Equivalent fractions
Equivalent fractions are different fractions that represent the same value. You create them by multiplying or dividing both the numerator and denominator by the same number, which is the same as multiplying by a form of 1 like 4/4. For example, 2/3 x 4/4 = 8/12, so 2/3 and 8/12 are equivalent. This concept is covered in Chapter 2 of Saxon Math Course 2 for 7th grade math and is critical for adding and subtracting fractions with different denominators, simplifying fractions, and solving proportions.
Key Concepts
Property Different fractions that name the same number are equivalent. You can create them by multiplying the original fraction by a form of 1, like $\frac{a}{a}$.
Examples "To give $\frac{2}{3}$ a denominator of 12: $\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}$." "Create another equivalent for $\frac{1}{2}$: $\frac{1}{2} \times \frac{5}{5} = \frac{5}{10}$.".
Explanation Think of it as giving a fraction a disguise! Multiplying it by a fancy '1' changes its look but not its value. This is key for getting common denominators before adding or subtracting.
Common Questions
What are equivalent fractions?
Equivalent fractions are fractions that look different but represent the same amount. For example, 1/2, 2/4, and 3/6 are all equivalent because they all equal one half. You can verify by cross-multiplying or simplifying to the same lowest-terms fraction.
How do you find an equivalent fraction?
Multiply or divide both the numerator and denominator by the same nonzero number. To give 2/3 a denominator of 12, multiply top and bottom by 4: 2/3 x 4/4 = 8/12. The value stays the same because you multiplied by 1.
Why are equivalent fractions important?
Equivalent fractions are essential for adding and subtracting fractions with different denominators. You need a common denominator, which means converting fractions to equivalent forms. They also help in simplifying answers and comparing fractions.
How do you check if two fractions are equivalent?
Cross-multiply: if a/b and c/d are equivalent, then a x d = b x c. For example, 2/3 and 8/12: 2 x 12 = 24 and 3 x 8 = 24. Since both products are equal, the fractions are equivalent.
What is the simplest form of a fraction?
A fraction is in simplest form when the numerator and denominator share no common factors other than 1. For example, 8/12 simplifies to 2/3 by dividing both by 4. This is also called reducing or writing in lowest terms.
Which textbook covers equivalent fractions in 7th grade?
Saxon Math Course 2 covers equivalent fractions in Chapter 2. Students learn to create equivalent fractions by multiplying by forms of 1 and apply this skill to operations with unlike denominators throughout the course.