y = 2\left(\frac23\right) + 3 = \frac43 + 3 = \frac43 + \frac93 = \frac133

Understanding the Equation: y = 2×(2/3) + 3 Simplified to 13/3

In algebra, simplifying expressions is a fundamental skill that helps students and math enthusiasts alike grasp equations more clearly. One useful example is the equation y = 2×(2/3) + 3, which demonstrates basic multiplication and addition—but the real value lies in arriving at the simplified fraction y = 13/3. In this SEO-optimized article, we’ll break down the steps to solve this equation, explore how to convert mixed numbers to improper fractions, and explain why mastering such calculations matters for math proficiency.

Understanding the Context

Breaking Down the Equation: y = 2×(2/3) + 3

At first glance, the equation appears simple, but careful attention reveals key algebraic and fraction-handling principles.

Start with:
y = 2 × (2/3) + 3

Step 1: Multiply 2 by 2/3
When multiplying, multiply the numerator:
2 × (2/3) = (2 × 2)/3 = 4/3

$y = 2\left(\frac{2}{3}\right) + 3 = \frac{4}{3} + 3 = \frac{4}{3} + \frac{9}{3} = \frac{13}{3}$

Key Insights

Step 2: Rewrite the equation
Now substitute back:
y = 4/3 + 3

Step 3: Express 3 as a fraction with denominator 3
To add, convert 3 into a fraction:
3 = 3/1 = 9/3 (since 3 × 3 = 9)

So now:
y = 4/3 + 9/3

Step 4: Add the fractions
Both terms now share the same denominator:
(4 + 9)/3 = 13/3

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Final Thoughts

Final Result

y = 13/3
This improper fraction equals approximately 4.33 when converted to a decimal.

Why Fraction Conversion Matters in Math

Understanding how to work with fractions—whether converting them to decimals, simplifying expressions, or finding common denominators—is essential across mathematics education. Equations like y = 2×(2/3) + 3 form the building blocks for more complex topics such as algebra, calculus, and real-world problem solving.

Displaying answers as fractions or improper forms like 13/3 preserves precision and supports deeper understanding. Additionally, mastering these calculations improves numerical literacy, which is critical for standardized tests, engineering, science, and everyday decision-making involving ratios and proportions.

Summary

Multiply 2 by 2/3 to get 4/3
Convert 3 to 9/3 to create a common denominator
Add 4/3 + 9/3 = 13/3
Final simplified form: y = 13/3

By learning these step-by-step techniques and embracing fraction operations, learners enhance their analytical skills and gain confidence in handling algebraic expressions.