Question

Express the following ratios as fractions. Reduce to lowest terms. 1: 7 ______

Short answer

\( \frac{1}{7} \) is the fraction in simplest form.

Step-by-step solution

Understanding the Ratio

A ratio of 1:7 expresses the relationship between two quantities. The number 1 is in relation to 7, which needs to be expressed as a fraction.

Expressing the Ratio as a Fraction

To convert the ratio 1:7 into a fraction, write it as \( \frac{1}{7} \). This fraction represents the same relationship as the ratio 1:7.

Simplifying the Fraction

Check if the fraction \( \frac{1}{7} \) can be simplified. Since 1 and 7 have no common divisors other than 1, the fraction is already in its simplest form.

Key concepts

Understanding Fractions

Fractions are a way to represent parts of a whole. When you view a number as a fraction, it is composed of two parts: the numerator and the denominator. The numerator indicates how many parts we have, while the denominator shows how many equal parts make up the whole. For example, in the fraction \( \frac{1}{7} \), the numerator is 1, which means there is one part. The denominator is 7, meaning the whole is divided into seven equal parts. Therefore, \( \frac{1}{7} \) represents one out of seven parts. Fractions can be used in various applications in everyday life such as dividing a pizza among friends or measuring ingredients while cooking. Understanding fractions is essential as it forms the basis for more advanced mathematical concepts.

Simplifying Fractions

Simplifying fractions means reducing them to their simplest form. A fraction is in its simplest form when the numerator and the denominator cannot be divided by any number other than 1 and themselves. This usually involves dividing both the numerator and the denominator by their greatest common divisor (GCD).When checking if a fraction is simplified, consider:

• Are both numbers only divisible by 1?
• Is there a smaller common factor?

In the fraction \( \frac{1}{7} \), the numbers 1 and 7 share no common factor other than 1. Hence, it is already simplified. Simplifying helps in making calculations easier in mathematics and ensures results are in the most manageable form.

Importance of Mathematics Education

Mathematics education is crucial as it lays the foundation for understanding the world. Learning mathematics helps develop problem-solving skills, critical thinking, and logical reasoning. It also plays a pivotal role in diverse fields like science, engineering, and economics. Fractions are often one of the first complex concepts introduced in mathematics education, demonstrating proportional relationships.

• They provide a basis for understanding ratios and proportions.
• Simplifying fractions aids in performing operations more efficiently.

As students progress through mathematics education, they learn to approach problems methodically, developing patience and precision.