Problem 50 - Fundamentals of Mathematics

Question

For the following 15 problems, convert each of the mixed numbers to its corresponding improper fraction. $$17 \frac{9}{10}$$

Step-by-Step Solution

Answer

The improper fraction is \( \frac{179}{10} \).

Step 1: Understand the Mixed Number

A mixed number consists of a whole number and a fraction. In this case, we have 17 as the whole number and \( \frac{9}{10} \) as the fraction.

Step 2: Multiply the Whole Number by the Denominator

To convert the mixed number to an improper fraction, multiply the whole number (17) by the denominator of the fraction (10). This gives us \( 17 \times 10 = 170 \).

Step 3: Add the Numerator to the Product

Now, take the result from Step 2, which is 170, and add the numerator of the fraction (9) to it. Thus, \( 170 + 9 = 179 \).

Step 4: Write the Improper Fraction

The improper fraction is composed of the sum from Step 3 as the numerator and the original denominator (10) as the denominator. Therefore, the improper fraction is \( \frac{179}{10} \).

Key Concepts

Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. Imagine them as numbers that stand between whole numbers. They're used frequently in everyday math because they're easy to understand. For example, think about cooking, where you might use a mixed number like "17 and nine-tenths" cups of flour. Here, 17 is the whole number, and \( \frac{9}{10} \) is the fractional part. Mixed numbers provide a clear way to express a count that is not exactly whole, making them practical for real-life scenarios.

Improper Fractions

Improper fractions are fractions where the numerator (the top number) is larger than or equal to the denominator (the bottom number). This can make them look a bit top-heavy. For example, let's take \( \frac{179}{10} \). Here, 179 is greater than 10, which makes this fraction improper. While they might seem unusual at first, improper fractions are very useful. They simplify complex calculations and make it easier to work with expressions, especially in algebra. These fractions are integral in areas like science and engineering where continuous values are handled.

Fractions Conversion

Fractions conversion involves changing one type of fraction into another, such as a mixed number into an improper fraction or vice-versa. The process of converting mixed numbers to improper fractions is straightforward. Simply multiply the whole number by the denominator, add the numerator, and place that result over the original denominator.

• Consider our example mix: 17 and \( \frac{9}{10} \).
• Multiply: \( 17 \times 10 = 170 \).
• Add the numerator: \( 170 + 9 = 179 \).
• The improper fraction is \( \frac{179}{10} \).

Fractions conversion is key in math as it allows different numbers and expressions to be compared or calculated accurately.

Whole Numbers

Whole numbers are numbers without fractions or decimals. They are countable integers that include zero, simple and steady. In our original exercise, the 17 in "17 and \( \frac{9}{10} \)" is an example of a whole number. Whole numbers are significant because they represent complete units like people or objects. When converting mixed numbers to improper fractions, the whole number plays a vital role. It is multiplied by the denominator to contribute to the total numerator of the resulting improper fraction. This process underscores the importance of integrating whole numbers with fractions in mathematical computations.