How to Find Half of 1 3/4 and Other Fractions

Understanding how to find half of a fraction, such as 1 3/4, is a fundamental skill in mathematics. This guide will explore a step-by-step process using both methods and explain the reasoning behind each step.

Step-by-Step Guide

Let's begin by breaking down the problem and demonstrating the process in detail.

Method 1: Converting Mixed Numbers to Improper Fractions

First, we convert the mixed number 1 3/4 to an improper fraction.

Convert the mixed number to a fraction: Take the whole part (1) and multiply it by the denominator of the fractional part (4). Add the numerator of the fractional part (3) to the result from step 1.

1 * 4 3 7. This gives us the improper fraction 7/4.

Now, divide the fraction by 2: Multiply 7/4 by the reciprocal of 2, which is 1/2: 7/4 * 1/2 7/8.

Hence, half of 1 3/4 is 7/8.

Method 2: Direct Division

Alternatively, you can handle the mixed fraction directly and then divide by 2.

First, convert 1 3/4 to an improper fraction: 1 3/4 4/4 3/4 7/4. Now, divide 7/4 by 2: 7/4 / 2 7/4 * 1/2 7/8.

Again, we find that half of 1 3/4 is 7/8.

General Rule for Finding Half of a Fraction

To find half of any fraction, you multiply the numerator by half (or divide the numerator by 2) while keeping the denominator constant.

Example: Half of 1/3

Half of 1/3 is simply 1 divided by 2, keeping the denominator the same.

Divide the numerator by 2: 1 ÷ 2 / 3 1/6.

Therefore, half of 1/3 is 1/6.

Understanding the Concept

The phrase "of" in mathematics typically means multiplication. To divide a fraction by a whole number, you can multiply the fraction by the reciprocal of the whole number.

Dividing a Fraction by 2

For a fraction like 1 3/4, converting it to an improper fraction and then dividing by 2 is one approach. But generally, half of a fraction is simply the numerator divided by 2.

The Result

Half of 1 3/4 (or 7/4) is 7/8. This can also be expressed as a decimal (0.875) or as a fraction (7/8).

Conclusion

In summary, whether you convert the mixed number to an improper fraction or directly manipulate the values, the result remains the same: half of 1 3/4 is 7/8.

Understanding these methods will help you tackle similar problems and enhance your overall mathematical skills.