Writing Equivalent Fractions
Writing equivalent fractions with a larger denominator requires multiplying both numerator and denominator by the same building factor. To write 2/5 with a denominator of 15, the building factor is 15 divided by 5 = 3, giving 6/15. This Grade 8 math skill from Yoshiwara Core Math Chapter 4 is the inverse of reducing fractions and is essential for adding and subtracting fractions with different denominators. Multiplying by the building factor is equivalent to multiplying by 1 (in the form n/n), so the value of the fraction does not change, it is simply expressed differently.
Key Concepts
Property To write an equivalent fraction with a larger denominator: 1. Divide the old denominator into the desired denominator. This gives you the 'building factor'. 2. Use that factor to multiply the old numerator.
This process is shown as: $$ \frac{\text{old numerator}}{\text{old denominator}} \times \frac{\text{building factor}}{\text{building factor}} = \frac{\text{new numerator}}{\text{new denominator}} $$.
Examples To write $\frac{2}{5}$ with a denominator of 15, the building factor is $15 \div 5 = 3$. We multiply to get $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.
Common Questions
How do you write an equivalent fraction with a larger denominator?
Divide the desired new denominator by the original denominator to find the building factor. Then multiply both the numerator and denominator by that building factor. For example, to write 3/4 as sixteenths: 16 / 4 = 4, so 3/4 = 12/16.
What is a building factor for fractions?
The building factor is the number you multiply both numerator and denominator by to create an equivalent fraction with a specific denominator. If you want denominator 24 and have denominator 8, the building factor is 24 / 8 = 3.
Why does multiplying numerator and denominator by the same number not change the fraction's value?
Multiplying by n/n is the same as multiplying by 1, which never changes a value. For example, 2/5 x 3/3 = 6/15, and 6/15 equals 2/5. The fraction looks different but represents the same amount.
When do 8th graders learn to write equivalent fractions?
Students study writing equivalent fractions in Grade 8 math as part of Chapter 4 of Yoshiwara Core Math, which covers fraction calculations.
Why is writing equivalent fractions important?
Writing equivalent fractions with a common denominator is the necessary first step for adding or subtracting fractions with unlike denominators. Without equivalent fractions, the pieces are different sizes and cannot be directly combined.
What is the relationship between equivalent fractions and the LCD?
To add two fractions with different denominators, you find the LCD and then write both fractions as equivalent fractions with that LCD as the denominator, using the building factor method.