7.5.4 Solving Proportions & Word Problems

Review Proportion Proportion – is it equal, is it fair? Popcorn Example: 2 Boxes 3 Boxes $9.00 $14.00 To find out if the ratios (fractions) are equal, you can… Option #1: Determine the relationship between the numerator and denominator for each ratio (otherwise known as find the unit rate) Option #2: Cross multiply the numerator of one ratio with the denominator of the other ratio. If the products are the same, the ratios are equal (otherwise known as cross products property) These methods only tell you if the ratios are proportional or not. They don’t tell you how to fix the ratios if they’re not proportional (psst…change one ratio or the other) But what if you don’t have all the information for both ratios? …

Many Methods to Solve Proportion Well, sometimes it’s easy to figure out… Option #1: Use mental math to find the relationship between the denominators or numerators example: 5 = x 7 21 7 goes into 21 three times. So, multiply 5 · 3 and you’ll get x=15. (tip: you already know the two ratios are equal because there is an equal sign there. But you can still use the cross products property to check your work. Option #2: Use multiplication property of equality, where you multiply both ratios by the denominator that is missing its numerator The 21s on the right cancel each other out, leaving only the x on the right side of the equal sign. 21· 5 = 105 and then 1· 7 = 7. After simplifying, you get 15. (tip: this method can ONLY be used when the x is in a numerator position!) 21· ·21

Many Methods, cont’d Option #3: Use cross products property and then divide each product by the number that is stuck with the variable. example: x = 7 8 · 7 = 56 x · 10 = 10x 8 10 Multiply 8 and 7 to get 56. Multiply x and 10 to get 10x. 56 = 10x 10 10 Divide 56 by 10 and divide 10x by 10. 5.6 = x

Word Problems: Slime You have learned the ingredients for making your own slime: water, glue, and borax. If you want it to have color, add as much food coloring as you want. But the ratio of the water, glue, and borax must be exact. Solve the following proportions using any of the three proportion solving methods you just learned: 1. 2. 3. Water ½ cup 1 cup Glue x cups Borax 1 tsp 2 tsp Water 1 cup x cups Water ½ cup 1 cup Glue y cups x cups

Word Problems: Salt Water You’re in science class and you’ve just learned that 1 liter of salt water holds 250 grams of salt. Back at home you need to add 3 liters of salt water to your salt water fish tank. How many grams of salt do you need to add to your bucket of tap water?

Word Problems: Toll Money You and your family are on your way to New York City to see a play on Broadway. Your contribution to the trip (because it was your idea) is to pay for the tolls on the road trip down state. After 30 miles your family car comes to the first toll booth where you have to pay $7.50. You hand over a $20 bill. Afterwards, looking at the change in your hand, you’re wondering (hoping) you have enough money to cover the full 146 mile trip. So…do you have enough money?

Homework Page 190 (#1, 2, 4, 6, 9, 13, 15, 20, 22, 33, 35, 36)