Math 5

MATHEMATICS 8 UNIT 5 Ratio Three-Term Ratios Equivalent Ratios and Proportion Rate Comparing Unit Rates/Prices

RATIO A ratio is a comparison of numbers with the same units. It is written as follows:

term

1:2

term

This symbol means “compared to” This ratio would be read “one compared to two”

RATIOS AND FRACTIONS Ratios can also be written as fractions

1 1:2 = 2

The first term of the ratio becomes the numerator of the fraction. The second term of the fraction becomes the denominator of the fraction. This also works in reverse to create a ratio from a fraction.

THREE TERM RATIO A three term ratio is simply a ratio with three terms.

term

1:2:4

term

term This ratio is read “one compared to two compared to four.”

EQUIVALENT RATIOS As with fractions, any time you multiply all the terms of a ratio by the same number, you produce an equivalent ratio.

x2

2:3 = 4:6 x2 This also works with division

EQUIVALENT RATIOS AND PROPORTIONS You can use equivalent ratios to help you solve proportion questions.

Example 1

X 5 = 6 18 x3

Remember: Whatever you do to the bottom, you have to do to the top. Whatever you do to the top, you have to do to the bottom. Compare the corresponding parts of each fractions and look for relationships. Five will not divide into X but six will divide into eighteen. 6 must be multiplied by 3 to get 18. Since you multiplied the bottom number by 3, you must also multiply the top number by 3.

5 6

=

15 18

Example 2 x4

2:5 = X:20 x4

2:5 = 8:20

RATE A RATE IS A COMPARISON OF TWO NUMBERS WITH DIFFERENT UNITS A RATE IS USUALLY WRITTEN AS A UNIT RATE IN WHICH THE SECOND TERM REPRESENTS 1 UNIT

90 km / hr Kilometres (distance)

Hours (time)

Different Units

At this rate, an object will travel 90 km in 1 hour

RATE RATE FOR 1

Example 1: A case of 24 Pepsi on sale for $4.99. How much does each can of Pepsi cost?

$4.99 = 499 cents

499 cents/ 24 cans ? cents / 1 can

divide by 24 to get the cost of one can of Pepsi

499 : 24 = ? : 1 divide by 24 to get one can of Pepsi

499 cents divided by 24 cans of Pepsi = 20.79 cents / can

499 : 24 = 20.79 : 1 Each can of Pepsi costs 20.79 cents

Example 2: You make $100 to work an 8 hour shift. How much do you make an hour? Quick Answer: Divide the $100 by the number of hours to find your hourly rate of pay. divided by

100 / 8 = 12.50 You make $12.50 / hr

SCALE DRAWINGS SCALE DRAWINGS ARE USED WHEN IT IS IMPOSSIBLE TO DRAW SOMETHING ON PAPER BECAUSE OF ITS SIZE, EITHER LARGE OR SMALL

Every scale drawing, like a blueprint or map, has a scale, which is a ratio comparing the length of the drawing on paper compared to the length of the actual object in real life.

The scale on a drawing of a crocodile is 1 : 60 measured in centimetres. The crocodile is 10 cm long on paper. How long is the actual crocodile?

1 : 60 = 10 : ? actual measurements of length

scale

1 : 60 = 10 : ? paper

real life

paper

real life

x 10

1cm : 60cm = 10cm : ?cm x 10

60 cm x 10 = 600 cm

1cm : 60cm = 10cm : 600cm The crocodile is 600 cm in real life

THE METRIC LADDER KILOMETRES (km) HECTOMETRES (hm) THE DECIMAL MOVES ONE PLACE TO THE LEFT FOR EVERY STEP YOU MOVE UP THE METRIC LADDER

DECAMETRES (dam) METRES (m) DECIMETRES (dm) CENTIMETRES (cm) MILLIMETRES (mm)

THE DECIMAL MOVES ONE PLACE TO THE RIGHT FOR EVERY STEP YOU MOVE DOWN THE METRIC LADDER