Word Problem in Maths.

HLTutors
12 Mar 202410:19
EducationalLearning
32 Likes 10 Comments

TLDRIn this educational video, the presenter guides viewers through solving a word problem using algebra. The problem involves Billy, who performs a series of operations on a number: he multiplies it by 8, adds 6, divides by 2, and ends up with 131. The video emphasizes the importance of reading and analyzing word problems step by step. The presenter uses algebra to set up an equation based on the operations described and solves for the original number 'a'. Through a clear explanation of algebraic principles, including combining like terms and cross-multiplication, the presenter arrives at the solution that the number Billy started with was 32. The video encourages viewers to practice solving similar problems and to follow the channel for more educational content.

Takeaways
  • 📚 The video is focused on solving word problems using algebra.
  • 🔍 The presenter emphasizes the importance of reading and analyzing word problems sentence by sentence.
  • 📝 The problem presented involves Billy who performs a series of operations on a number to arrive at 131.
  • 🔢 The operations include multiplying by 8, adding 6, and dividing by 2.
  • 🍎 The presenter uses the variable 'a' to represent the unknown number Billy is thinking of.
  • 📈 The process involves translating the word problem into an algebraic equation: 8a + 6.
  • ⚖️ The equation is balanced by setting 8a + 6 equal to 131 * 2 after cross-multiplication.
  • 🧩 The next step is to isolate the variable 'a' by moving the constant term to the other side of the equation.
  • ➗ To solve for 'a', the presenter divides both sides of the equation by the coefficient of 'a', which is 8.
  • 🎯 The final answer is found to be 32, which is the original number Billy thought of before the operations.
  • 📺 The video encourages viewers to watch more algebra videos for better understanding and to follow the channel for similar content.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is solving word problems using algebra.

  • What is the process Billy goes through with the number he thought of?

    -Billy multiplies the number by 8, adds 6, and then divides by 2 to end up with 131.

  • What is the first step in solving word problems according to the video?

    -The first step is to read the problem carefully, not just once, but multiple times to understand and analyze it sentence by sentence.

  • What does the video suggest to call the number Billy thought of?

    -The video suggests to call the number Billy thought of 'a'.

  • Why is it important to watch algebra videos before solving word problems like this?

    -It's important because understanding algebraic principles, such as how to handle equations and combine like terms, is essential for solving these problems correctly.

  • What mathematical operation is represented by '8a + 6' in the script?

    -'8a + 6' represents multiplying the number 'a' by 8 and then adding 6 to the result.

  • What does the video mean by 'cross multiplication'?

    -Cross multiplication is a method used to solve equations involving fractions, where you multiply each term of the equation by the denominators of the fractions to eliminate them.

  • What is the equation formed after cross multiplying in the script?

    -The equation formed after cross multiplying is '(8a + 6) * 1 = 131 * 2'.

  • What is the next step after cross multiplying in the script?

    -The next step is to simplify the equation by performing the multiplication on both sides and then isolating the variable 'a'.

  • What is the final answer to the word problem in the script?

    -The final answer to the word problem is that the number Billy thought of was 32.

  • What does the video suggest doing if you want more of this kind of word problems?

    -The video suggests following, sharing, liking, and subscribing to their channel for more word problems and related content.

Outlines
00:00
🔍 Solving Algebraic Word Problems

The video introduces a word problem involving algebra where Billy thinks of a number, performs a series of operations (multiplies by 8, adds 6, and divides by 2), and ends up with 131. The challenge is to find the original number Billy thought of. The presenter emphasizes the importance of reading and analyzing word problems methodically. The problem is translated into an algebraic equation: (8a + 6) / 2 = 131, where 'a' represents the unknown number. The process involves forming an equation, isolating the variable 'a', and solving for it.

05:02
📚 Step-by-Step Algebraic Solution

This paragraph walks through the algebraic process of solving for 'a'. The equation 8a + 6 = 131 * 2 is set up by cross-multiplying to eliminate the fraction. The result is 8a + 6 = 262. The next step is to isolate 'a' by moving the constant term to the other side of the equation, resulting in 8a = 256. Finally, by dividing both sides by the coefficient of 'a' (which is 8), the solution a = 32 is found. This means Billy originally thought of the number 32 before performing the series of mathematical operations.

10:02
📢 Engaging with More Word Problems

The final paragraph serves as a call to action for viewers interested in solving more word problems. It encourages them to follow the channel, share the content, like it, and subscribe to stay updated on new video releases. The presenter signs off with a friendly 'see you next time, bye', indicating the end of the video and inviting viewers to engage with future educational content.

Mindmap
Keywords
💡Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. It is used to solve a wide range of problems, including word problems. In the context of this video, algebra is the primary tool used to determine the number Billy thought of before performing a series of mathematical operations. The script uses algebraic expressions to represent the operations Billy performs on the unknown number.
💡Word Problems
Word problems are mathematical problems that are presented in a narrative or story format, often requiring the solver to translate the narrative into a mathematical equation or set of equations. The video's theme revolves around solving word problems using algebra. The script provides a step-by-step guide on how to approach and solve a specific word problem involving a series of arithmetic operations.
💡Variable
In algebra, a variable is a symbol, usually a letter, that stands for an unknown number or value. In the script, the variable 'a' is introduced to represent the number Billy thought of. The entire process of solving the word problem involves manipulating algebraic expressions that include this variable to find its value.
💡Multiplication
Multiplication is one of the four basic arithmetic operations, where two numbers are combined to give a product. In the video script, Billy multiplies the number he thought of by 8, which is represented algebraically as '8 * a'. This operation is a key step in the process of solving the word problem.
💡Addition
Addition is the process of combining two or more numbers to get a sum. In the context of the video, after multiplying the number by 8, Billy adds 6 to the result, which is algebraically expressed as '8a + 6'. This step is part of the sequence of operations that lead to the final answer.
💡Division
Division is the arithmetic operation of dividing a number by another number. In the video's word problem, Billy divides the result of his multiplication and addition by 2, which is represented as '(8a + 6) / 2'. This division is the final operation before arriving at the number 131.
💡Equation
An equation is a mathematical statement that asserts the equality of two expressions. In the script, the equation '8a + 6 = 131' is formed after setting up the problem with the given operations. Solving this equation is essential to finding the value of 'a', which is the original number Billy thought of.
💡Coefficient
A coefficient is a numerical factor that multiplies a variable in an algebraic term. In the video, the coefficient of 'a' is 8, as seen in the term '8a'. The script explains that to isolate the variable 'a', the equation must be divided by its coefficient, which in this case is 8.
💡Cross Multiplication
Cross multiplication is a technique used to solve equations involving fractions. In the script, when setting up the equation '8a + 6 = 131', the script suggests writing 131 as '131/1' to facilitate cross multiplication, which helps in eliminating the fraction and simplifying the equation.
💡Solving for a Variable
Solving for a variable involves manipulating an equation to isolate the variable and determine its value. The video script demonstrates this process by showing how to isolate 'a' in the equation '8a + 6 = 131'. The steps include subtracting 6 from both sides and then dividing by the coefficient of 'a' (which is 8) to find that 'a' equals 32.
Highlights

Introduction to solving word problems using algebra.

Billy thinks of a number and performs a series of operations to reach 131.

The importance of reading and analyzing word problems sentence by sentence.

Assigning a variable 'a' to represent the unknown number Billy thought of.

Multiplication of the number by 8 and addition of 6 as the first operation.

Division of the result by 2 as the final operation leading to 131.

Setting up an equation to solve for the variable 'a'.

Explanation of not combining like terms with different variables.

Forming a fraction on both sides of the equation to solve for 'a'.

Cross-multiplication technique to simplify the equation.

Isolating the variable 'a' by moving the constant term to the other side of the equation.

Changing the sign of the term when moving it across the equation.

Solving for 'a' by dividing both sides of the equation by the coefficient of 'a'.

Final answer reveals that the number Billy thought of was 32.

Encouragement to practice similar word problems for better understanding.

Invitation to follow, share, like, and subscribe for more educational content.

Transcripts

Browse More Related Video

A pump can fill a pool in 10hrs. Another pump can fill it in 15hrs. Both pumps together will take?

Radical equation | Radical simplification | math tricks |Math Olympiad | unique math tricks

How To Solve Word Problems of Any Kind . Nutshell maths-2

Sets, Indices, and Algebra Test 1 - JS Learning Academy

3 turns of a screw driver moves a 2” screw down 1/8“. How many turns to lower the screw 100%?

Algebra SYSTEM WORD PROBLEM – Let’s solve it step-by-step...

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Algebra SolvingWord ProblemsEducational ContentMath PuzzleBilly's NumberMultiplicationDivisionAdditionProblem SolvingMath Tutorial