Building Fractions
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to build equivalent fractions by multiplying numerator and denominator by the same nonzero number. This technique is essential for adding or subtracting fractions with unlike denominators and for rewriting fractions in a specific form.
Key Concepts
Property To build a fraction is to convert it to an equivalent form with a larger denominator. This is done by multiplying the numerator and denominator by the same (nonzero) quantity, called the building factor . This is an application of the fundamental principle of fractions:.
$$\frac{a}{b} = \frac{a \cdot c}{b \cdot c}, \quad \text{if } c \neq 0$$.
Examples To build the fraction $\frac{3}{4}$ to have a denominator of 28, the building factor is 7. So, $\frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28}$.
Common Questions
What does it mean to build a fraction?
Building a fraction means creating an equivalent fraction with a specific denominator by multiplying both the numerator and denominator by the same number.
Why does multiplying numerator and denominator by the same number not change the value?
Multiplying by n/n is the same as multiplying by 1, which does not change the value of the fraction.
How do you build a fraction with a specific denominator?
Divide the target denominator by the current denominator to find the multiplier, then multiply both numerator and denominator by that number.
When do you need to build fractions?
You need to build fractions when adding or subtracting fractions with unlike denominators, requiring a common denominator.
Where is building fractions taught in Grade 6?
Building fractions is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.