Lesson 6: Numbers Divisible by 11

 

A number is divisible by 11, if the difference between
the last three digits and the rest of the number
to the left is divisible by 11.

 
 
 

 

 

 

 

 

 

 

 

 

 


Exercise 6: Numbers that are divisible by 11.

 

(1)  For each number below, write Yes if it is divisible by 11, write No if it is not.

 

   253,275      275,253      396,495      495,396      671,220      220,671

 

     _____       _____        ______       ______        ______       ______

 

 

   1,353,220     2,750,297     1,100,253     1320,726     1,199,979     2750,616

 

     _____         _____           ______          ______         ______       ______

 

 

(2)  Write two whole numbers, both divisible by 11. _______ and _______

 

Is the sum of the two numbers divisible by 11? ____________________

 

Is the difference of the two numbers divisible by 11? ________________

 

 

(3)  Write two more whole numbers, both divisible by 11. _______ and _______

 

Is the sum of the two numbers divisible by 11? ____________________

 

Is the difference of the two numbers divisible by 11? ________________

 

Lesson 5: Solving Open Equations with Addition and Subtraction

 

To solve the equation x + 1 = 9, find the value of the variable x.
 

To solve the equation x – 1 = 8, find the value of the variable x.
 
Text Box: To solve an open equation is to find the value of the variable in the open equation by addition and subtraction.

   

 

 

 

 

 

 

 

 

 

X – a = b

X = b + a

 

X + a = b

X = b – a

 

X – a – b + c + d = e

X = e + a + b – c – d

 
 

 

 

 

 


Exercise 5: Solve open equations using addition and subtraction.

 

(1)   Rearrange each equation below, by moving all of the numbers to the right and all of the variables to the left of the equal sign.

10 + x = 20

 

x = 20 -10

 

x – 10 = 20

 

____________

 

x + 14 = 20

 

____________

 

x – 43 = 2

 

____________

 

 
 

13 + y = 34

 

____________

y + 27 = 58

 

____________

 

y – 37 = 61

 

___________

 

y – 63 = 21

 

___________

 

 
 

21 + x – 15 – 7 = 3

 

_________________________

 

y – 45 – 12 + y + 28 = 0

 

_________________________

 

z + 38 + z – 21 + 31 = 25

 

_________________________

 

x + y + z – 2 – 5 – 7 = 9

 

_________________________
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Rectangular Callout: (3) Add the numerators (since they have like denominators).Lesson 11: Adding Mixed Numbers with Unlike Denominators

 

To add two mixed numbers with unlike denominators:

(1)  Convert the fractions into fractions with like denominators.

(2)  Add the whole numbers.

(3)  Add the fractions (that is, add the numerators).

(4)  Reduce the result to its simplest form.

 
Rectangular Callout: (2) Add the whole numbers.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


          You can use modeling to add two mixed numbers with unlike denominators.