Problem 63 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a fraction or as a mixed number in simplest form. $$ 4 \frac{7}{8}+9 \frac{1}{8} $$

Step-by-Step Solution

Answer

The answer is 14.

Step 1: Identify the Whole and Fractional Parts

In the mixed numbers \(4 \frac{7}{8}\) and \(9 \frac{1}{8}\), identify the whole number part and the fractional part. Here, the whole numbers are 4 and 9, and the fractions are \(\frac{7}{8}\) and \(\frac{1}{8}\).

Step 2: Add Fractional Parts

Add the fractional parts from each mixed number. In this case \(\frac{7}{8} + \frac{1}{8} = \frac{8}{8}\). This simplifies to 1.

Step 3: Add Whole Numbers

Add the whole numbers we identified in Step 1: \(4+9=13\).

Step 4: Combine the Results

Add the results found in Step 2 and Step 3. Here, \(13 + 1 = 14\)

Key Concepts

Simplifying Fractions

When we come across a fraction, it's important to know if it can be simplified. Simplifying fractions makes them easier to understand and work with. Consider a fraction where the numerator (top number) and the denominator (bottom number) can both be divided by the same number. For example, \( \frac{6}{8} \) can be simplified because both numbers are divisible by 2. So, we divide the numerator and the denominator by 2 to get \( \frac{3}{4} \), which is the simplified form.

In our exercise, when adding the fractional parts together, \( \frac{7}{8} + \frac{1}{8} = \frac{8}{8} \), you might notice that \( \frac{8}{8} \) is actually equal to 1. When the numerator and denominator are the same, it means we have 1 whole. Therefore, anytime you see a fraction like this, you can simplify it by recognizing it as a whole number instead of a fraction.

Mixed Number Addition

Adding mixed numbers involves combining both the whole and fractional parts of the numbers carefully. A mixed number is simply a whole number combined with a fraction. For instance, \(5 \frac{3}{4}\) means 5 plus \( \frac{3}{4} \) of another whole.

When adding mixed numbers, you add the whole numbers and the fractions separately. If the fractions add up to a whole number, like in our exercise, you also add this to the sum of the whole numbers. In case the fraction sum exceeds a whole number, you would convert it into a mixed number of its own by dividing the numerator by the denominator, and then add any whole number resulting from that division to the sum of the whole numbers.

Fractional Parts

Understanding Fractional Parts

You must understand what the fractional part of a mixed number represents. It shows how much of a whole is added to the whole number part. The fraction \( \frac{7}{8} \) in the mixed number \(4 \frac{7}{8}\) tells us that we have 7 parts out of a total of 8 parts needed to make another whole.

The exercise demonstrates a simple scenario where the two fractional parts result in a complete whole. Remember, just like whole numbers, fractions represent parts of a sum and can themselves be added together. And if the fractional parts add up to a number with the same numerator and denominator, like \( \frac{8}{8} \), it means you've added up to one whole unit.

Whole Numbers Addition

Adding whole numbers is a foundational skill in mathematics. It involves combining two or more numbers to find their sum. In our mixed number addition exercise, the whole numbers 4 and 9 are added to get 13. This is the whole number part of our final answer.

Whole numbers are easier to work with because they don't include fractions or decimals. Always add the whole numbers first when working with mixed numbers, then add the fractional parts. If the fractional parts make another whole number, don't forget to include that in your final sum!