Problem 43 - Algebra 1

Question

Write a question that can be used to solve the equation. Then use mental math to solve the equation. \(\frac{y}{15}=8\)

Step-by-Step Solution

Answer

The value of y when \(\frac{y}{15}=8\) is 120.

Step 1: Identify the Question

The question that could be proposed related to the equation could be: 'What is the value of y when \(\frac{y}{15}=8\)?' This question has been generated keeping the equation in mind where the value of y has to be identified when it gets divided by 15 to result in 8.

Step 2: Solve for y

The given equation is \(\frac{y}{15}=8\). To find the value of y, this equation needs to be rearranged by multiplying both sides with 15. That gives us: y = \(8 \times 15\), which requires a simple multiplication.

Step 3: Perform the Calculation

Perform the multiplication of 8 times 15: y = \(8 \times 15 = 120\)

Key Concepts

Understanding Mental Math

Mental math is like giving our brain a workout without using any tools like calculators or paper. Imagine you're at a store and need to quickly figure out if you have enough money. That's where mental math comes in!

When solving equations using mental math, it's all about breaking numbers down into simpler parts. For example, with the equation \(\frac{y}{15} = 8\), we mentally calculate how many 15s make up 8. We can rearrange this equation to \(y = 8 \times 15\) and then think of it as adding 15 to itself 8 times. Mental math helps us keep numbers in our head and reach a solution faster.

So, practicing mental math not only sharpens your math skills but also boosts your quick problem-solving abilities!

Mastering Multiplication

Multiplication is one of the fundamental operations in arithmetic that allows for quick addition of the same number. It's like knowing a shortcut you can take.

In the original problem, we encountered the equation \(\frac{y}{15} = 8\). To find \(y\), we needed to multiply 8 by 15. Here's a neat way to approach multiplication mentally:

• Break it down: 15 is the same as 10 and 5 together. So, you can think of multiplying by 15 as multiplying by these two parts.
• Calculate \(8 \times 10 = 80\)
• Next, calculate \(8 \times 5 = 40\)
• Add the results: \(80 + 40 = 120\)

Breaking the multiplication into smaller steps makes it easier to handle, especially without a calculator.

Multiplication is a powerful tool not only for solving equations but also for dealing with everyday math challenges effortlessly.

Exploring Algebraic Manipulation

Algebraic manipulation is about rearranging equations to make them easier to solve. It's like untangling a knot to see clearly what's underneath.

With the equation \(\frac{y}{15} = 8\), our goal is to solve for \(y\). We accomplish this by performing the opposite operation to what's given. Here, "\(y\) divided by 15" means we need to multiply both sides by 15 to get \(y\) alone:

• Original equation: \(\frac{y}{15} = 8\)
• Multiply both sides by 15: \(y = 8 \times 15\)

This step cancels the division by 15 and isolates \(y\) on one side of the equation.

Rearranging equations through algebraic manipulation is a crucial skill in math. It allows you to transform complex problems into easier-to-solve forms by applying inverse operations. By mastering these techniques, you'll be able to handle algebraic challenges effectively.