7 Maths Revision - Algebra and Fractions

Distributive Law/ Number line

100

Expand 4(x+2) 

= (4 x x )+ (4 x 2)

= 4x+8

200

Expand 6(x + 1)

= (6 x x) + (6 x 1)

= 6x + 6 

300

Construct a number line and place the following numbers accurately on the line: 

-1, -1/8, 1/8, 3/4, 1

-1                                    0                               1

_________________________________________

-1                         -1/8         1/8                    3/4        1

(Convert 3/4 to 6/8) 

400

Expand -4(n-3)

= (-4 x n) - (-4 x -3)

= -4n - -12

= -4n + 12

500

Expand -6(h-6)

= (-6 x h) - (6 x -6)

= -6h - -36

= -6h + 36

Solve for x and substitution

100

Solve for the vale of x:

4x + 4 = 16

4x + 4 = 16

-4            -4 

4x = 12

/4      /4

x = 3

200

Substitute x=3 into 4x+4 (hint use FSSS) 

4x + 4 

x=3

(4x3) + 4 

=16 

Therefore if x=3, then 4x +4=16

300

Solve for x: 

5x + 15 = 45 

5x + 15 = 45

- 15          -15

5x = 30

/5     /5 

x = 6

400

Substitute x=6 into 5x + 15  (Hint use FSSS)

5x + 15 

x=6 

(5 x 6) + 15 

= 45 

Therefore is x=6, then 5x + 15=45

500

Convert temperatures from Celsius to Fahrenheit can be calculated using the formula F = 2C + 30, where C=Celsius (°C ) and F = Fahrenheit (° ). Calculate the Fahrenheit temperature for 10°C. 

F = 2C + 30 

C = 10 

F = 2 x 10 + 30 

= 20 + 30

F = 50° 

Therefore 10° C converted to Fahrenheit is 50° F

Adding and Subtracting Fractions

100

Calculate 4/6 + 1/6

5/6

200

Calculate 7/9 - 5/9

2/9

300

Calculate 2/5 - 1/10

Convert 2/5 to 4/10 

4/10 - 1/10 

= 3/10

400

Gary had 1 1/2 bags of cement in his shed. He used 2/3 of a bag to mix up some concrete. Determine what fraction of a full bag he has left. 

Convert 1 1/2 to an improper fraction = 3/2 

Convert 3/2 and 2/3 to equivalent fractions 

3/2 = 9/6    2/3 = 4/6 

9/6-4/6 = 5/6 

Therefore Gary has 5/6 bags remaining. 

500

Jayden, Corey and Isaac were sharing the driving trip along the coast. Jayden drove 3/5 of the distance and Isaac drove 3/20. Determine the fraction of the total distance Corey drove. 

Convert to equivalent fractions: 3/5 = 12/20 

12/20 + 3/20 = 15/20 

20/20-15/20 = 5/20

Simplest form = 1/4

Therefore Corey drove 1/4 distance of the trip. 

Converting improper fractions and mixed numbers

100

Convert 19/5 to a mixed number 

3 4/5

200

Convert 5 1/4 to an improper fraction 

(5 x 4 + 1 / 4 

= 21/4

300

Convert 4 6/7 to an improper fraction 

(4 x 7 + 6) / 7

= 34/7

400

Dave is leading a group of 12 people on a bushwalk. He brought 30L of water to supply the group. 

Determine the amount of litres each group member receives as both an improper fraction and mixed number in simplest form. 

30/12 = 5/2 

5/2 = 2 1/2

500

7 pizzas were each sliced into 6 equal pieces. If 3 1/2 of the pizzas are eaten, determine how many slices are left over. 

7 x 6 = 42 slices total 

3 1/2 pizzas = 7/2

7/2 = 21/6 slices 

42 - 21 = 21 slices left over

Therefore if 3 1/2 of the pizzas are eaten, there are 21 slices left over. 

Ordering fractions and comparing fractions, decimals and percentages

100

Convert 0.7 to a fraction 

70/100

= 7/10

200

Convert 60% to a fraction 

60% = 60/100

= 3/5

300

Convert 1 to a fraction and percentage 

100/100 

100%

400

Convert the following numbers to a fraction and organise into ascending order: 

1, 0.8, 1/2, 10%, 0.3

1 = 100/100 0.8 = 80/100 1/2 = 50/100, 10% = 20/100 0.3 = 30/100

10%, 0.3, 1/2, 0.8, 1

500

Convert the following numbers to a fraction and organise into ascending order: 

0.6, 1, 1/5, 90%, 40%

0.6 = 60/100 1 = 100/100 1/5 = 20/100 90% = 90/100 40% = 40/100

1/5, 40%, 0.6, 90%, 1