1/3 X (15 + 6) = ??????????????
Mathematics can sometimes seem complex, but many problems boil down to understanding basic operations like addition, multiplication, and fractions. One such problem that often confuses students and learners alike is: 1/3 X (15 + 6) = ??????????????. This question involves both parentheses and fractions, which are fundamental concepts in algebra and arithmetic. To tackle it effectively, we need to explore the order of operations, how to handle fractions, and step-by-step solutions to similar problems. In this article, we will delve into the process of solving this expression, making it easier for you to understand and apply these concepts in your math journey.
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Understanding the Components of the Expression
Before jumping into the solution, it’s important to parse the components of the expression:
1/3 X (15 + 6) = ??????????????
- 1/3: A fraction representing one part of three equal parts.
- (15 + 6): An addition operation enclosed in parentheses.
- X: Multiplication symbol.
- = ??????????????: The unknown we need to find.
This expression combines fractions, parentheses, and multiplication. The key to solving it is understanding how to handle each part properly.
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Order of Operations: PEMDAS/BODMAS
Mathematics follows specific rules for the order in which operations are performed, often summarized as PEMDAS or BODMAS:
- P/B: Parentheses/Brackets
- E/O: Exponents/Orders
- MD: Multiplication and Division (from left to right)
- AS: Addition and Subtraction (from left to right)
Applying these rules ensures consistent and correct results across all math problems.
Applying the Order to Our Expression
In the expression 1/3 X (15 + 6):
- Parentheses (15 + 6) should be evaluated first.
- Then, multiply 1/3 by the result of the parentheses.
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Step-by-Step Solution
Let’s now go through the steps to solve the expression:
- Calculate inside the parentheses:
15 + 6 = 21
- Multiply 1/3 by the result:
1/3 × 21
- Simplify the multiplication:
To multiply a fraction by a whole number, multiply the numerator by the whole number, then divide by the denominator:
(1 × 21) / 3 = 21 / 3
- Simplify the fraction:
21 ÷ 3 = 7
Result:
1/3 × (15 + 6) = 7
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Understanding Fractions in Multiplication
Multiplying fractions by whole numbers is a common task in mathematics. Here’s a quick guide:
How to Multiply a Fraction by a Whole Number
- Method 1: Convert the whole number to a fraction (e.g., 21 becomes 21/1), then multiply numerators and denominators:
(1/3) × (21/1) = (1 × 21) / (3 × 1) = 21/3 = 7
- Method 2: Multiply the whole number by the numerator, then divide by the denominator:
Whole number × numerator / denominator
In our example, 21 × 1 / 3 = 21/3 = 7.
Why is this method effective?
Because it maintains the integrity of the fraction and ensures accurate results when dealing with mixed types of numbers.
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Practical Applications of the Expression
Understanding how to evaluate expressions like 1/3 X (15 + 6) is important in various real-world contexts, such as:
- Budgeting and Finance: Calculating fractions of amounts, like one-third of total expenses.
- Cooking and Recipes: Dividing ingredients into parts, e.g., one-third of a mixture.
- Construction and Engineering: Determining fractional measurements or proportions.
- Education and Learning: Building foundational skills in algebra and arithmetic.
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Common Mistakes to Avoid
When solving expressions like this, learners often make some common errors:
1. Ignoring the Parentheses
Always evaluate parentheses first; skipping this step leads to incorrect answers.2. Misapplying the Order of Operations
Remember that multiplication and division come before addition and subtraction unless parentheses dictate otherwise.3. Forgetting to Simplify Fractions
Always reduce your fraction to its simplest form if possible, to make calculations easier and results clearer.4. Confusing Multiplication with Addition
Ensure that multiplication is performed after parentheses are evaluated, not before.---
Additional Practice Problems
To reinforce your understanding, try solving these similar problems:
- Calculate: 2/5 × (20 - 4)
- Evaluate: 3/4 × (18 + 12)
- Solve: 5/8 × (16 + 8)
- Find the value of: 1/2 × (30 - 10)
- Determine: 4/7 × (14 + 7)
By practicing these types of problems, you'll become more comfortable with fractions, parentheses, and the order of operations.
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Summary
In conclusion, solving the expression 1/3 X (15 + 6) = ?????????????? involves understanding the order of operations, dealing with fractions, and simplifying your calculations step-by-step. The key takeaways are:
- Always evaluate parentheses first.
- Convert and multiply fractions carefully.
- Simplify the result to its lowest terms.
- Practice regularly with similar problems to build confidence.
The final answer to the original problem is:
1/3 × (15 + 6) = 7
Mastering these concepts not only helps with this specific problem but also lays a strong foundation for more advanced mathematical topics. Keep practicing, and soon, solving such expressions will become second nature!
