Solving Division and Addition with Fractions: A Comprehensive Guide

Introduction

When dealing with mathematical operations, it's important to understand how to handle fractions, especially when performing division and addition. This guide will provide you with a step-by-step approach to solving the problem of dividing 30 by 1/2 and then adding 40. Let's dive into the detailed explanation and calculations involved.

The Problem: 30 Divided by 1/2 and Added to 40

The problem presented is simple but requires a clear understanding of fraction division and addition. The given expression is:

y 30 ÷ 1/2 40

Calculations

Let's break down the problem step by step:

Step 1: Division by a Fraction

When you divide by a fraction, it is equivalent to multiplying by its reciprocal. In this case:

y 30 ÷ 1/2

is the same as:

y 30 × 2/1

which simplifies to:

y 30 × 2

So:

y 60

Step 2: Adding 40

Next, we add 40 to the result of the division:

y 60 40

So:

y 100

Alternative Interpretation

Let's consider the alternative interpretation provided in the problem statement:

If you have 30 whole items (such as pies), and you divide each item into two halves, you will have 60 half items. Adding 40 more whole items to these half items, you get a total of 100 items (or 70 full items if considering each half as 1/2).

Mathematical Explanation

Here is the detailed mathematical explanation:

Dividing by 1/2

Dividing a number by 1/2 is equivalent to multiplying by 2, as dividing by a fraction is the same as multiplying by its reciprocal (1/2 × 2 1).

Adding Numbers

After performing the division, you simply add the result to the additional number (40 in this case).

Conclusion

Understanding how to handle division by fractions and addition in such problems is crucial for solving more complex mathematical equations. By following these steps, you can easily solve similar problems and understand the underlying concepts better.

To summarize: 30 divided by 1/2 equals 60, and adding 40 to that result gives:

y 100