RATES, RATIOS and PROPORTIONS

RATES, RATIOS and PROPORTIONS RATIOS A ratio compares the magnitude (size) of two quantities. There are two types of ratios: partpart and part-whole. RATIOS A ratio compares the magnitude (size) of two quantities. There are two types of ratios: partpart and part-whole.

Ex 1: If there are seven boys and twelve girls in a class, then the ratio of boys to girls can be expressed as 7 to 12, , or 7:12 (part-part ratio). RATIOS A ratio compares the magnitude (size) of two quantities. There are two types of ratios: part-part and part-whole. Ex 1: If there are seven boys and twelve girls in a class, then the ratio of boys to girls can be expressed as 7 to 12, , or 7:12 (partpart ratio). Ex 2: Suppose there is a wall made up of twelve blocks, five

white blocks and seven red blocks. The ratio of white blocks to the total number of blocks is , which is a part-whole ratio. The ratio of white blocks to red blocks is , which is a part-part ratio. RATES When the quantities being compared have different dimensions (units), then the ratio is called a rate. RATES

When the quantities being compared have different dimensions (units), then the ratio is called a rate. Ex 1: A phone company charges \$0.84 for 7 minutes of long distance. The rate is \$ 0.84/7 minutes, which is equal to \$0.12 per minute. RATES When the quantities being compared have different dimensions (units), then the ratio is called a rate.

Ex 1: A phone company charges \$0.84 for 7 minutes of long distance. The rate is \$ 0.84/7 minutes, which is equal to \$0.12 per minute. Ex 2: A student reads 10 pages in 8 minutes. This rate is 10 pages/8 minutes, which is equal to 5 pages per 4 minutes. RATES When the quantities being compared have different dimensions (units), then the ratio is called a rate.

Ex 1: A phone company charges \$0.84 for 7 minutes of long distance. The rate is \$ 0.84/7 minutes, which is equal to \$0.12 per minute. Ex 2: A student reads 10 pages in 8 minutes. This rate is 10 pages/8 minutes, which is equal to 5 pages per 4 minutes. Ex 3: If a 12-ounce box of cereal sells for \$2.40, and a 16-ounce box sells for \$2.88, which is the better buy? The unit rate of the first box is \$0.20/ounce (\$2.40/12 ounces), and the unit rate of the second box is \$0.18/ounce (\$ 2.88/16 ounces). Therefore, the second box is a better buy.

PROPORTIONS A proportion is a statement of equality between two ratios or rates. PROPORTIONS A proportion is a statement of equality between two ratios or rates. In a proportion, if then ad = bcd = bd = bcc.

PROPORTIONS Ex: A person drives 126 miles in 3 hours. At the same speed (rate), how far (x) would the driver travel in 4 hours? The proportion can be written as PROPORTIONS Multiplying across by the multiplicative inverse yields:

( or x = (4)(126)/(3) = 168 miles.(126)/(3) = 168 miles. In summary rate and proportion, together with ratio, are used for solving many real-world problems that involve comparing different quantities. Lets take a closer look at rates and ratios Recall that rates are ratios in which the

quantities being compared have different units (and thus, different dimensions). Lets take a closer look at rates and ratios (contd) Recall that rates are ratios in which the quantities being compared have different units (and thus, different dimensions). It follows that ratios must compare quantities with the same units (and thus, same

dimensions). Lets take a closer look at rates and ratios (contd) It follows that ratios must compare quantities with the same units (and thus, same dimensions). Therefore, dimensions on ratios cancel each other out: no dimension

Lets take a closer look at rates and ratios (contd) Therefore, dimensions on ratios cancel each other out: no dimension RATIOS have NO DIMENSIONS. In Physics

many physical quantities are RATIOS. In Physics many physical quantities are RATIOS. RATIOS in Physics are so important, they have (as a class) a name: adimensional quantities. In Physics many physical quantities are RATIOS. RATIOS in Physics are so important, they have

(as a class) a name: adimensional quantities. This name comes from a- + dimensional (without) + dimensional Adimensional Quantities The prefix a- means without, such as in adiabatic (without change in pressure); asymmetric (without symmetry) and asexual (without gender).

Adimensional Quantities The prefix a- means without, such as in adiabatic (without change in pressure); asymmetric (without symmetry) and asexual (without gender). The suffix -less also means without, and can be used in the same way: dimensionless, regardless and genderless.

The Brad Pitts and Angelina Jolies of Physics Famous rates: Density The Brad Pitts and Angelina Jolies of Physics Famous rates: Density Speed

The Brad Pitts and Angelina Jolies of Physics Famous rates: Density Speed Velocity The Brad Pitts and Angelina Jolies of Physics

Famous rates: Density Speed Velocity Acceleration The Brad Pitts and Angelina Jolies of Physics Famous rates: Density

Speed Velocity Acceleration Field The Brad Pitts and Angelina Jolies of Physics Famous rates: Density Speed

Velocity Acceleration Field Potential The Brad Pitts and Angelina Jolies of Physics Famous rates: Density Speed

Velocity Acceleration Field Potential Coefficients of expansion The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1. Trigonometric functions (sin, cos and tan)

The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1. Trigonometric functions (sin, cos and tan) 2. Magnification (glasses, lenses and mirrors) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities:

1. Trigonometric functions (sin, cos and tan) 2. Magnification (glasses, lenses and mirrors) 3. Mach number (objects speed relative to sounds) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1. 2. 3.

4. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities:

1. 2. 3. 4. 5. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle)

Friction coefficients The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1. 2. 3. 4. 5.

6. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle) Friction coefficients Albedo (percentage of light reflected by celestial bodies) The Brad Pitts and Angelina Jolies of

Physics Famous adimensional quantities: 1. 2. 3. 4. 5. 6. Trigonometric functions (sin, cos and tan)

Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle) Friction coefficients Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening ) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities:

1. 2. 3. 4. 5. 6. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds)

The number (circumference to diameter ratio for a circle) Friction coefficients Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening ) 8. Mechanical advantages The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1.

2. 3. 4. 5. 6. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle)

Friction coefficients Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening ) 8. Mechanical advantages 9. Efficiency (of simple machines) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities:

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. Trigonometric functions (sin, cos and tan) Magnification (glasses, lenses and mirrors) Mach number (objects speed relative to sounds) The number (circumference to diameter ratio for a circle) Friction coefficients Albedo (percentage of light reflected by celestial bodies) Oblateness (also called ellipticity and flattening ) Mechanical advantages

Efficiency (of simple machines) Structural (load) efficiency The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 1. Trigonometric functions (sin, cos and tan) 2. Magnification (glasses, lenses and mirrors) 3. Mach number (objects speed relative to sounds) 4. The number (circumference to diameter ratio for a circle)

5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines) 10. Structural (load) efficiency 11. Opacity/transparency of surfaces The Brad Pitts and Angelina Jolies of Physics

Famous adimensional quantities: 1. Trigonometric functions (sin, cos and tan) 2. Magnification (glasses, lenses and mirrors) 3. Mach number (objects speed relative to sounds) 4. The number (circumference to diameter ratio for a circle) 5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines)

10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 2. Magnification (glasses, lenses and mirrors) 3. Mach number (objects speed relative to sounds) 4. The number (circumference to diameter ratio for a circle)

5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines) 10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) 13. Conversion coefficients

The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 3. Mach number (objects speed relative to sounds) 4. The number (circumference to diameter ratio for a circle) 5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines)

10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) 13. Conversion coefficients 14. Percentage, percent relative and relative errors The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 4. The number (circumference to diameter ratio for a circle)

5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines) 10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) 13. Conversion coefficients 14. Percentage, percent relative and relative errors

15. Indexes of refraction, reflection and absorption The Brad Pitts and Angelina Jolies of Physics Famous adimensional quantities: 5. Friction coefficients 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines)

10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) 13. Conversion coefficients 14. Percentage, percent relative and relative errors 15. Indexes of refraction, reflection and absorption 16. pH The Brad Pitts and Angelina Jolies of Physics

Famous adimensional quantities: 6. Albedo (percentage of light reflected by celestial bodies) 7. Oblateness (also called ellipticity and flattening) 8. Mechanical advantages 9. Efficiency (of simple machines) 10. Structural (load) efficiency 11. Opacity/transparency of surfaces 12. Eccentricity (ratio of large to small axes of an ellipse) 13. Conversion coefficients 14. Percentage, percent relative and relative errors

15. Indexes of refraction, reflection and absorption 16. pH 17. Decibel ADIMENSIONAL QUANTITIES HAVE NO UNITS!!! NONE ZERO ZILCH NADA

THE END Lilian Wehner

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