Question

Subtract the following fractions and mixed numbers. Reduce to lowest terms. \(\frac{4}{9}-\frac{3}{9}=\) ______

Short answer

\( \frac{1}{9} \)

Step-by-step solution

Align the Fractions

The fractions to be subtracted are \( \frac{4}{9} \) and \( \frac{3}{9} \). Both fractions already have the same denominator, which is 9. This means we can directly subtract the numerators.

Subtract the Numerators

Subtract the numerator of the second fraction (3) from the numerator of the first fraction (4). This gives us: \( 4 - 3 = 1 \).

Write the Resulting Fraction

The result of the subtraction is the fraction \( \frac{1}{9} \), since we keep the common denominator.

Simplify the Fraction

Check if the fraction \( \frac{1}{9} \) can be simplified further. Since 1 and 9 have no common factors other than 1, this fraction is already in its simplest form.

Key concepts

Fractions

Fractions are a way to represent parts of a whole. They consist of two numbers: a numerator and a denominator. The numerator is the top number, and it indicates how many parts of the whole we have or are considering. The denominator is the bottom number, showing into how many equal parts the whole is divided. For example, in the fraction \( \frac{4}{9} \), 4 is the numerator and 9 is the denominator. This means that we have 4 parts out of a total of 9.

Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. They represent quantities that are more than one whole unit, but not completely whole numbers either. For instance, the mixed number 2\(\frac{1}{3}\) means you have 2 whole units plus one-third of a unit. Mixed numbers are particularly useful when subtracting large fractions, as they give a clearer picture of the size of the numbers involved.

Common Denominator

When subtracting fractions, having a common denominator is crucial. It allows us to easily compare the fractions and perform operations like subtraction. The denominator represents the same partition of the whole, ensuring consistent parts. In the original exercise, the fractions \( \frac{4}{9} \) and \( \frac{3}{9} \) already share a common denominator, 9. This means we can directly subtract their numerators. If fractions do not share the same denominator, you would need to find the least common denominator by determining the least common multiple (LCM) of the denominators before proceeding.

Simplifying Fractions

Simplifying fractions involves reducing them to their simplest form. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. This is also referred to as reducing a fraction. In the original solution, the fraction \( \frac{1}{9} \) was already in its simplest form since 1 and 9 do not share any other common factors. Simplifying makes fractions easier to understand and compare. It is an essential step in fraction operations, ensuring clarity and simplicity in mathematical expressions.