Equivalent Fractions

Fraction Basics: Understanding what a fraction is, how it represents the division of a whole into equal parts, and how to write and identify the parts of a fraction (numerator and denominator).

Equivalent Fractions: Learning what equivalent fractions are and how to find them by multiplying or dividing the numerator and denominator by the same number.

Simplifying Fractions: Knowing how to simplify fractions by dividing both the numerator and denominator by their greatest common factor to make them easier to work with and compare.

Comparing and Ordering Fractions: Understanding how to compare and order fractions by finding common denominators, using number lines or visual models, or converting them to decimals or percentages.

Adding and Subtracting Fractions: Learning how to add and subtract fractions with like and unlike denominators, by finding common denominators or using equivalent fractions.

Multiplying and Dividing Fractions: Knowing how to multiply and divide fractions by multiplying the numerators and denominators, or by flipping and multiplying, and how to simplify the result.

Mixed Numbers and Improper Fractions: Understanding the difference between mixed numbers and improper fractions, converting between them, and how to add, subtract, multiply and divide them.

Fraction Operations with Whole Numbers: Knowing how to add, subtract, multiply and divide fractions with whole numbers, by converting them to fractions or mixed numbers, or using common denominators.

Fractions and Ratios: Understanding how to write fractions as ratios and vice versa, and how to use ratios to solve proportion problems.

Fraction Application Problems: Solving real-life problems that involve fractions, such as cooking recipes, money, distances, and measurements, by using fraction arithmetic and modeling.

Simple equivalent fractions: Fractions that have the same value, but they are expressed differently. For example, 1/2 and 2/4 are simple equivalent fractions.

Multiplying both the numerator and denominator by the same number: If we multiply both the numerator and denominator of a fraction with the same number, we get an equivalent fraction. For example, if we multiply 2/3 by 2/2, we get 4/6 which is an equivalent fraction of 2/3.

Dividing both the numerator and denominator by the same number: If we divide both the numerator and denominator of a fraction with the same number, we get an equivalent fraction. For example, if we divide 6/9 by 3/3, we get 2/3 which is an equivalent fraction.

Using common factors: Fractions can be simplified to their lowest equivalent by finding the largest factor that is common to both the numerator and denominator, and then dividing both by that factor. For example, 6/9 can be simplified to 2/3 by dividing both the numerator and denominator by the common factor 3.

Using prime factorization: Fractions can also be simplified by using prime factorization of the numerator and denominator. For example, 20/24 can be simplified to 5/6 by finding the prime factors of both 20 and 24 (2x2x5 and 2x2x2x3), and cancelling out any common factors.

Using reciprocals: The reciprocal of a fraction is obtained by interchanging the numerator and denominator. Fractions are equivalent if they have the same value as their reciprocal. For example, 3/4 and 4/3 are equivalent fractions as they are reciprocals of each other.

Using mixed numbers: A mixed number can be converted to an equivalent fraction by multiplying the whole number by the denominator, and then adding the numerator. For example, 2 1/4 can be converted to 9/4.

Using decimal and percentage equivalents: Fractions can be expressed as their decimal and percentage equivalents, which can also be equivalent to other fractions. For example, 1/2 is equivalent to 0.5 and 50%.

Adding or subtracting the same number from both the numerator and denominator: If we add or subtract the same number from both the numerator and denominator of a fraction, we get an equivalent fraction. For example, 2/3 can be converted to an equivalent fraction 4/6 by adding 1 to both the numerator and denominator.