PROPORTIONAL REASONING

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Presentation transcript:

PROPORTIONAL REASONING A POWERFUL CONCEPT

A proportion is a statement that two ratios are equal. RATIOS & PROPORTIONS A proportion is a statement that two ratios are equal.

RATIOS & PROPORTIONS 30 = 30 TRUE EXAMPLE#1: Is a proportion? Find the cross products. 30 = 30 TRUE If TRUE, the statement is a proportion.

RATIOS & PROPORTIONS 20 = 21 FALSE EXAMPLE#2: Is a proportion? Find the cross products. 20 = 21 FALSE If FALSE, the statement is NOT a proportion.

RATIOS & PROPORTIONS Are the following proportions? FALSE – Not a proportion FALSE – Not a proportion TRUE – this is a proportion TRUE – this is a proportion

PROPORTION OR NOT? 3 7 = 27 63

PROPORTION OR NOT? 4 9 = 7 63

Solving Proportions 2 Ways: 1st - We can find equivalent fractions to solve proportions. 2nd - We cross multiply to solve proportions.

equivalent fractions to solve proportions. Solving Proportions Let’s try using equivalent fractions to solve proportions.

Solving Proportions 6 9 = 𝑥 18 𝑥 7 = 24 21 𝑥 50 = 6 10 4 7 = 44 𝑥 We can find equivalent fractions to solve proportions 6 9 = 𝑥 18 𝑥 7 = 24 21 𝑥 50 = 6 10 4 7 = 44 𝑥

Solving Proportions 𝑥 9 = 10 18 15 6 = 𝑥 4 We cross multiply to solve proportions 𝑥 9 = 10 18 15 6 = 𝑥 4

RATIOS & PROPORTIONS 10 EXAMPLE#4: Solve the proportion: Find the cross products. Divide both sides by 10. 10

RATIOS & PROPORTIONS 6 18 = 4 𝑐 6 6 EXAMPLE#6: Solve the proportion: 6 18 = 4 𝑐 EXAMPLE#6: Solve the proportion: Find the cross products. Divide both sides by 10. 6 6

Steps in solving practical problems using proportion ---------- = ------------- Label the two quantities you are comparing Plug in the given values and solve.

How many pizzas? Ms. Marx bought 9 pizzas for 25 students. Tonight, 300 students will be attending a Math night to sharpen their math skills. How many pizzas would Ms. Marx need to buy for the students?

How many Pizzas ? ------------ = --------------- Label ------------ = --------------- Label Plug in given values and solve. 9 25 = 𝑥 300 𝑝𝑖𝑧𝑧𝑎 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠

Your turn Four students went to see a movie for $30.00. How much would 20 students spend if they want to watch the same movie.

A possible solution 4 30 = 20 𝑥 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑐𝑜𝑠𝑡

Scale factor is a proportion Inches = 15 = Centimeters 38.1 25 x

Percent is a Proportion too! Percent is “out of 100”. Percent of a number is used in tax, tip, discount and lots of other everyday math! One way to find the percent “of” a number is to change % to a decimal and multiply! What is 20% of $50.00? Change 20% to a decimal: 0.20 x 50 = 10 What is 4.5% of 20? Change 4.5% to 0.045 x 20 = 0.9

Setup of a Percent Proportion Is = part Of = whole The Percent Proportion puts the % into a decimal. This can be used to find the Percent of a number.

Tax In Virginia, the state sales tax is 6.5%. You want to buy a $195 bicycle in Virginia. How much is the tax? READ the question! This is ONLY asking for the tax. Change 6.5% to a decimal = 0.065 0.065 x 195 = 12.675 Money is always rounded to the nearest hundredth!(penny) 6.5% of $195 is $12.68 OR Set up a proportion To solve for the tax. X = 12.675 = $12.68 𝑥 195 = 6.5 100

Discount Discount is the Percent of a Number Mrs. Parker buys a new Beach Chair for $35.00. She gets a 25% discount for being a teacher. What is the sale price of the beach chair? First find 25% of $35.00. 0.25 x 35 = $8.75 This is the amount SUBTRACTED from $35.00. (Savings) $35.00 - $8.75 = $26.25 for the chair. Sometimes the question asks for the amount discounted and other times for the sale price.

Tip Mrs. Roan treats the Math teachers to lunch at Flip Flops. The bill was $67.58 and she wants to leave a 20% tip. How much is the tip? What is 20% of $67.58. Change 20% to 0.20 x 67.58 = 13.516 Money rounded to the hundredth = $13.52 for the tip. Check the question. Are they asking for the tip amount or the total including the tip?

Consumer Math Remember to READ THE QUESTION! (What are they asking?) For tax and tip, find the %, then ADD for total cost. Sales Price with Discount, find % then SUBTRACT for final price.