N2-G123 Ratios

Ratio compares two or more quantities.

            Symbol of ratio is :     

Ratio of quantity A to quantity B s written as     

                  A : B                                                    

** Ratio has no unit of measure

Example

Write the ratio 200:  250 in its simplest form

                  200 : 250

                  20÷5 : 25 ÷ 5

                      4 : 5

                  

                  a : b: c => a: b , b : c

Equivalent Ratios

Example

                       4 : 10 

                = 4 _÷2 : 10_÷2

                =     2 : 5

4 : 10 and 2 : 5 are equivalent ratios.

Ratio in its simplest form

Example

Write 8 : 12: 36 in its simplest form

Step: Find the common factors for the given numbers and reduce

            8 _÷4 : 12_÷4 : 36_÷4

            2 : 3 : 9

       

Example: Write the ratio 200:  250 in its simplest form

                    200 : 250

                  20÷5 : 25 ÷ 5

                        4 : 5

Example

The ratio of the number of tables to the number of chairs is 1 : 4 in the restaurant. There are 6 tables, how many chairs are there?

Step 1 : Write the ratio and number of tables

T  C

1 : 4

Step 2 : Write the number of tables on both side of the ratio and multiply

T   C

1  : 4

                    x 4   x4

= 4  : 16

Step3 : Answer 

There are 16 chairs

Ratio with different Unit of Measure (UOM)

The UOM must be the same when comparing two of more quantities

Example:

John has $1 and Sally has 80cts as their daily allowance. What is the ratio of their allowance?

Step 1 : Convert the amount to the same unit (of the 'smaller' UOM)

$1 = 100cts

Step 2 :  Write the ratio and reduce the the lowest term

100 : 80

₅  10 : 8 ₄

      5 : 4

Step 3 : Write the Answer

The ration is 5 : 4

Ratio involving Fractions and Decimals

Example

Express the following ratios in its simplest form.

  1.2 : 3 

Step 1 : Multiply 10 to both side (to remove the decimal)

x10.  1.2. :   3 x 10

12 :  30

Step 2 : Reduce the simplest term

<< divide by 6 for both side >>

    2    12 :  30     5        

The ratio is 2 :  5

Example

Express the following ratios in its simplest form.

b.         1 ¾.  :    2 ½    

Step 1: Change both to improper fractions

    7  :  5

             4     2

Step 2 :  Make both side to have the same denominator

<< multiply 2 , by 2 >>

    7  :  5  x 2

             4     2  x 2

    7  :  10  

             4      4 

Step 3 : Write the numerators as the ratio

7 : 10

Connecting Ratio with Fraction

For a ratio   A : B, the 'total number of parts' = A + B

Thus in fraction form,    A's part is A / A+B

              B's part is B / A+B 

Example

There are 10 girls and 15 boys.

The ratio of the number of girls to the number of boys = 

10 : 15    or    2   :   3

The total part = 2 + 3 = 5

=>  Number of girls = 2/3 of number of boys

=>  Number of girls = 2/5 of the total

=>  Number of boys = 3/2 of number of girls

=>  Number of boys = 3/5 of the total.

Example

Abby and Bobby have 10 oranges altogether. 

The oranges are to be divided in the ratio of 3 : 2

How many oranges will each of them get?

Step 1: Find the total parts 

Total = 3 + 2 = 5

Step 2 : Compute their fraction's

  Abby = 3/5 , Bobby = 2/5

Step 3 : Compute by multiplying total quantity with the fractions

Abby has 3/5 x 10 = 6 oranges

Bobby has 2/5 x 10 = 4 oranges

Practice

1.  Express the following ratios in its simplest form.

(a) 4 :  20 [1 : 5]

(b) 35 : 14 [7 : 2] 

(c)    64 : 56 : 16 [8 : 7 : 2] 

2.   Express the following ratios in its simplest form.

a.   ⅚ kg :  2 kg                        [5 : 12 ]

b.  1.6 cm : 4 mm                     [4 : 1 ]

c.  1 ½ hr : 20 mins                  [9 : 2 ]

d.  250 ml : 1 litre                     [1 : 4 ]

3.  Mary and Andy share a pizza in the ratio of 1 : 2. Andy gets 4 slices of the pizza. How many slices does Mary get? [2]

4.  Alice, Betty and Coby share their marbles in the ratio of 2 : 3 : 5. Find the amount each gets for each of the marbles.

a.  420 (b) 70                   [a. 84, 126, 210     b. 14, 21, 35]

R1 - Ratio Practice

(Part 1) TEACHING(15-20mins)                                           

1. Ratio, equivalent ratio, dividing a qty in a given ratio

(Part2) PRACTICE (35-60mins)

1. 18 : 24 =        : 4

2. 5 : 3 : 8 = 35 :        : 56

3.  1  :  1 =  3  : ____

     4     6

4. 0.6 :  5 = 24  : _____

             8

5.  ¾ : 1 ½ =  _____ : ______

6.  200g : 1kg = _______ : _______

7.  15 seconds :  30 mins :  1 hour  =  _______  :  ______  :  ______

8.  A: B = 3 :2  , A : C = 3 : 8

            B  :  C =  ______ :  ______

9.  A  :   B =  7  :  2 ,   B  :  C = 5  :  1

           A  :  B  :  C  =  ______  : _______  : _______

10.  A  :  B  =  6  :  7,  B  :  C  = 4  :  5

           A  :  B  :  C  =  ______  : _______  : _______

(II) Word Problems (25- 45 mins)                     

11. Ray and Carla shared a packet of sweets in the ratio of 2 : 7. IF there were 45 sweets in the packet, how many sweets did Carly receive?

12. A piece of rod was cut into 2 pieces in the ratio of 3 : 5. If the length of the shorter piece was 18 cm, find the length of the original piece of rod.

13. 2/5 of Ann’s saving is as much as ¼ of Joel’s saving. Find the ratio of Ann’s saving to Joel’s saving.

14.  Chan and David shared some marbles. Chan had 2/7 of the number of marbles David had. What was the ratio of the total number of marbles the boys had to the number of stickers Chan had to the number of marbles David had? (18/9/p1/s)

(1) 9:2:7 

(2) 9:7:2 

(3) 7:2:5 

(4) 7:5:2 

15.  Mat and Minah had some cookies in the ratio 5 : 2. Mat ate 38 cookies and Minah made another 43 cookies. Then Mat and Minah had the same number of cookies. How many cookies did Minah have at first? (27/p1/s)

For question 16 and 17.
The ratio of Anson's savings to Billy’s savings became 3:11 after Anson gave 1/10 of his savings to Billy. Both later spent the same amount of money at a book fair. In the end, the ratio of Anson’s savings to Billy’s savings became 1:9 and Billy had $264 more than Anson. (11/p2/s)

16. What was the ratio of Anson's savings to Billy’s savings at first?

17. How much savings did Anson had at first?

Extra
Ratio Word Problems Method

I. Solve 1-steps Word Problems 
II. Word Problems: 2 sets of ratio 
III. Word Problems: Overlap/Common-Part Ratio 

1.  Kenny’s mass is 7/3 of Lionel’s mass. The total mass of the boy is 85 kg.
(a) Find the ratio of Kenny’s mass to Lionel mass.

(b) What fraction of Kenny’s mass is Lionel’s mass?

(c) what fraction of the total mass of the boys is Kenny mass?

(d) Find Kenny’s mass.

2.*  15 mangoes cost $10. Three brothers shared the cost of 60 mangoes in the ratio 1 : 2 : 2. What was the cost for the smallest share?

3.*  Bobby has a number of 10c, 20c and 50c coins in the ratio 5 : 2 : 1. The total value of all the coins is $166. What is the total value of the 20c coin?

4.*  There are three types of cookies in a box. The ratio of the number walnut cookies to chocolate cookies is 4  :  5. The ratio of the number of raisin cookies to the total number of walnut and chocolate is 5 : 6.

What fraction of the cookies in the box are chocolate cookies?

5.*  Zoe drew three circles to form a figure. The areas of the circles were in the ratio 1 : 4: 16. She then shaded some parts of the figure as shown. What fraction of the figure was 

shaded?

6*. In the figure below, PQRS is a rectangle and QRT is a right-angled triangle with sides measuring 30 cm, 40 cm and 50 cm. The perimeter of the shaded part is 174 cm.

What is the ratio of the area of the triangle to the area of the shaded part? Give your answer in the simplest form.

TheMathbooklets Content Page 

Practice Content Page 

Ratio Answer Keys

1.         3

2.         21

3.         2

4.         25

5.         1:2

6.         1:5

7.         1:120:240

8.         1:4

9.         35:10:2

10.      24:28:35

11.      10

12.      48cm

13.      8:5

14.

15.      54