$\begin{array}{l}\frac{1 \cdot 3}{4 \cdot 3}+\frac{1 \cdot 2}{6 \cdot 2}= \\ \frac{3}{12}+\frac{2}{12}=\frac{5}{12}\end{array}$

Question

littleguyteam littleguyteam

01-11-2026
Mathematics

Answered

$\begin{array}{l}\frac{1 \cdot 3}{4 \cdot 3}+\frac{1 \cdot 2}{6 \cdot 2}= \\ \frac{3}{12}+\frac{2}{12}=\frac{5}{12}\end{array}$

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T10:41:23-05:00

Verify the first fraction conversion: $\frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}$.
Verify the second fraction conversion: $\frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}$.
Combine the fractions using the common denominator: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.
The full equation $\frac{1 \cdot 3}{4 \cdot 3} + \frac{1 \cdot 2}{6 \cdot 2} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$ is correct, resulting in $\boxed{\frac{5}{12}}$.

Explanation

Analysis of the Expression

We are asked to verify the equality of the mathematical expression:
\[\frac{1 \cdot 3}{4 \cdot 3} + \frac{1 \cdot 2}{6 \cdot 2} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}.\]
This expression involves adding two fractions by first converting them to a common denominator of 12. We will analyze each part of this equality chain to confirm its accuracy.

Evaluating the First Fraction

First, we evaluate the first term: $\frac{1 \cdot 3}{4 \cdot 3}$.
Multiplying the numerator and the denominator, we get:
\[\frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}.\]
This simplifies to $\frac{1}{4}$ because both the numerator and denominator are divisible by 3. Thus, the first part of the equality $\frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}$ is correct.

Evaluating the Second Fraction

Next, we evaluate the second term: $\frac{1 \cdot 2}{6 \cdot 2}$.
Multiplying the numerator and the denominator, we get:
\[\frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}.\]
This simplifies to $\frac{1}{6}$ because both the numerator and denominator are divisible by 2. Thus, the second part of the equality $\frac{1 \cdot 2}{6 \cdot 2} = \frac{2}{12}$ is correct.

Concluding the Summation

Now, we compute the sum of these fractions using the common denominator of 12:
\[\frac{3}{12} + \frac{2}{12} = \frac{3+2}{12} = \frac{5}{12}.\]
Since both components of the sum are correct, the entire expression $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$ is correct. Therefore, the original equality holds true.

Examples

Adding fractions is essential in daily life, such as in cooking where you might need to combine different measurements. For instance, if a recipe calls for $\frac{1}{4}$ cup of flour and $\frac{1}{6}$ cup of sugar, and you want to know the total volume of these dry ingredients, you would perform exactly this type of calculation: $\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$ of a cup. This simple arithmetic helps ensure your measurements are precise and your culinary results turn out perfectly every time.