Flashcards › Ratios/Rates/Proprtions/Percents

What is a ratio? A ratio is a comparison of two numbers or measures that have the same unit. What are the numbers in a ratio called? The numbers in a ratio are called terms. What type of things can ratios compare? Ratios can compare part of something to all of it./ Ratios can compare one part to another part of the same thing./ Ratios can compare a part of one thing to a part of another./ Ratios can compare all of something to all of something else. There are 29 students in Ms. Smith Class. There are 11 girls and 18 boys. What is the ratio of girls to boys? The ratio of girls to boys is 18 to 11. There are 29 students in Ms. Smith Class. There are 11 girls and 18 boys. What is the ratio of boys to girls? The ratio of boys to girls is 11 to 18. There are 29 students in Ms. Smith Class. There are 11 girls and 18 boys. What is the ratio of girls to the whole class? The ratio of girls to the whole class is 11 to 29. There are 29 students in Ms. Smith Class. There are 11 girls and 18 boys. What is the ratio of boys to the whole class? The ratio of boys to the whole class is 18 to 29. There are four sqares and three cricles. What is the ratio of squares to circles? The ratio of squares to circles is 4 to 3. There are four sqares and three cricles. What is the ratio of circles to squares? The ratio of circles to squares is 3 to 4. There are four sqares and three cricles. What is the ratio of squares to all shapes? The ratio of sqares to all shapes is 4 to 7. There are four sqares and three cricles. What is the ratio of circles to all shapes? The ratio of circles to all shapes is 3 to 7. How can ratios be expressed? Example: 4 to 3. This ratio can be expressed as: 4 to 3, 4:3, and 4/3. How do we express equivalent ratios? To write equal ratios multiply both terms by the same number or divided both terms by the same number. Multiply To Get An Equal Ratio: 6/9 = ?/36 ? = 24 Divide To Get An Equal Ratio: 20/10 = 10/? ? = 5 Multiply To Get An Equal Ratio: 4/5 = ?/25 ? = 20 Divide To Get An Equal Ratio: 15/6 = 5/? ? = 2 Multiply To Get An Equal Ratio: 8/12 = ?/48 ? = 32 Divide To Get An Equal Ratio: 16/10 = 8/? ? = 5 Multiply To Get An Equal Ratio: 9/7 = ?/14 ? = 18 Divide To Get An Equal Ratio: 24/8 = 12/? ? = 4 What is a proportion? A proportion is an equation stating two ratios are equivalent. What is a rate? A rate is a ratio between two quantities of different units, like miles and hours, or dollars and gallons. What is unit rate? A unit rate is a comparison of one unit. When the second number of a rate is 1 it is a unit rate. 60 miles per hour 60 miles/1 Hour 20 miles per gallon 20 miles/1 Gallon What is unit price? Unit price is the cost of something per unit. Unit price can help you find the better deal when buying different things. How do we calculate unit price? You can calculate unit price by dividing the unit by the price. Example: 80z/$1.29 How do we solve proportions using equivalent fractions? To solve a proportion using equivalent fractions, ask yourself what numbers each term are being multiplied or divided by. Solve The Proportion: 12/24 = n/12 n = 6 Solve The Proprtion: n/15 = 6/30 n = 2 How do we solve proportions using cross multiplication? In a proportion the product of the means (the second and third terms of the proportion) equals the produce of the extremes (the first and last terms of a proportion). Solve The Proprtion: n/9 = 12/4 Step 1: Cross Multiply 4n = 108 Step 2: Divide Each Side By n to solve. 4n/4 = 108/4 n = 27 Step 3: Fill in Term in Proportion 27/9 = 12/4 Step 4: Cross Multiply to Check 27 x 4 = 108 9 x 12 = 108 What is a percent? Percent means “out of one hundred.” The symbol for percent is %. How can percents be written? Percent can be thought of as the ratio of a number to 100, or the numerator of a fraction in which the denominator is 100. Percents can be represented as fractions and decimals. Example: 60% = 60/100 or 3/5 or 0.6 40 % = 40/100 or 2/5 or 0.4 How do we solve percent problems? (Decimal Method) Step 1: Change the percent to an equivalent decimal. Step 2: Multiply. How do we solve percent problems? (Fraction Method) Step 1: Change the percent of a fraction in lowest terms. Step 2: Multiply. How do we solve percent problems? (Proprtion Method) Step 1: Set up proportion. Step 2: Cross Multiply. Step 3: Divide to Solve Proportion. Solve The Proprtion: Decimal Method: Find 50% of 80 Step 1: Change the percent to an equivalent decimal. 50% = 0.5 Step 2: Multiply: 0.5 x 80 = 40 Solve The Proprtion: Fraction Method: Find 50% of 80 Step 1: Change the percent of a fraction in lowest terms. 50% = 50/100 or 1/2 Step 2: Multiply: 1/2 x 80 = 40 Solve The Proprtion: Proprtion Method: What percent of 30 is 6? Step 1: Set up proportion: 6/30 = n/100 Step 2: Cross Multiply 600 = 30n Step 3: Divide to Solve Proportion n = 20 6 is 20% of 30. Solve The Proprtion: Proption Method: 60 is 48% of what number? 60 is 48% of what number? 60 is the part; 48 is the percent; the base is what is missing. Step 1: Set up proportion: 60/n = 48/100 Step 2: Cross Multiply 6,000 = 48n Step 3: Divide to Solve Proportion n = 125 60 is 48% of 125 How do we calculate discounts and bonuses? To calculate a discount or bonus, you need to find how much of a percent of the whole the discount is, and then add or subtract that amount from the original number. Calcualte The Discount: The regular price of a pair of shorts is $40.00. During a sale, the store gives a discount of 25%. How much will the price of the shorts be? Step 1: Find 25 % 94 $40 40 x .25 or 40 x 25/100 = 10.00 Step 2: Subtract the discount from the original prince. 40.00-10.00 = 30.00 The shorts will cost you $30 Claculate The Bonus: Ms. Smith earns $50 for teaching Saturday School. This week Principal Neering is giving Ms, Smith a 25% bonus. How much money will she make this week? Step 1: Find 25% of 50 50 x .25 or 25/100 = 25.00 Step 2: Add the bonus to the original amount. 50.00 + 25.00 = 75.00 Ms. Smith will make $75 this week. Solve: 30% of 45 = w w = 13.5 Solve: 55% of w = 220 w = 400 Solve: w of 300 = 81 w = 27% Solve: 150% of w = 450 w = 300 Solve: 40% of w = 120 w = 300 Solve: w of 8 = 640 w = 80 Solve: 120% of w = 450 w = 375 Review Of Rates, Ratios, Proportions, And Percents