key term - Like Fractions

Definition

Like fractions are fractions that have the same denominator. They can be added, subtracted, multiplied, and divided easily because the common denominator allows the fractions to be combined directly without needing to find a least common denominator first.

5 Must Know Facts For Your Next Test

1. When adding or subtracting like fractions, you simply add or subtract the numerators and keep the same denominator.
2. Multiplying like fractions involves multiplying the numerators and multiplying the denominators.
3. Dividing like fractions involves inverting the second fraction and multiplying the first fraction by the inverted second fraction.
4. Converting mixed numbers to improper fractions is a helpful step when adding or subtracting mixed numbers with like denominators.
5. Reducing like fractions to simplest form involves dividing both the numerator and denominator by their greatest common factor.

Review Questions

• Explain the process of adding like fractions with common denominators.
  • To add like fractions with common denominators, you first identify that the fractions have the same denominator. Then, you simply add the numerators together and keep the same denominator. For example, to add $\frac{2}{5}$ and $\frac{3}{5}$, you would add the numerators: $\frac{2}{5} + \frac{3}{5} = \frac{5}{5}$. This results in the mixed number $1\frac{0}{5}$, which can then be simplified to $1$.
• Describe the steps to multiply like fractions.
  • Multiplying like fractions involves multiplying the numerators together and multiplying the denominators together. For example, to multiply $\frac{2}{3}$ and $\frac{4}{3}$, you would first multiply the numerators: $2 \times 4 = 8$. Then you would multiply the denominators: $3 \times 3 = 9$. The final result is $\frac{8}{9}$. This process works because the common denominators allow the fractions to be combined directly without needing to find a least common denominator first.
• Explain how converting mixed numbers to improper fractions can be helpful when adding or subtracting mixed numbers with like denominators.
  • When adding or subtracting mixed numbers with like denominators, it can be helpful to first convert the mixed numbers to improper fractions. This allows you to add or subtract just the numerators, keeping the same denominator. For example, to add $2\frac{3}{5}$ and $1\frac{4}{5}$, you would first convert them to improper fractions: $\frac{13}{5}$ and $\frac{9}{5}$. Then you can add the numerators: $\frac{13}{5} + \frac{9}{5} = \frac{22}{5}$, which can then be converted back to the mixed number $4\frac{2}{5}$.

Related terms

Fraction:

A fraction represents a part of a whole and is expressed as a numerator over a denominator.

Equivalent Fractions:

Fractions that represent the same amount, even though the numerator and denominator are different.

Least Common Denominator (LCD):

The smallest common denominator that two or more fractions can be converted to in order to add or subtract them.