Fractions and Measurements Quiz

Simplify the following fractions: a) 18/24 b) 45/60

Answer explanation

To simplify 18/24, divide both by 6 to get 3/4. For 45/60, divide both by 15 to get 3/4. Thus, a) 3/4 and b) 3/4 are the simplified forms.

Add and subtract the following fractions: a) 3/8 + 5/16 b) 7/12 - 5/18

Answer explanation

For a) 3/8 + 5/16, convert 3/8 to 6/16, then add: 6/16 + 5/16 = 11/16. For b) 7/12 - 5/18, convert to a common denominator (36): 21/36 - 10/36 = 11/36. Final answers: a) 11/16, b) 11/36.

Multiply and divide the following fractions: a) 4/9 × 3/5 b) 8/15 ÷ 2/3

Answer explanation

a) 4/9 × 3/5 = 12/45, which simplifies to 4/15. b) 8/15 ÷ 2/3 = 8/15 × 3/2 = 24/30, which simplifies to 4/5. Thus, the answers are 4/15 and 4/5.

Convert the following fractions to decimals: a) 7/8 b) 3/20

Answer explanation

To convert 7/8 to a decimal, divide 7 by 8, which equals 0.875. For 3/20, divide 3 by 20, resulting in 0.15. Thus, 7/8 = 0.875 and 3/20 = 0.15.

Perform the following calculations: a) 0.75 + 0.46 b) 1.32 - 0.89 c) 0.8 × 0.35 d) 4.5 ÷ 1.2

Answer explanation

a) 0.75 + 0.46 = 1.21 b) 1.32 - 0.89 = 0.43 c) 0.8 × 0.35 = 0.28 d) 4.5 ÷ 1.2 = 3.75. The calculations show the results for each operation.

Calculate the area of the following shapes: a) A rectangle with a length of 12 cm and a width of 8 cm. b) A circle with a radius of 7 cm (π = 3.14).

Answer explanation

a) Area of rectangle = length × width = 12 cm × 8 cm = 96 cm². b) Area of circle = π × radius² = 3.14 × (7 cm)² = 3.14 × 49 cm² = 153.86 cm². The areas are 96 cm² and 153.86 cm² respectively.

Find the volume of: a) A cuboid with dimensions 5 m × 4 m × 3 m. b) A cylinder with a height of 10 cm and a radius of 3 cm (π = 3.14).

Answer explanation

a) Volume of cuboid = length × width × height = 5 m × 4 m × 3 m = 60 m³. b) Volume of cylinder = πr²h = 3.14 × (3 cm)² × 10 cm = 94.2 cm³. Thus, the volumes are 60 m³ and 94.2 cm³.

Solve the following equation: 3x + 5 = 20

Answer explanation

To solve 3x + 5 = 20, subtract 5 from both sides: 3x = 15. Then, divide by 3: x = 5. Thus, the solution is x = 5.

Solve the following equation: 2x - 7 = 13

Answer explanation

To solve 2x - 7 = 13, add 7 to both sides: 2x = 20. Then, divide by 2: x = 10. Thus, the solution is x = 10.

Simplify the following expression: 4(3x + 2)

Answer explanation

To simplify 4(3x + 2), distribute 4 to both terms inside the parentheses: 4 * 3x + 4 * 2 = 12x + 8. The simplified expression is 12x + 8.