💫 • Module 3 : Fractions, Equations, and Geometry

Question 1

What is an equivalent fraction for 2/4?

Answer 1

½, since both fractions represent the same value.

Question 2

Simplify 12/18.

Answer 2

⅔, by dividing both the numerator and denominator by 6.

Question 3

Add ⅗ + ⅖.

Answer 3

5/5 =1

Question 4

Subtract 7/10 - 3/10.

Answer 4

4/10 = 2/5

Question 5

Multiply 2/3 x 4/5.

Answer 5

8/15.

Question 6

Divide 3/4 ÷ 2/5.

Answer 6

A: 15/8.

Multiply the numerators and the denominators:
3 x 5 =15 and 4 x 2=8.
So, 3/4 ÷ 2/5 =15/8

Question 7

Find ¼ of 36.

Answer 7

36 x ¼ = 9.

Question 8

Convert 40% to a fraction.

Answer 8

40/100 = 2/5.

Question 9

Solve 2𝑥 + 3 = 11.

Answer 9

A: 𝑥=4

2𝑥 + 3 = 11.
2𝑥 + 3 - 3 = 11 - 3 (cancel 3 on both sides)
2𝑥 = 8
(Divide 2 on both sides)
𝑥=4

Question 10

Find 25% of 60.

Answer 10

Multiply 60 by 25/100 :
= 1500 ÷ 100 =15.
So, 25% of 60 is 15.

Question 11

Convert ⅞ to a decimal.

Answer 11

Divide the numerator by the denominator:
7 ÷ 8=0,875.

Question 12

Simplify 2 1/4 (mixed number)

Answer 12

Convert to an improper fraction:
2 1/4 =9/4.

1 — Multiply the whole number by the denominator of the fraction:
2 x 4 =8.
2 — Add the result to the numerator of the fraction:
8 + 1=9.
3 — Write the result as the numerator and keep the denominator the same:
So, 2 1/4 =9/4

Question 13

What is the formula for finding the area of a parallelogram?

Answer 13

Area = base x height.

Example : For a base of 5cm and a height of 3cm, the area is 5 x 3 =15cm²

Question 14

How do you find the perimeter of a polygon, given all the lengths?

Answer 14

Add the lengths of all the side together.

Example : For a rectangle with sides 4cm and 6cm, the perimeter is 4+4+6+6=20cm.

Question 15

How do you calculate the area of a trapezium?

Answer 15

Area = ½ x (a + b) x h

Where an and b are the lengths of the parallel sides, and h is the height.

Example : For a trapezium with parallel sides of 4cm and 6cm, and a height of 3cm, the area is ½ x (4+6)x3= 15cm²

Question 16

What is the formula for the area of a triangle?

Answer 16

Area = ½ x base x height.

Example : For a triangle with a base of 4cm, and height of 5cm, the area is ½ x 4 x 5 = 10cm²

Question 17

How do you calculate the area of a sector of a circle?

Answer 17

Area of a sector = θ/360 x πr²
Where θ is the central angle in degrees and r is the radius.

Example : For a sector with a central angle of 90°, and a radius of 4 cm, the area is 90/360 x π x 4² = 3.14cm²

Question 18

What is the formula for the length of an arc?

Answer 18

Arc length = θ/360 x 2πr
Where θ is the central angle and r is the radius.

Example : For an arc with a central angle of 60° and radius of 6 cm, the length is 60/360 x 2π x 6 = 6.28cm.

Question 19

How do you calculate the probability of an event? (Theoretical probability)

Answer 19

Probability = number of successful outcomes/Total number of possible outcomes.

Example : If you roll a dice, the probability of rolling a 3 is 1/6.

Question 20

What is experimental probability?

Answer 20

Experimental probability = Number of successful outcomes/Total number of trials

Example : If you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6/10 =0,6.

Question 21

What does a sample space show in probability?

Answer 21

All possible outcomes of an experiment.

Example : The sample space for flipping a coin is {Heads, Tails}.

Question 22

How do you calculate the perimeter of a sector?

Answer 22

Add the arc length and the two radii.

Example : Arc length of 6cm and radius of 4cm :
6+4+4=14cm.

Question 23

What is a linear equation?

Answer 23

An equation where the variable has a power of 1, forming a straight line when graphed.
Example :
2𝑥+3=7 —> 𝑥=2

Question 24

How do you calculate relative frequency?

Answer 24

Number of favorable outcomes/Total number of trials

Question 25

How do you find the probability that an event does not happen?

Answer 25

1 - P(Event)