RATIOS A5.

If 3: 8 = 6:B; Find the value of B.

Solution

3   =   6                            [cross multiply]

8        B

3 x B = 6 x 8

3B = 48

3B = 48                      [divide by 3 on both sides]

3        3

B = 16

Hence the value of B is 16

PERIMETER OF A SEMI CIRCLE A7

Find the perimeter of the following semi-circle.

Solution

Perimeter = ∏D + D

                      2

Perimeter = ( ¹¹22  X ¹⁴98 )    +  98

                      ₁7         ₁2

                = (11 x 14 ) + 98

                = 156 + 98

                = 254

Hence perimeter is 254 cm

AREA OF PARALLELOGRAM B8

Find area of the following parallelogram.

solution

Area = base x height

         = 40 x 8

         = 320

Hence area = 320m²      

PERIMETER OF A SQUARE A5

Find the perimeter of the square below.

Solution

Perimeter = 4  x  side

                = 4 x 44

                = 176

Hence perimeter 176 cm.

ALGEBRA B39

Simplify 10p + 6m + 7p + 2m + p

Solution

=10p + 6m + 7p + 2m + p

  

=(10p + 7p  + p) + (6m + 2m) [collecting the like terms]

= 18p + 6m (adding the like terms)

Hence 10p + 5m + 7p + 2m + p = 18p + 7m

ALGEBRA B38

F - 8 = 7. Find the value of  F

Solution

F  - 8 = 7

F  – 8 + 8 = 7 + 8

F  – 0 = 15

F  = 15

Hence  F = 15

RATIOS A4

If 3: 8 = 10:B; Find the value of B.

Solution

3   =  10                            [cross multiply]

8        B

3 x B = 10 x 8

3B = 80

3B = 80                      [divide by 3 on both sides]

3        3

B = 26²/3

Hence the value of B is 26²/3

ALGEBRA B37

Simplify 10p + 6m + 7p + 2m + 4p

Solution

=10p + 6m + 7p + 2m + 4p

=10p + 7p  + 4p + 6m + 2m ( collecting the like terms)

= 21p + 6m ( adding the like terms)

Hence 10p + 5m + 7p + 2m + 4p = 21p + 7m

ALGEBRA B36

Simplify 5(4m)

Solution

 =5(4m)

=5 x 4 x m

=(5 x 4) x m

=(20) x m

=20m

Hence 5(4m) = 20m

PERIMETER OF A SEMI CIRCLE A6

Find the perimeter of the following semi-circle.

Solution

Perimeter = ∏D + D

                          2

Perimeter =( ¹¹22  X ⁸56 )    +  56

                          ₁7         ₁2

            = (11 x 8 ) + 56

            = 88 + 56

            = 144

Hence perimeter is 144 cm.

ALGEBRA B35

W - 6 = 7. Find the value of  W

Solution

W - 6 = 7

W – 6 + 6 = 7 + 6

W – 0 = 13

W = 13

Hence  W = 13

ALGEBRA B34

Simplify 8p + 6r + 7p + 2r + 4p

Solution

= 8p + 6r + 7p + 2r + 4p

= (8p + 7p  + 4p) + (6r + 2r)         [ collecting the like terms]

= 19p + 8r ( adding the like terms)

Hence 8p + 5r + 7p + 2r + 4p = 19p + 8r

RATIOS A3

If 3:2 = 11:B; Find the value of B.

Solution

3   =  11                            [cross multiply]

2       B

3 x B = 11 x 2

3B = 22

3B = 22                      [divide by 3 on both sides]

3        3

B =  22                      

          3

B = 7¹/3

Hence the value of B is 7¹/3

ALGEBRA B33

Simplify 10(6g)

Solution

 =10(6g)

=10 x 6x g

=(10 x 6) x g

=(60) x g

=10g

Hence 10(6g) = 60g

ALGEBRA B32

W - 3 = 7. Find the value of  W.

Sulution

W - 3 = 7

W – 3 + 3 = 7 + 3

W – 0 = 10

W = 10

Hence  W = 10

AREA OF PARALLELOGRAM B7

Find area of the following parallelogram.

solution

Area = base x height

         = 30 x 8

         = 240

Hence area = 240m²      

RATIOS A2

If 3:5 = 11:3B; Find the value of B.

Solution

3   =  11                             [cross multiply]

5       3B

3x3B = 11x5

9B = 55

9B = 55                      [divide by 9 on both sides]

9        9

B = ⁵⁵/9

B = 6¹/9

Hence the value of B is 6¹/9

ALGEBRA B31

Simplify 8a + 6r + 5a + 2r + 4a

Solution

= 8a + 6r + 5a + 2r + 4a

= (8a + 5a  + 4a) + (6r + 2r)             [collecting the like terms]

= 17a + 8r ( adding the like terms)

Hence 8a + 5r + 5a + 2r + 4a = 17a + 8r

ALGEBRA B30

Simplify 4(6f)

Solution

 =4(6f)

=4 x 6x f

=(4 x 6) x f

=(24) x f

=24f

Hence 4(6f) = 24f

PERIMETER OF A SQUARE A4

Find the perimeter of the square below.

Solution

Perimeter = 4  x  side

                = 4 x 44

                = 176

hence perimeter 176 cm.

ALGEBRA B29

R - 9 = 2. Find the value of  R.

Solution

R - 9 = 2

R – 9 + 9 = 2 + 9

R – 0 = 11

R = 11

Hence  R = 11

AVERAGE A10.

Find the average of 6, 8, 7 and 3.

Solution

6 + 8 + 7 + 3 = 24

Total of numbers = 24

Given Numbers = 4

Average = Total of numbers ÷ Given Numbers

                = 24 ÷ 4   

                = 6

Hence average is 6

PERIMETER OF A SEMI CIRCLE A5

Find the perimeter of the following semi-circle.

Solution

Perimeter = ∏D + D

                          2

Perimeter =( ¹¹22  X ¹³91 )    +  91

                         ₁7          ₁2

            = (11 x 13 ) + 91

            = 143 + 91

            = 234

Hence perimeter is 234 cm

ALGEBRA B28

Simplify 3a + 6r + 5a + 2r + 4a

Solution

= 3a + 6r + 5a + 2r + 4a

= (3a + 5a  + 4a) + (6r + 2r)    [ collecting the like terms]

= 12a + 8r ( adding the like terms)

Hence 3a + 5r + 5a + 2r + 4a = 12a + 8r

ALGEBRA B27

Simplify 9(6f)

Solution

=9(6f)

=9 x 6x f

=(9 x 6) x f

=(54) x f

=54f

Hence 9(6f) = 54f

ALGEBRA B26

R - 8 = 20. Find the value of  R.

Solution

R - 8 = 20

R – 8 + 8 = 20 + 8

R – 0 = 28

R = 28

Hence  R = 28

AVERAGE A9

Find the average of 4, 3, 7 and 6.

Solution

4 + 3 + 7 + 6 = 20

Total of numbers = 20

Given Numbers = 4

Average = Total of numbers ÷ Given Numbers

                = 20 ÷ 4   

                = 5

Hence average is 5

RATIOS A1

If 3: 5 = 10 : C; Find the value of C.

Solution

3   =  10

5        C

3 x C = 5 x 10

3C = 50

3C = 50

3        3

C = 16²/3

Hence the value of C is 16²/3

PERIMETER OF A SQUARE A3

Find the perimeter of the square below.

Solution

Perimeter = 4  x  side

                = 4 x 33

                = 132

hence perimeter 132 cm.

ALGEBRA B25

W - 3 = 20. Find the value of  W

Solution

W - 3 = 20

W – 3 + 3 = 20 + 3  [add 3 on both sides]

W – 0 = 23

W = 23

Hence  W = 23

AVERAGE A8

Find the average of 2, 3, 5 and 6.

Solution

2 + 3 + 5 + 6 = 16

Total of numbers = 16

Given Numbers = 4

Average = Total of numbers ÷ Given Numbers

              = 16 ÷ 4   

              = 4

Hence average is 4

AREA OF PARALLELOGRAM B6

Find area of the following parallelogram.

solution

Area = base x height

         = 22 x 10

         = 220

Hence area = 220m²      

ALGEBRA B24

W - 9 = 20. Find the value of  W.

Solution

W - 9 = 20

W – 9 + 9 = 20 + 9

W – 0 = 29

W = 29

Hence  W = 29

ALGEBRA B23

Simplify 9(5a)

Solution

 =9(5a)

=9 x 5 x a

=(9 x 5) x a

=(45) x a

=45a

Hence 9(5a) = 45a

PERIMETER OF A SEMI CIRCLE A4

Find the perimeter of the following semi-circle.

Solution

Perimeter = ∏D + D

                       2

Perimeter = ( ¹¹22  X ¹²84 )    +  84

                       ₁7         ₁2

            = (11 x 10 ) + 84

            = 110 + 84

            = 194

Hence perimeter is 194 cm

ALGEBRA B22

Simplify 10p + 6m + 2m + p + 3m

Solution

= 10p + 6m + 2m + p+ 3m

= (10p + p)  + (6m + 2m + 3m) ( collecting the like terms)

= 11p + 11m ( adding the like terms)

Hence 10p + 6m + 2m + p + 3m = 11p + 11m

ALGEBRA B21

P - 4 = 13. Find the value of  P

Solution

P - 4 = 13

P – 4 + 4 = 13 + 4   [add 4 on both sides.]

P – 0 = 17

P = 17

Hence  P = 17

ALGEBRA B20

Simplify 19(2k)

Solution

 =19(2k)

=19 x 2 x k

=(19 x 2) x k  [collecting like terms together]

=(38) x k

=38k

Hence 19(2k) = 38k

AVERAGE A7

Find average of 10, 30 and 20.

Solution

10 + 30 + 20 = 60

Total of numbers = 60

Given Numbers = 3

Average = Total of numbers ÷ Given Numbers

              = 60 ÷ 3   

              = 20

Hence average is 20

AREA OF PARALLELOGRAM B5

Find area of the following parallelogram.

solution

Area = base x height

         = 20 x 8

         = 160

Hence area = 160dm²      

PERIMETER OF A SQUARE A2

Find the perimeter of the square below.

Solution

Perimeter = 4  x  side

                = 4 x 20

                = 80

hence perimeter 80 cm.    

AVERAGE A6

Find average of 40, 30 and 20.

Solution

40 + 30 + 20 = 90

Total of numbers = 90

Given Numbers = 3

Average = Total of numbers ÷ Given Numbers

             = 90 ÷ 3   

             = 30

Hence average is 30

ALGEBRA B19

Simplify 9(3a)

Solution

 =9(3a)

=9 x 3 x a

=(9 x 3) x a

=(27) x a

=27a

Hence 9(3a) = 27a