1. Ratios and Proportions
3.1
Ratios and Proportions
1. Solve problems involving ratios.
2. Solve for a missing number in a proportion.
3. Solve proportion problems.
4. Use proportions to solve for missing lengths in figures that are similar.
Check for handout.
You may use calculators in this chapter!!

2. Ratio: A comparison of two quantities using a quotient (fraction).
The word to separates the numerator and denominator quantities.
The ratio of 12 to 17 translates to
Numerator
Denominator
Unit ratio: A ratio with a denominator of 1.

3. Ratios
A bin at a hardware store contains 120 washers and 85 bolts. Write the ratio of washers to bolts in simplest form.
The ratio of washers to bolts
Express the ratio as a unit ratio. Interpret the answer.
There are 1.41 washers for every bolt.

4. Ratios
The price of a 10.5 ounce can of soup is $ Write the unit ratio that expresses the price to weight.
The ratio of price to weight
Interpret the answer.
The soup costs $.16 per ounce.

5. Ratios
One molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. What is the ratio of hydrogen atoms to the total number of atoms in the molecule?
The ratio of hydrogen atoms to total atoms

6. Proportions Proportion: two ratios set equal.
Cross-products of proportions are always equal!
Only works if there is an equal (=) sign!
No!

7. Solving Proportions 1. Calculate the cross products.
2. Set the cross products equal to each other.
3. Solve the equation.

8. Solving Proportions 1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.

9. Solving Proportions 1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation. 3 1
Multiply by reciprocal.
Or clear the fraction. 1 1

10. Solving Proportions 1. Calculate the cross products.
2. Set the cross products equal.
3. Solve the equation.

11. Solving Proportions
Gary notices that his water bill was $24.80 for 600 cubic feet of water. At that rate, what would the charges be for 940 cubic feet of water?

12. Solving Proportions
Chevrolet estimates that its 2012 Tahoe will travel 520 miles on one tank of gas. If the tank of the Tahoe holds 26 gallons, how far can a driver expect to travel on 20 gallons?

13. Angles that have the same measure. The symbol for congruent is .
Congruent angles:
Angles that have the same measure.
The symbol for congruent is .
Similar figures:
Figures with congruent angles and
proportional side lengths.
The two figures are similar. Find the missing length. 10 8 6 5 x

14. Similar Figures
The two figures are similar. Find the missing lengths. Round your answer to the nearest hundredth.
10.5 km
6.5 km
4.6 km x y
12.8 km