Problem 304 - Prealgebra

Question

In the following exercises, simplify. $$(77)(801)$$

Step-by-Step Solution

Answer

61677

Step 1: Understand the Problem

The goal is to multiply the numbers 77 and 801 and simplify the result.

Step 2: Multiply the Numbers

Calculate the product of the two numbers: \( 77 \times 801 \)

Step 3: Perform the Multiplication

Multiply 77 by 801: \(77 \times 801 = (77 \times 800) + (77 \times 1) \)Breaking it down: \(77 \times 800 = 61600\)\(77 \times 1 = 77\)Add the two results together: \(61600 + 77 = 61677\)

Step 4: Simplify the Answer

After performing the multiplication, the simplified result is:\( 77 \times 801 = 61677 \)

Key Concepts

Simplification

Simplification, in math, means making an expression or a problem as simple as possible so that it is easy to work with or understand. When we simplify arithmetic operations like multiplication, it often involves breaking the problem down into smaller parts.
For example, to simplify the multiplication of 77 and 801, we can break down 801 as 800 + 1. This allows us to handle the multiplication in two simpler steps.

• First, multiply 77 by 800
• Then, multiply 77 by 1

Finally, by adding these two results together, we get the simplified and final answer. Simplification helps make calculations easier and reduces the possibility of errors.

Multiplication Steps

Understanding the steps involved in multiplication can make solving problems much simpler. Here’s how to tackle the multiplication of 77 and 801 step-by-step:

• Step 1: Understand the Problem - The main goal is to find out what 77 times 801 equals.
• Step 2: Break Down the Problem - Notice that 801 can be expressed as 800 + 1.
• Step 3: Multiply Separately - Instead of multiplying directly, multiply 77 by each part of the breakdown:
• 77 × 800
• 77 × 1
• Step 4: Combine the Results - Add the results from the separate multiplications

Using this breakdown:
$$77 \times 801 = (77 \times 800) + (77 \times 1)$$
Calculating each part:

• $$77 \times 800 = 61600$$
• $$77 \times 1 = 77$$
• Add them together -> $$61600 + 77 = 61677$$

Arithmetic Operations

Arithmetic operations include basic math operations like addition, subtraction, multiplication, and division. Multiplication is one of these core operations and is essentially repeated addition. For example, multiplying 77 by 801 means you add 77 to itself 801 times.
Breaking down more complex multiplications, like in our example, can simplify the process:

• First understand the numbers involved (77 and 801).
• Look for ways to break them down into simpler components (e.g., 801 = 800 + 1).
• Use properties of arithmetic operations to handle the smaller pieces.

This way, we can solve seemingly tough math problems through simple, manageable steps.
Knowing how to use these operations efficiently is fundamental in solving all kinds of math problems, from basic arithmetic to complex algebra.