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DemingEarly College High SchoolUnit 1.0 Arithmetic 1.3 Percentages & Ratios
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems The word percent comes from the Latin phrase for “per one hundred”. A percent is a way of writing out a fraction. That is good because it is a fraction with a denominator that is always 100.Thus, 65% =
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems To convert a fraction to a percent, the denominator is written as 100.For example: In converting a percent to a fraction, the percent is written with a denominator of 100., and the result is simplified.For example:
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems 1. How do you write 4/5 as a percent? 2. How do you write 157% as a decimal?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems 1. How do you write 4/5 as a percent? 2. How do you write 157% as a decimal?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems 3. How do you write 95/10 as a percent? 4. How do you write 20% as a fraction?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems 3. How do you write 95/10 as a percent? 4. How do you write 20% as a fraction?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems The basic percent equation is the following:is= %of 100The placement of each variable depends on what the question asks.
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems Example 1 - Find 40% of 80.Basically, the problem is asking, “What is 40% of 80?” The 40% is the percent, and 80 is the number to find the percent “of”. The equation is:Solving the equation by cross multiplication, the problem becomes 100x = 80*40=3200. Solving for x gives x = 32.
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100Example 2 – What percent of 100 is 20?The 20 fills in the “is” portion, while 100 fills in the “of”. The question asks for the percent, so that will be the unknown x. The following equation is set up:Cross-multiplying gives the equation 100x = 20 * 100 =2000.Solving for x gives the answer of 20%
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100Example 3 – 30% of what number is 30?The following equation uses the clues and numbers in the problem: Cross-multiplying results in the equation 30(100) = 30x.Solving for x gives the answer x = 100.
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100 1. What is 37.5% of 80? 2. 24 is 120% of what number?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100 1. What is 37.5% of 80? 2. 24 is 120% of what number?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100 3. What percent of $8 is $2? 4. 36 is 40% of what number?
Unit 1.0 Arithmetic 1.3 Percent 1.3.1 Percent Problems is = %of 100 3. What percent of $8 is $2? 4. 36 is 40% of what number?
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems A ratio compares the size of one group to the size of another. For example there may be a room with 4 tables and 24 chairs. The ratio of tables to chairs is 4:24. Such ratios behave like fractions in that both sides of the ratio can be multiplied or divided by the same number and the ratio does not change. 4:24 = 2:12 = 1:6
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems One quantity is proportional to another quantity if the first quantity is always some multiple of the second.For instance, the distance travelled in five hours is always five times the average speed travelled in those five hours.The distance is proportional to the speed.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems One quantity is inversely proportional to another quantity if the first quantity is divided by the second quantity.The time it takes to travel one hundred miles will be given by 100 miles divided by the average speed travelled over those 100 miles.The time is inversely proportional to the speed.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems When dealing with word problems, there is no fixed series of steps to follow, but there are some general guidelines to use. It is important that the quantity to be found is identified. Then, it can be determined how the given values can be used and manipulated to find the final answer.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems Example 1: George wants to travel to visit Fred, who lives one hundred and fifty miles away. If he can drive at fifty miles per hour, how long will his trip take?The quantity to find is the time of the trip.The time of the trip is the distance to travel divided by the speed to be travelled.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems Example 2: Sylvia wishes to paint a wall that measures twenty feet wide by eight feet high. It costs ten cents to paint one square foot. How much money does Sylvia need for paint?The dimensions of the wall are 20 feet wide and 8 feet high. Since the area of a rectangle is length times width, the area of the wall is 160 s.f.Cost is equal to area times unit price:
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems 1. A 5-foot piece of copper wire cost $58.20. What is the price per inch? 2. Find the number of apartments per floor if the building has 69 floors and 759 apartments.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems 1. A 5-foot piece of copper wire cost $58.20. What is the price per inch? 2. Find the number of apartments per floor if the building has 69 floors and 759 apartments.
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems 3. Jack did 6,747 in 173 days. On the average how many push-ups did he do per day? 4. Which is a better buy? 4-pack of lottery tickets for $19.73 or a 5-pack for $24.28?
Unit 1.0 Arithmetic 1.3 Percent 1.3.2 Rate, Percent, and Measurement Problems 3. Jack did 6,747 in 173 days. On the average how many push-ups did he do per day? 4. Which is a better buy? 4-pack of lottery tickets for $19.73 or a 5-pack for $24.28?
