Fractions to Decimals
Convert 7/20 to a decimal.
0.35
Convert 0.48 to a percentage.
48%
A rectangle has a length of 14 cm and a width of 9 cm. Find the perimeter.
46cm
A rectangle has a length of 13 cm and a width of 6 cm. Find the area.
78 cm²
Two angles on a straight line are 118° and x°. Find x.
62°
Convert 5/8 to a decimal.
0.625
Convert 1.35 to a percentage.
135%
A square has an area of 81 m². Find its perimeter.
36m
A compound shape is made from two rectangles. One rectangle is 8 m by 5 m and the other is 6 m by 4 m. Find the total area.
64 m²
Angles around a point are 95°, 110°, 80° and x°. Find x.
75°
Angles around a point add to 360°.
95 + 110 + 80 = 285
x = 360 − 285
x = 75°
Convert 11/6 to a decimal. Give your answer using recurring decimal notation.
1.8̅3
A student completes 0.875 of a project. Convert this decimal to a percentage.
87.5%
A rectangle has an area of 126 cm² and a width of 9 cm. Find its perimeter.
46cm
A large rectangle measures 15 cm by 10 cm. A smaller rectangle measuring 6 cm by 4 cm is cut out. Find the remaining area.
126 cm²
Working:
Large rectangle = 15 × 10 = 150 cm²
Cut-out rectangle = 6 × 4 = 24 cm²
Remaining area = 150 − 24 = 126 cm²
Two vertically opposite angles are labelled 4x + 12° and 92°. Find x.
20
Vertically opposite angles are equal.
4x + 12 = 92
4x = 80
x = 20
A recipe uses 3/16 of a kilogram of sugar. Convert this amount to a decimal.
0.1875 kg
A swimming tank is 0.0625 full. Convert this decimal to a percentage.
6.25%
A rectangular garden has an area of 168 m². The width is 12 m. Find the perimeter.
52 m
Working:
Length = 168 ÷ 12 = 14 m
Perimeter = 2(14 + 12)
Perimeter = 52 m
An L-shaped figure is made from a rectangle measuring 14 m by 9 m. A missing corner is cut out. The missing corner has sides of 5 m and 4 m. Find the area of the L-shape.
106 m²
Large rectangle = 14 × 9 = 126 m²
Missing corner = 5 × 4 = 20 m²
L-shape area = 126 − 20 = 106 m²
Parallel lines are cut by a transversal. One co-interior angle is 124°. Find the other co-interior angle.
56°
Co-interior angles on parallel lines add to 180°.
x = 180 − 124
x = 56°
A student says 17/40 = 0.425. Without using a calculator, explain whether they are correct.
Yes, they are correct.
Working:
17/40 = 17 ÷ 40
Multiply numerator and denominator by 25:
17/40 = 425/1000
425/1000 = 0.425
A decimal is halfway between 0.36 and 0.5. Convert this decimal to a percentage.
43%
Halfway between 0.36 and 0.50:
0.36 + 0.50 = 0.86
0.86 ÷ 2 = 0.43
0.43 = 43%
An L-shaped path is made from a 12 m by 8 m rectangle with a 4 m by 3 m rectangle removed from one corner. Find the perimeter of the remaining shape.
P = 40m
For a corner cut-out, the two removed outer lengths are replaced by the two inner lengths.
So the perimeter remains the same as the original rectangle:
P = 2 × 12 + 2 × 8
P = 24 + 16
A compound shape can be split into two rectangles.
The first rectangle is 18 cm by 7 cm.
The second rectangle has an area of 64 cm² and a width of 8 cm.
Find the total area of the compound shape.
190 cm²
Working:
First rectangle = 18 × 7 = 126 cm²
Second rectangle = 64 cm²
Total area = 126 + 64 = 190 cm²
Parallel lines are cut by a transversal. Two alternate angles are labelled 5x − 15° and 3x + 25°. Find the value of x and the size of each angle.
x = 20 and each angle is 85°
Working:
Alternate angles are equal when lines are parallel.
5x − 15 = 3x + 25
2x = 40
x = 20
Substitute:
5 × 20 − 15 = 100 − 15 = 85°
3 × 20 + 25 = 60 + 25 = 85°