General Mathematics

General MathematicsADE 101LECTURE No. 6 Ratio, Rate and ProportionTodays ObjectivesStudents and Teachers will be able toUnderstand What is Ratio, Rate & Proportion?Make the difference between Ratio, Rate and ProportionSolve the Sums Involving Ratio, Rate & ProportionKNOWLEDGE TEST What is a fraction?A FractionA RatioDifference between Fraction and RatioFraction shows a part of same thing.Difference between Fraction and RatioRatio is the relationship between two different thingsRatiosare the comparison of two or more numbers.Symbol of RatioRepresentation of a RatioThe ratio of 3 boys to 5 girls can be written as:

c)

a) 3 to 5b) 3: 5

Which ratio shows the ratio of 2 fish to 3 bear?

ABCDE

Which ratio shows the ratio of 1 soccer ball to 3 basketball?

ABCDE

Which ratio shows the ratio of 3 butterflies to 1 apple?

ABC DERatios can show comparisons between:part to partred to green 1 to 2green to red 2 to 1Ratios can show comparisons between:part to wholered to whole 1 to 3green to whole 2 to 3Ratios can show comparisons between:whole to partwhole to red 3 to 1whole to green 3 to 2

Compare octagon to all shapes1 to 81 : 81/8

Compare all shapes to trapezoid8 to 18 : 18/1

Compare pentagons to hexagons2 to 32 : 32/3A ratio in fraction form can be expressed in simplest form by dividing the numerator and denominator by a common factor.

8 8=

3 3=

1 girl to every 2 boys2 girls to every 4 boys3 girls to every 6 boys4 girls to every 8 boysgirls : boys = 4 : 8girls : boys = 3 : 6girls : boys = 2 : 4girls : boys = 1 : 2But the simplest ratio is still 1 : 2But the simplest ratio is still 1 : 2But the simplest ratio is still 1 : 2This is the simplest ratio is 1 : 2The dinner queueRatio of girls to boys?202 boys to every 1 girl4 boys to every 2 girls6 boys to every 3 girls8 boys to every 4 girlsboys : girls = 8 : 4boys : girls = 6 : 3boys : girls = 4 : 2boys : girls = 2 : 1But the simplest ratio is still 2 : 1But the simplest ratio is still 2 : 1But the simplest ratio is still 2 : 1This is the simplest ratio is 2 : 1The dinner queueRatio of Boys to girls? 21Does order matter?There are 20 boys and 10 girls in 6D. a) girls : boys = 2 : 1b) boys : girls = 2 : 1

ORDER MATTERS!Be careful what you write!boys : girls = 2 : 1 means 2 boys to every girl girls : boys = 2 : 1 means 2 girls to every boy22Rate40 miles/hour 10 meters/second $12/day 5o games/year

Q. Is 90 m/9s is a rate?

Q. Is $60 /5h is a rate?

Speed of 1st car is 120 m/3 h and speed of 2nd car is 150 m/5h. Which one is going faster?To express a ratio as a rate per unit, write the ratio as a fraction and then divide the numerator by the denominator.395 miles in 5 hours

=79 miles per hourmileshours

mileshoursExpress each ratio as a rate.5 inches of rain in 30 days

=

inch of rain per day120 words in 3 minutes

=40 words per minute

wordsper minute 5 5Formula for Rate

Graph for rate Equal RatiosEqual ratios are like equivalent fractions. They name the same quantity.Equal RatiosExamples of Equal Ratios:

ProportionsTwo equal ratios form a proportion.Ratio and Proportion: Different Words!

Ratio: to every

Proportion: out of331 girl out of 32 girls out of 63 girls out of 94 girls out of 12Simplest proportion of girls is still 1 out of 3Simplest proportion of girls is still 1 out of 3Simplest proportion of girls is still 1 out of 3This is the simplest proportion of girls = 1 out of 3What proportion is girls?The dinner queue34What fraction is boys?Simplest proportion of boys?What fraction is boys?Simplest fraction of boys?What fraction is boys?Simplest fraction of boys? 4 / 66 / 98 / 12Simplest fraction of boys is still 2 / 3Simplest fraction of boys is still 2 / 3Simplest fraction of boys is still 2 / 3Simplest fraction of boys? This is the simplest fraction of boys = 2 / 3What fraction is boys?What fraction is boys?2 / 3The dinner queue35Proportion of boys?Simplest proportion of boys?Proportion of boys?Simplest proportion of boys?Proportion of boys?Simplest proportion of boys?Proportion of boys?4 boys out of 66 boys out of 98 boys out of 12Simplest proportion of boys is still 2 out of 3Simplest proportion of boys is still 2 out of 3Simplest proportion of boys is still 2 out of 3Simplest proportion of boys?This is the simplest proportion of boys = 2 out of 32 boys out of 3What proportion is boys?The dinner queue36Ratio, Proportion or Fraction?two out of five This is a

proportiontwo fifths This is a

fractionfour tenths This is a

fractionfour to every ten This is a

ratioten to every four This is a

ratiofour out of tenThis is a proportion4/10This is a

fraction4:10 This is a

ratio37Ratio, Proportion or Fraction?3 United fans to every 2 Rangers fans This is a

ratio9 girls out of 10 use soap This is a

proportion3 boys out of 10 use deodorant This is a

proportion38Ratio, Proportion or Fraction?3 out of 4 pizza-munchers love olives This is a

proportionHalf of all girls in 6D love History This is a fractionOne third of all road accidents involve drinking This is a fraction39ProportionsIn a proportion the product of the means is equal to product of the extremes.Proportions3 : 5 = 6 : 10ExtremesMeansProportions

MeansExtremes6 x 5 = 3 x 10 30 = 30ProportionsDetermine if the following are proportions.

1)

2)Proportions

3 x 60 = 5 x 36180 = 180Yes, it is a proportion.

4 x 15 = 8 x 860

64No, it is not a proportion.AssignmentQ. No. 1:In a class room there are 10 girls and 15 boys. What is the ratio of boys to girls?

Q. No. 2:A classroom has 30 students. There are 20 males. What is ratio of males to females?

Q. No. 3:A man earns $250 in a 5-day week. What is his pay for 3-day?

Q. No. 4:A man pays $600 rent for 3-months, what is the rental rate in dollars per month?Thank You