at solving problems. Many people are surprised to learn this occurs when they study mathematics. Math tends to be one of those subjects that people either love or hate.

Regardless of your level of enthusiasm, there are key math tips that can help you navigate difficult problems more fluidly. Let’s explore some of the most notable math tricks to keep in mind.

1. Multiplying by 6

This is one of the best ways to improve your fast math skills. When you multiply six by an even number, the answer you get will always end in the same digit as the number you multiply it by. For instance, imagine you multiply six by four. The answer is 24.

Multiplying six by two, four, six, and eight produces similar results. Keep this tip in mind so you can streamline your workflow. The less often you have to use a calculator, the better.

2. Multiplying 5 Times Any Number

If you’re multiplying five by an even number, take the number you’re multiplying five by and halve it. If you’re multiplying five by four, you’d reduce four to two. You then add zero to that number.

In the above example, you’d get 20. If you’re multiplying five by an odd number, you subtract one from that number. Multiplying five by five would require you to briefly multiply five by four.

You then halve this number and add five as the last digit. You’d get 25 by using this method for the aforementioned problem.

3. Squaring Numbers Ending in Five

This one’s a bit more specific than the others on this list, but it’s still fairly useful. Let’s consider 35 in this example. First, multiply the first digit by itself.

You then add one to this number. Afterwards, put 25 at the end. This would give you 12 and 25. Combine these two numbers to get 1,225.

In the situations where this tip is applicable, you’ll find it saves you a substantial amount of time. Numbers that end in five are some of the most common you’ll encounter.

4. Subtracting from 1,000

Dealing with the number 1,000 is something most people do daily. This is true when calculating expenses, paying bills, etc. When subtracting a number from 1,000, subtract each number from nine except for the last digit. Instead, subtract the last number from 10.

For example, assume you subtract 365 from 1,000. You would subtract three from nine, subtract six from nine, and then subtract five from 10. The answer would be 635. Try it out with different numbers to see for yourself!

5. Multiplying by 9

Need to quickly multiply a number by nine? Let’s assume you’re multiplying nine by three. Subtract one from the number you’re multiplying by nine. For context, you’d subtract one from three to get two.

Then, subtract that number from nine. In this case, subtracting two from nine will yield seven. Combine these two numbers to get the result.

To clarify, multiplying nine by three would get you 27.

6. Multiplying Numbers Ending in Zero

This is a great way to make large numbers seem much more manageable. It simply involves multiplying the other digits of the number and adding extra zeros at the end. Let’s consider 200 multiplied by 400.

You’d multiply two by four and then add the total number of zeros in the original problem at the end. When working with 200 x 400, there are four zeros total. If you follow these instructions correctly in this problem, you’d get 80,000.

7. Division Tips

You can make division much easier for yourself when you quickly understand when a number can be evenly divided by certain other numbers. If a number ends in zero, you can divide it by 10. When dividing large numbers, add up the digits together.

If they’re evenly divisible by nine, then so is the original number. If the last three digits of a number are evenly divisible by eight, you can divide the original number by eight.

The same is true if the number ends with three zeros. Add up the digits of an even number you’re working with. If this result is divisible by three, then you can divide the original by three evenly.

To check if a number is divisible by five, it simply needs to end in a zero or a five. Numbers that end in two zeros or two digits that are divisible by four are also divisible by four.

You can assess if a number is divisible by three if you add up the number’s digits and they’re also divisible by three. Numbers that end in zero, two, four, six, or eight are divisible by two.

9. Finding Percentages

Many people hate working with percentages, but there are ways to streamline this process. Imagine you need to find 5% of 235.

Move the decimal one place to the left, which would give us 23.5 in this case. You can then divide this number by two to get the answer to the original problem.

10. Complex Multiplication

You can quickly multiply large numbers by using this technique. However, it only works if one of the numbers is even. Halve the even number and double the other number. When multiplying 20 x 135, this would briefly create 10 x 270, which in turn yields 2,700.

11. Finding Least Common Multiples

Using the least common multiple solving techniques is essential for keeping your workflow quick and free of interruptions. First, find the greatest common factor (GCF). This is the largest factor that all numbers share.

So, the GCF of 18 and 30 is six. Divide either number by the GCF. Multiply the answer by the remaining number. For instance, you could use 18 divided by six.

This will yield three, which you would multiply by 30 to get 90.

Keep These Math Tricks in Mind

The math tricks in this guide will ensure you overcome issues you would’ve otherwise struggled with. Whether you learn math as part of your job or curriculum, you can take your performance to the next level.

Looking for other useful lifestyle information that can help you out in the future? Our blog has plenty of articles like this one. Be sure to check them out today!

This article is published by NYTech in collaboration with Syndication Cloud.

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