Solving Formulas with Fractions
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to solve formulas that contain fractions for a specified variable. Students apply inverse operations to both sides of an equation containing fractional expressions, clearing denominators through multiplication to isolate the target variable.
Key Concepts
Property To solve a formula for a specific variable, first clear any fractions by multiplying the entire equation by the LCD. Next, gather all terms containing the desired variable on one side of the equation. If there are multiple terms with the variable, factor the variable out, and then divide both sides by the remaining factor to isolate it.
Examples Solve the formula $S = \frac{a}{1 r}$ for $r$. Multiply by $1 r$ to get $$S(1 r) = a$$. Distribute $S$ to get $$S Sr = a$$. Then, $$ Sr = a S$$, so $$r = \frac{a S}{ S}$$ or $$r = \frac{S a}{S}$$. Solve $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ for $u$. The LCD is $fuv$. Multiply by the LCD to get $$uv = fv + fu$$. Move terms with $u$ to one side: $$uv fu = fv$$. Factor out $u$: $$u(v f) = fv$$. The solution is $$u = \frac{fv}{v f}$$. Solve $h = \frac{2A}{b 1 + b 2}$ for $b 1$. Multiply by $b 1+b 2$ to get $$h(b 1+b 2) = 2A$$. Distribute $h$: $$hb 1 + hb 2 = 2A$$. Then $$hb 1 = 2A hb 2$$, and $$b 1 = \frac{2A hb 2}{h}$$.
Explanation Rearranging formulas is like solving a puzzle. First, get rid of fractions. Then, herd all the pieces with your target variable to one side. If it appears in multiple terms, factor it out to isolate it.
Common Questions
How do you solve a formula that has fractions for a variable?
Multiply both sides of the equation by the LCD (least common denominator) to eliminate the fractions, then solve the resulting equation.
What is clearing the denominator?
Clearing the denominator means multiplying both sides of an equation by the LCD so that all fractions disappear, leaving an equation with whole number coefficients.
What is an example of solving a formula with fractions?
Solve 1/2 x + 3 = 7 for x: multiply both sides by 2 to get x + 6 = 14, then x = 8.
Can you clear the denominator if the equation has two different denominators?
Yes. Find the LCD of all denominators, then multiply every term by the LCD to clear all fractions at once.
Where is solving formulas with fractions taught?
Solving formulas with fractions is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.