Showing posts with label equal fractions. Show all posts
Showing posts with label equal fractions. Show all posts

Sunday, 4 November 2018

F4-L10 Fractions Practice : Division and Word Problems


(Part 1) Revise (~15mins)                                            Start Time : 

2. Solving 2-step word problems

(Part2) Practice (~50mins)

(I) Multiplication/Division (~15 mins)                               Working
1.      2 ÷                           2 .        2 x 1                                       
                3                                            3

3.      6 ÷                            4.         6 x 4               
               5                                              5

5.      12 ÷                          6.         12 x 6
                 7                                              7        

7.      1 ÷ 3                             8.          3
         2    4                                          2    4


9.      5 ÷ 7                             10.   5 ÷ 7
         6  12                                     6   12


11.    ÷ 8.                          12.  7 ÷ 14
         5    15                                18     15
13.     20 ÷ 6
                  5

(II) Word Problems/PSLE (~35 mins)                   Start Time:                             
14.         Mariam has a piece of rope 10 m long.
She cuts them into equal pieces, each 7/6 m long, except for the last rope which
is less than 7/6 m long. What is the length of the last rope? (6/p2/18f) 

15.         A string was 3m long. Zoe cut it into pieces of length 1/9 m long each. How many pieces did she get?

16.         The product of two numbers is 4/5. If one of the numbers is 5/6, what is the other number?

17.         4 cakes were shared among a group of children. Each child got 2/9 of a cake. How many children were there in the group?
18.         Zack spent 1/3 of his money on food. He then used 1/4 of the remainder to buy 3 breads. What fraction of his money did he spend on each bread?

19.         Find the value of 1/6 ÷ 4/9. Give your answer in the simplest form. (16/p1/18s)

20*.       Find the value of 4/5 ÷ 12. Give your answer as a fraction in the simplest form.

21.         The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether? (7/p2/18s)

22.         A fruit seller had 33 more watermelons than papayas. After he sold 1/3 of the watermelons and 4/5 of the papayas, he had 57 more watermelons than papayas. How many papayas did he have at first? (10/p2/18s)
Extra Practices
 (1)    'Equal/Same' Word Problems  (optional) 

 (2)    General Word Problems  (optional)
1.     35 ÷ 5
                7

2.   45 ÷    12
                  5

3.  Ken bought 24kg of peanut. He sold 3/8 of it and packed the remaining peanut into smaller packets of 4/5 kg each.
            a. How many packets of peanut are packed? 
            b. How much peanut was left unpacked?

4.         Jane has a number of happy face stickers in three colours: yellow, orange and red. 2/7 of the stickers are yellow. The number of yellow stickers is twice the number of orange stickers. What fraction of the stickers are red?

5.         A fruit seller had 33 more watermelons than papayas. After he sold 13 of the watermelons and 4/5 of the papayas, he had 57 more watermelons than papayas. How many papayas did he have at first?

6* A shop had a number of computers for sales. After selling 32 of them in the morning and 5/8 of the remainder in the afternoon, it was left with ¼ of the computers. How many computers were sold altogether?

7.         The fraction 2/ lies between 1/8 and 1/9. Find the missing whole number in the box. 

8.         3/5 of the children in the playgroup were boys. The instructor divided the boys equally such that each group of boys had 1/10 of the number of children in the playgroup. The instructor then divided the girls equally into groups such that each group of girls had 1/5 of the number of children in the playgroup.        
            (a) Find the number of groups of boys and girls
            (b)  If there were 16 girls in the class, how many boys were there in the group?

9.         Every month, Peter spends 1/3 of his salary, save 3/8 of the remainder and shares the rest of his salary equally among his father, mother and sister. 
            a.  What fraction of his salary does each of them receive?
            b.  If his salary is $5400, how much does he give his sister each month?
Answer Keys
1.  6
2.  2/3
3.  15
4.  4 4/5
5.  14
6.  10 2/7
7.  2/3
8.  3/8
9.  2 11/12
10.  1 3/7
11.  3/4
12.  5/12
13.  16 2/3
14.  4/7 m
15.  27
16.  24/25
17.  18
18.  1/18
19.  3/8
20.  1/15
21.  
22.  120

Monday, 1 October 2018

F7 Fractions : Equal or Same Fractions


‘EQUAL/SAME’FRACTIONS
(a) Sentence Construction

Words Problems with ‘equaling fractions’ are usually constructed as 
              
Words such as SAME or EQUAL are good clues.

(b)  Relationship between the numbers in the sentence.
There are two main objects(actors) each associated with a fraction. The Units of the respective fractions are equal

(c)  Drawing Model for EQUAL/SAME
Example: 
¾ of Ali’s money is the same as 9/11 of Mary’s money
   ->¾ of Ali’s money (assume it is $x) is the same as 9/11 of Mary‘s money(also $x).
Using Model,
                      
-> 3/4 of Ali’s money(assume it is $x)  is the same as 9/11 of Mary‘s money(also $x).

Model Method for ‘EQUAL/SAME’ Fractions Word Problems

Step 1:  Circle/Underline keywords. Write Objects / Who
Step2aDraw for each object: ‘Equal portion’ of  numerator, and denominators as total units
Step2bEqual numerator’s to same portion of U <Fraction values are unchanged)

Step 3:  Solve

Example:  
 1/4 of the boys is equal to 2/5 of the girls. There are 10 girls. How many boys are there?


Step 1:  Circle/Underline keywords. Write Objects / Who
            Boys     
Girls

Step2aDraw for each object: ‘Equal portion’ of  numerator, and denominators as total units

              

Step2bEqual numerator’s to same portion of U <Fraction values are unchanged)    
numerators: Boy = 1, and girl = 2.  Equate numerator-> Boy = 1x2 / 4x2 = 2/8  

            Girls -> 2/5, Boys -> 2/8
             

Step 3:  Solve
              
          There are 10 girls. 
               5U = 10, u = 2
         Boys -> 8u = 8 x 2 = 16
    There are 16 boys

Example
¾ of Ali’s money is the same as 9/11 of Mary’s money. There have $46 altogether. How much does each of them have?

<< Read the sentence carefully and spot the word patterns>>


Step 1:  Circle/Underline keywords. Write Objects / Who
            Ali     
            Mary

Step2aDraw for each object: ‘Equal portion’ of  numerator, and denominators as total units
            
Step2bEqual numerator’s to same portion of U <Fraction values are unchanged)   
Ali = 3, and Mary = 9.  Ali = 3x3 / 3x4 = 9/12
 

Step 3:  Solve
             
 They have $46 
      11U + 12U = 23U
      23U = 46
      U = 2
            Ali has 12x2 = $24. 
            Mary has 11x2 = $22.

Example:
3/5 of John’s marbles is the equal to 2/7 of Harry’s. John has 30 marbles. How many does Harry have?

Step 1:  Circle/Underline keywords. Write Objects / Who
            John
            Harry

Step2aDraw for each object: ‘Equal portion’ of  numerator, and denominators as total units
           

Step2bEqual numerator’s to same portion of U <Fraction values are unchanged)
John = 3, Harry = 2. John’s fraction = 3x2/5x2 =6/10, Harry’s = 2x3/7x3= 6/21
   

Step 3:  Solve
            
            John has 30 marbles
            10U = 30
               U = 3 
            Harry has 3 x 21 = 63 marbles.


Example
Linda bought some white sugar and some brown sugar for baking a cake. She used an equal amount of white and brown sugar. She had ¾ of the white sugar and 3/8 of brown sugar left. What fraction of the sugar which Linda bought was used for baking?
Step 1:  Circle/Underline keywords. Write Objects / Who
            White   
Brown
Step2a: Draw for each object:Equal portion’ of  numerator, and denominators as total units. 
For this question, the used portion is the ‘equal’ portion -> ¼ for white sugar and 5/8 for brown sugar
          
Step2b: Equal numerator’s to same portion of U <Fraction values are unchanged)
numerators: White = 1, and brown = 5.  Equate numerator-> white = 1 x 5 

            White -> 5/20, Brown -> 5/8
           
Step 3:  Solve
Total portion = 20 + 8 = 28
Used portion = 5 + 5
Fraction used = 10/28 = 5/14
      ~~~~ END ~~~~ :)