Question

Learning task 3:Solve the following problem using the 4-step plan. Use the concept of GCF or LCM in each problem. Write your answer in your notebook. ​

Answer 1

Answer:

z1.35

2.398

3.540

Step-by-step explanation:

Answer 2

The answers are 124, 28 and 12.

Given:

Question 1

• Number of students = 8,10,12
• Chocolate bars left each time = 4

Question 2

• Number of boys = 117
• Number of girls = 135

Question 3

• Remainder when there are 28 books = 4
• Remainder when there are 39 books = 3

To find:

The smallest number of chocolates

Number of groups that can be formed with students

Largest possible number of students

Solution:

• Let the number of chocolates in the box be x.
• Therefore, the number of chocolates without the remainder = x - 4
• Hence x - 4 is a multiple of 8,10,12.
• To get the smallest number of chocolates, ie. the smallest x, x - 4 must be the LCM of 8,10,12 which is 120.

$x - 4 =120\\x=124$

Therefore the smallest number of chocolates is 124.

• Each group has an equal number of members
• Hence the number of students in each group must be a factor of both 117 and 135.
• Hence the number of students will be the HCF of 117 and 135 which is 9.
• Therefore the number of groups $\frac{117}{9}+\frac{135}{9} = 28$

Hence the number of groups is 28.

• Books divided among students when 28 books were there                $= 28-4=24$
• Books divided among students when 39 books were there$= 39-3=36$      
• Hence the number of students must be a factor of both 24 and 36
• Therefore the largest number of students will be the HCF of 24 and 36 which is 12

The largest number of students is 12.                        

#SPJ3