In this Grade 7 lesson from Saxon Math, Course 2, students learn how to solve implied ratio problems by setting up proportions using a case 1–case 2 ratio box. They practice writing and solving proportions with cross multiplication across real-world contexts such as unit pricing, rates, and equivalent ratios. The lesson builds students' ability to recognize constant ratios between two quantities and apply proportional reasoning to find unknown values.
Section 1
📘 Implied Ratios
An implied ratio compares two situations with a constant rate. We organize the information in a ratio box to write a proportion and solve for the unknown value.
Next, you'll apply this method with worked examples involving costs, production rates, and abstract number comparisons.
Section 2
Solving With Ratio Boxes
A ratio box organizes information for two situations (Case 1, Case 2). Use it to set up a proportion and solve for an unknown value, .
If 12 books weigh 40 pounds, how much do 30 weigh? .
If 5 pencils cost 1.20 dollars, how much do 12 cost? .
Feeling lost in a word problem? A ratio box is your map! It neatly sorts your numbers into two cases, letting you build a proportion to find the missing piece of the puzzle. It turns chaos into clarity!
Section 3
Cross multiply
To solve a proportion, multiply the numerator of one fraction by the denominator of the other. For , the result is .
Given , cross multiplying gives .
Given , cross multiplying gives .
Cross multiplication is a magical trick to eliminate fractions from a proportion. Just multiply diagonally across the equals sign to turn a tricky fraction equation into a simple one that’s much faster and easier to solve for the unknown.
Section 4
Keep Units Consistent
The units in a proportion must be consistent. You cannot mix different units of measurement, like minutes and hours, in the same ratio comparison.
Correct: .
Incorrect: .
Don't let mixed units trick you! Proportions demand that units match. Before solving, always convert measurements to be the same, like changing 1 hour into 60 minutes. This ensures your calculation is accurate and makes sense.
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Section 1
📘 Implied Ratios
An implied ratio compares two situations with a constant rate. We organize the information in a ratio box to write a proportion and solve for the unknown value.
Next, you'll apply this method with worked examples involving costs, production rates, and abstract number comparisons.
Section 2
Solving With Ratio Boxes
A ratio box organizes information for two situations (Case 1, Case 2). Use it to set up a proportion and solve for an unknown value, .
If 12 books weigh 40 pounds, how much do 30 weigh? .
If 5 pencils cost 1.20 dollars, how much do 12 cost? .
Feeling lost in a word problem? A ratio box is your map! It neatly sorts your numbers into two cases, letting you build a proportion to find the missing piece of the puzzle. It turns chaos into clarity!
Section 3
Cross multiply
To solve a proportion, multiply the numerator of one fraction by the denominator of the other. For , the result is .
Given , cross multiplying gives .
Given , cross multiplying gives .
Cross multiplication is a magical trick to eliminate fractions from a proportion. Just multiply diagonally across the equals sign to turn a tricky fraction equation into a simple one that’s much faster and easier to solve for the unknown.
Section 4
Keep Units Consistent
The units in a proportion must be consistent. You cannot mix different units of measurement, like minutes and hours, in the same ratio comparison.
Correct: .
Incorrect: .
Don't let mixed units trick you! Proportions demand that units match. Before solving, always convert measurements to be the same, like changing 1 hour into 60 minutes. This ensures your calculation is accurate and makes sense.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter