Understanding and Solving the Equation: What to Add to 3 3/8 to Make 5
Understanding equations that involve the addition or subtraction of fractions can be a key skill in many mathematical contexts, whether you're in school, in business, or solving everyday problem-solving challenges. This article will explore the process of finding what must be added to 3 3/8 to obtain 5. We will cover the steps to convert fractions, work with improper fractions, and solve equations using algebra.
Solving the Equation Using Algebra
The given equation is: 3 1/8x 5. This is a linear equation where x represents the value we are trying to find.
Step 1: Express 3 1/8 as an Improper Fraction
First, convert 3 1/8 into an improper fraction. To do this, multiply 3 by the denominator (8) and then add the numerator (1). The result is the new numerator, with the denominator remaining the same.
3 1/8 (3 × 8 1) / 8 25/8
Step 2: Set Up the Equation and Solve for x
The equation now looks like this: (25/8)x 5. To solve for x, divide both sides by 25/8.
Step 3: Divide Both Sides by 25/8
When you divide by a fraction, you multiply by its reciprocal.
(25/8)x ÷ (25/8) 5 ÷ (25/8)
x 5 × (8/25) 40/25
Simplify the fraction:
x 1 15/25 1 6/8 1 3/4
Converting to a decimal, x 1.75 or 1 3/4 as a mixed number.
Alternative Method: Direct Addition
Another way to solve the problem is to directly add to achieve 5. We need to determine how much more is needed to go from 3 3/8 to 5.
Step 1: Convert 5 to a Fraction with the Same Denominator
Convert 5 to a fraction with the same denominator as 3 3/8, which is 8.
5 40/8
Step 2: Subtract 3 3/8 from 40/8
Start with 40/8 and subtract 3 3/8 (which is 27/8).
40/8 - 27/8 13/8
Convert 13/8 to a mixed number, which is 1 5/8.
x 1 5/8 or 1.625 as a decimal.
Summary of Key Points
1. **Convert Mixed Numbers to Improper Fractions:** This step simplifies the equation and makes solving easier. 2. **Use the Reciprocal When Dividing by a Fraction:** This method is a fundamental algebraic technique. 3. **Direct Addition:** An alternative approach involves converting the target number to a common denominator and subtracting the starting number in fraction form.
Understanding these methods can help you solve similar problems involving fractions and improve your overall mathematical skills.
Note: If you are a math teacher and notice any inaccuracies in the formulation or writing, please provide corrections to help improve the clarity and accuracy of the explanations.