Problem 68 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$1 \frac{3}{4}$$

Step-by-Step Solution

Answer

175\%

Step 1: Convert Mixed Number to Improper Fraction

To convert the mixed number \(1 \frac{3}{4}\) into an improper fraction, you multiply the whole number by the denominator and add the numerator. Here, \(1 \times 4 + 3 = 7\), so the improper fraction is \(\frac{7}{4}\).

Step 2: Divide the Numerator by the Denominator

To convert the fraction \(\frac{7}{4}\) into a decimal, divide the numerator by the denominator. Performing the division gives \(7 \div 4 = 1.75\).

Step 3: Convert Decimal to Percent

To change the decimal \(1.75\) into a percent, multiply by 100 and add the percent sign. This is calculated as \(1.75 \times 100 = 175\). Thus, \(1 \frac{3}{4} = 175\%\).

Key Concepts

Mixed Numbers

A mixed number combines a whole number with a proper fraction. You often see mixed numbers in day-to-day life, like when measuring ingredients for a recipe. For instance, if a recipe calls for 1 3/4 cups of flour, that is a mixed number.

• Whole Number: This is the number in front of the fraction. In 1 3/4, the whole number is 1.
• Proper Fraction: This completes the mixed number. The fraction in 1 3/4 is 3/4.

To work with mixed numbers, especially in calculations, it's often easier to first convert them into improper fractions. This simplifies arithmetic operations like addition, subtraction, or conversion to decimals and percentages.

Improper Fractions

When you convert a mixed number into an improper fraction, you put everything over a single denominator. An improper fraction has a numerator larger than its denominator, such as 7/4.

Here’s how to change a mixed number to an improper fraction:

• Multiply the whole number by the denominator of the fraction part.
• Add the numerator to the result from the first step.
• Place this sum over the original denominator.

For example, with 1 3/4: - Multiply the whole number (1) by the denominator (4): 1 x 4 = 4. - Add the numerator (3): 4 + 3 = 7. - Write it as 7/4.

Now you have an improper fraction, and you're ready for the next step in conversions or operations.

Fraction to Decimal Conversion

Converting a fraction to a decimal is an important skill in many areas of math and science. It involves dividing the numerator by the denominator. This process can make it easier to compare, add, subtract, or convert to a percentage.

Consider the improper fraction 7/4:

• Divide 7 by 4, which equals 1.75.
• This decimal, 1.75, represents the same quantity as the fraction 7/4.

Once converted to a decimal, you can easily transform it into a percentage. Simply multiply by 100. In our example, 1.75 becomes 175%, showing the same value in a different form. This process clarifies and simplifies various numeric operations.