Question

A company claims its soap is \(99 \frac{44}{100}\) percent pure. What is \(\frac{44}{100}\) reduced to its lowest form? A. \(\frac{44}{100}\) B. \(\frac{22}{50}\) C. \(\frac{11}{25}\) D. \(\frac{4}{10}\)

Short answer

Option C: \(\frac{11}{25}\)

Step-by-step solution

Identify the fraction to be reduced

The fraction to be reduced is \(\frac{44}{100}\).

Find the greatest common divisor (GCD)

Identify the greatest common divisor (GCD) of the numerator (44) and the denominator (100). The GCD of 44 and 100 is 4.

Divide the numerator and denominator by the GCD

Divide the numerator and the denominator by the GCD found in the previous step. \(\frac{44 \div 4}{100 \div 4} = \frac{11}{25}\).

Choose the correct option

The reduced form of \(\frac{44}{100}\) is \(\frac{11}{25}\), which matches option C.

Key concepts

greatest common divisor

To simplify a fraction such as \(\frac{44}{100}\), you first need to find the greatest common divisor (GCD) or greatest common factor (GCF). The GCD is the largest number that divides both the numerator and the denominator with no remainder.
The process involves:

• Listing the factors of both numbers. The factors of 44 are 1, 2, 4, 11, 22, 44 and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.
• Identifying the highest number that appears in both lists.

Here, the GCD of 44 and 100 is 4. Using the GCD helps you evenly reduce the fraction.

numerator and denominator

A fraction consists of two main parts: the numerator and the denominator. The numerator is the top number and represents how many parts you have. The denominator is the bottom number and shows the total number of equal parts.
In the fraction \(\frac{44}{100}\), 44 is the numerator, and 100 is the denominator. When simplifying, both parts need to be divided by the same number without changing the value of the fraction. It helps to create a simpler representation of the ratio.

simplifying fractions

Simplifying fractions means reducing them to their simplest form where the numerator and the denominator have no common factors other than 1. To simplify \(\frac{44}{100}\):

• Find the GCD, which is 4.
• Divide both the numerator and the denominator by 4.

So, \(\frac{44 \div 4}{100 \div 4} = \frac{11}{25}\). This makes the fraction easier to understand and work with in equations and comparisons.
In summary, reducing fractions simplifies calculations and offers a clearer understanding of the proportion.