How to Solve Math Problems Involving Fractions Step by Step

Fractions can be a challenge, especially when you're trying to solve complex problems involving multiple operations. In this guide, we will walk through solving the following math problem:

Problem: Solve 1/16 9/10 1 2/6 5/7

In this guide, we will explore two methods to solve this problem: the multiply the numerators and denominators by the opposing denominators method and following the BODMAS rule. Let's dive in!

Method 1: Multiply the Numerators and Denominators by the Opposing Denominators

This method involves converting each fraction to have a common denominator before adding them all together.

Step 1: Convert 1/16 to a fraction with a common denominator of 160

To convert 1/16 to a fraction with a common denominator of 160, we multiply the numerator and denominator by 10:

1/16 * 10/10  10/160

Step 2: Convert 9/10 to a fraction with a common denominator of 160

To convert 9/10 to a fraction with a common denominator of 160, we multiply the numerator and denominator by 16:

9/10 * 16/16  144/160

Step 3: Add the fractions together

Now that both fractions have the same denominator, we can add them together:

10/160   144/160  154/160

Step 4: Simplify the fraction

To simplify 154/160, we divide both the numerator and the denominator by their greatest common divisor, which is 2:

154/160 / 2/2  77/80

The final answer is 77/80, which can also be written as a decimal: 0.9625.

Method 2: Follow the BODMAS Rule

The BODMAS rule (Brackets, Orders, Division and Multiplication, Addition, Subtraction) helps us solve the problem in the correct order. Let's follow it step by step:

Step 1: Convert all mixed numbers to improper fractions

First, convert 1 2/6 to an improper fraction:

1   2/6  6/6   2/6  8/6

Step 2: Simplify fractions

The fraction 8/6 can be simplified to 4/3:

8/6  4/3

Step 3: Apply BODMAS rule

Now, follow the BODMAS rule to solve the expression:

1/16   9/10   4/3   5/7

This involves adding the fractions step by step. To do this, find a common denominator for all the fractions, which is the least common multiple (LCM) of 16, 10, 3, and 7. The LCM of these numbers is 1680.

The detailed steps are as follows:

Convert 1/16 to a fraction with a denominator of 1680:

1/16 * 105/105  105/1680

Convert 9/10 to a fraction with a denominator of 1680:

9/10 * 168/168  1512/1680

Convert 4/3 to a fraction with a denominator of 1680:

4/3 * 560/560  2240/1680

Convert 5/7 to a fraction with a denominator of 1680:

5/7 * 240/240  1200/1680

Now, add these fractions together:

105/1680   1512/1680   2240/1680   1200/1680  5057/1680

Finally, simplify 5057/1680, which is approximately 2.9935.

Conclusion

Both methods yield different results due to the differences in the approach. The first method gives a fraction 77/80, while the second method gives a numerical result approximately equal to 2.9935. Understanding these methods helps in solving complex fraction problems efficiently.

Key Takeaways

Understand the difference between converting to a common denominator and simplifying fractions. Know how to apply the BODMAS rule to solve problems involving multiple operations. Practice using both methods to solve similar problems for better understanding and accuracy.

Related Keywords

Fractions - A mathematical concept representing a part of a whole. Step-by-step solution - A methodical approach to solving problems in a sequential manner. BODMAS rule - An acronym used to determine the order of operations in mathematical expressions.