Conversion (Units)

Time Conversion

Concepts: 
6 Times Tables

Big to Small

First (Single Unit)
Convert from hours to minutes

2 hours = 2 x 60 minutes = 120 minutes

5 hours = 5 x 60 minutes = 300 minutes


Convert from minutes to seconds

7 minutes = 7 x 60 seconds = 420 seconds

8 minutes = 8 x 60 seconds = 480 seconds


Second (Mixed Units)
Convert from hours and minutes to minutes

4 hours 5 minutes 
= 4 x 60 minutes + 5 minutes
= 240 minutes + 5 minutes
= 245 minutes

6 hours 24 minutes 
= 6 x 60 minutes + 24 minutes
= 360 minutes + 24 minutes
= 384 minutes

Convert from minutes and seconds to seconds

12 minutes 54 seconds 
= 12 x 60 seconds + 54 seconds
= 720 seconds + 54 seconds
= 774 seconds

14 minutes 28 seconds 
= 14 x 60 seconds + 28 seconds
= 840 seconds + 28 seconds
= 868 seconds

21 minutes 41 seconds
= 21 x 60 seconds + 41 seconds
= 1260 + 41 seconds
= 1301 seconds


Small to Big

First (Single Unit: Whole Numbers)

Convert from minutes to hours

360 minutes = (360 / 60) hours = 6 hours



480 minutes = (480 / 60) hours = 8 hours



540 minutes = (540 / 60) hours = 9 hours


Convert from seconds to minutes


600 seconds = (600 / 60) minutes = 10 minutes


720 seconds = (720 / 60) minutes = 12 minutes


840 seconds = (840 / 60) minutes = 14 minutes

Second (Mixed Units, Mixed Numbers)

366 minutes = (366 / 60) hours = 6 hours 6 minutes
or
= 6 6/60 hours = 6 1/10 hours

492 minutes = (492 / 60) = 8 hours 12 minutes
= 8 12/60 hours = 8 1/5 hours

Patterns (Tokens)

Patterns (Rods)

Angles (Parallelogram and Triangle)

In the figure below, not drawn to scale, ABCD is a parallelogram, DE and AE are straight lines. Find the ∠AED.

Label the point with a 90 angle as F.

Method 1
CFE = 90 (adjacent angles on straight line BFC)
BCE = 65 (corresponding angles)
AED = 180 - 90- 65 = 25 (angle sum of triangle CFE)

Method 2
AFB = 90 (adjacent angles on straight line BFC)
ABC = 65 (diagonally opposite angles of parallelogram ABCD)
AED = BAF = 180 - 90 - 65 = 25 (angle sum of triangle BAF, alternate angles)

Angles (Isosceles Triangle)

The figure below is not drawn to scale. Given that TP = SP, find ∠RTS

TRS = 40 + 24 = 64 (exterior angle = interior opposite angles of triangle TPR)

TSP = (180 - 24) / 2 = 78 (base angles of isosceles triangle TSP)

RTS = 180 - 78 - 64 = 38 (angle sum of triangle RTS)

TRP = 180 - 40 - 24 = 116 (angle sum of triangle TRP)

TSP = (180 - 24) / 2 = 78 (base angles of isosceles triangle TSP)

RTS = 116 - 78 = 38 (exterior angle = interior opposite angles of triangle RTS)

Angles (2 Isosceles Triangles)

First

The figure below is not drawn to scale. ABC is an isosceles triangle where BA = BC. Given that D is the midpoint of BC and AC is 1/2 of BA, find ∠ADB.

Method 1

∠DCB = (180 - 20) / 2 = 80 (base angles of isosceles triangle ABC)

∠ADC = (180 - 80) / 2 = 50 (base angles of isosceles triangle ACD)

∠ADB = 180 - 50 = 130 (adjacent angles on straight line BDC)

Angles (Isosceles Triangle and Parallelogram)

First

The following figure is not drawn to scale. Given that ABCD is a parallelogram and ∠ADE is an isosceles triangle, find ∠y.

ADC = 180 - 118 = 62 (co-interior angles of parallelogram ABCD)

Y = 62 / 2 (exterior angle = interior opposite angles, base angles of isosceles triangle ADE)

DAB = 118 (diagonally opposite angles of parallelogram ABCD)

y = (180 - 118) / 2 = 31 (co-interior angles of trapezium ABCE)

Second

Study the figure below and find ∠FCB.

Method 1

FCD = EFA = (180 - 84) / 2 = 48 (base angles of isosceles triangle EAF, corresponding angles)

DCB = 180 - 68 = 112 (co-interior angles of parallelogram ABCD)

FCB = 112 - 48 = 64

Method 2

CFB = (180 - 84) / 2 = 48 (base angles of isosceles triangle EAF, vertically opposite angles)

FBC = 68 (diagonally opposite angles)

FCB = 180 - 48 - 68 = 64 (angle sum of triangle FCB)