Mathematics
Grade 7
15 min
Do the ratios form a proportion: word problems
Do the ratios form a proportion: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Define ratio and proportion in their own words.
Extract relevant quantities from word problems to form two ratios.
Apply the cross-multiplication property to determine if two ratios form a proportion.
Simplify ratios to their lowest terms to check for proportionality.
Solve real-world word problems by determining if given ratios form a proportion.
Explain the meaning of a proportion in the context of a word problem.
Ever wonder if two recipes will taste the same if you double one ingredient but not another? 🤔 We'll learn how to check if things are 'in proportion'!
In this lesson, you'll learn how to identify and compare ratios presented in word problems. You'll discover different methods to determine if two ratios are equivalent...
2
Key Concepts & Vocabulary
TermDefinitionExample
RatioA comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.If there are 3 red apples and 5 green apples, the ratio of red to green apples is 3:5.
ProportionAn equation that states that two ratios are equivalent (equal).The equation 1/2 = 3/6 is a proportion because both ratios are equivalent.
Equivalent RatiosTwo or more ratios that represent the same relationship between quantities, even if the numbers are different.The ratios 1:2 and 2:4 are equivalent because they both simplify to 1:2.
Cross-MultiplicationA method used to check if two ratios form a proportion by multiplying the numerator of one ratio by the denominator of the other.To check if 1/2 = 3/6, you would multiply 1x6 and 2x3. Since 6=6, they are proportional.
Un...
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Core Formulas
Definition of a Proportion
Two ratios $\frac{a}{b}$ and $\frac{c}{d}$ form a proportion if $\frac{a}{b} = \frac{c}{d}$.
This rule states that for two ratios to be a proportion, they must represent the same relationship or value. You can check this by simplifying both ratios or by using cross-multiplication.
Cross-Multiplication Property
If $\frac{a}{b} = \frac{c}{d}$ is a proportion, then $a \times d = b \times c$. Conversely, if $a \times d = b \times c$, then $\frac{a}{b} = \frac{c}{d}$ is a proportion.
This property provides a quick and reliable way to determine if two ratios are equivalent. You multiply the 'cross' terms (numerator of the first by denominator of the second, and vice-versa). If the products are equal, the ratios form a proportion.
5 more steps in this tutorial
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Easy
A recipe for a smoothie calls for 3 bananas for every 2 apples. A different recipe for a larger batch calls for 6 bananas for every 4 apples. Do the ratios of bananas to apples in both recipes form a proportion?
A.No, because 3 + 2 is not equal to 6 + 4.
B.Yes, because the second recipe is exactly double the first.
C.No, because the number of fruits is different.
D.Yes, but only if you add one more apple.
Easy
Which of the following methods is a valid way to determine if the ratios a/b and c/d form a proportion?
A.Check if a + d = b + c.
B.Check if a / c = d / b.
C.Check if a × d = b × c.
D.Check if a - b = c - d.
Easy
A car travels 120 miles in 2 hours. A bus travels 180 miles in 3 hours. Do the ratios of miles to hours for the car and the bus form a proportion?
A.Yes, because both have a unit rate of 60 miles per hour.
B.No, because the distances and times are different.
C.No, because 120 × 3 is not equal to 180 × 2.
D.Yes, because 180 - 120 = 3 - 2.
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