Solving Ratio Word Problems with Equivalent Ratios
This Grade 7 math skill from Reveal Math, Accelerated teaches students to solve ratio word problems by setting up and using equivalent ratios. Students translate real-world scenarios into ratio relationships, then find unknown quantities by scaling or cross-multiplying to create equivalent ratios.
Key Concepts
Property To solve a word problem using proportions, first identify the two quantities being compared and set up two equal ratios. Let a variable represent the unknown quantity. Ensure that the units are placed consistently in the numerators and denominators of the ratios. $$\frac{\text{unit A quantity 1}}{\text{unit B quantity 1}} = \frac{\text{unit A quantity 2}}{\text{unit B quantity 2}}$$.
Examples A doctor prescribes $5 \text{ ml}$ of medicine for every $25 \text{ lbs}$ of weight. For a child weighing $80 \text{ lbs}$, we set up:.
$$ \frac{5 \text{ ml}}{25 \text{ lbs}} = \frac{a}{80 \text{ lbs}} $$ To solve, note that $80$ is $3.2$ times $25$, so multiply $5 \text{ ml}$ by $3.2$ to find $a = 16 \text{ ml}$.
Common Questions
How do you solve a ratio word problem using equivalent ratios?
Write the known ratio, then set up an equivalent ratio with the unknown quantity, and solve by scaling or cross-multiplying.
What are equivalent ratios?
Equivalent ratios are ratios that express the same relationship, like 2:3 and 4:6. They are created by multiplying or dividing both terms by the same number.
Why are equivalent ratios useful in word problems?
Equivalent ratios let you find an unknown value when you know the proportional relationship, which is a key strategy in Grade 7 ratio and proportion problems.
What is an example of a ratio word problem?
If a recipe uses 2 cups of flour for every 3 cups of sugar, how much flour is needed for 9 cups of sugar? Set up 2/3 = x/9 and solve to get x = 6.
Where is this skill covered in Reveal Math Accelerated?
Solving ratio word problems with equivalent ratios is a Grade 7 topic in the Reveal Math, Accelerated textbook.