1 / 17

Understanding Proportions, Scale Drawings, and Percentages in Mathematics

This guide covers essential concepts in solving proportions, utilizing scale drawings, and converting between percents and decimals. A proportion is defined as an equation equating two ratios, which can be expressed in various forms. We'll explore how to set up proportions, solve them in different contexts, and apply them to real-life scenarios, such as calculating actual lengths from scale drawings. Additionally, we’ll discuss percent equations, enabling conversions between decimals and percentages for better mathematical understanding and problem-solving skills.

mikhail
Télécharger la présentation

Understanding Proportions, Scale Drawings, and Percentages in Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5-1 • Objective: Solving proportions

  2. An equation in which two ratios are equal is called a proportion. • A ratio is the comparison of two numbers written as a fraction. • A proportion can be written using colon notation like this a:b::c:d • Or as the more recognizable (and useable) equivalence of two fractions.

  3. Proportions • To set up a proportion think part/whole part part ______ _____ = whole whole If you can travel 120 miles on 6 gallons of gas, how far can you drive on 8 gallons of gas? (8)gas (6)gas ______ ______ x=160 6x=960 = (x) miles 120miles

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

  5. RATIOS & PROPORTIONS Find the missing numbers to make the following proportions. 10 10 9 9

  6. 5-2 • Objective: Solve proportions involving scale drawings and models

  7. SCALE DRAWINGS • A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.

  8. SCALE DRAWINGS USING PROPORTIONS EXAMPLE#1: ¼ in = 5 ft is a scale for a rock band’s concert stage. A. The scale length of the drum stand is 1 in. What is the actual length of the drum stand? Cross multiply. Divide by .25 .25 .25

  9. SCALE DRAWINGS USING PROPORTIONS Given a scale of .5 in = 4 ft, find the actual length for each scale length given. .5 .5 .5 .5

  10. 5-3 • Objective: Solve problems by using the percent equations

  11. PERCENTS & DECIMALS • Percent (%) means per hundred. • To change a decimal to a percent • Multiply the decimal by 100 • Write a percent sign after it Multiply the decimal by 100(move the decimal point 2 places to the right) Write a percent sign after it

  12. To change a percent to a decimal • Divide the percent by 100 • Omit the percent sign • Divide the percent by 100 (move decimal 2 places to the left) • Omit the percent sign

  13. PERCENTS AND DECIMALS Convert the following decimals to percents: E. 0.445 44.5% A. 0.15 15% 1.5% F. 0.1111 11.11% B. 0.015 0.5% 62.5% G. 0.005 C. 0.625 104.2% H. 1.042 D. 0.9 90%

  14. PERCENTS AND DECIMALS Convert the following percents to decimals: E. 1.5% 0.015 A. 23.45% 0.2345 0.25 F. 35% 0.35 B. 25% 0.00005 0.125 G. 0.005% C. 12.5% 3.1 H. 310% D. 45% 0.45

  15. The percent equation P r = 100 B Percent r (percentage) = 100 Base

  16. Figuring out what goes where? • Remember is/of • “is” will always be “P” • “of” will always be “B” What number is 15% of 10 What percent of 60 is 3 3 r P r = = 100 100 60 10

More Related