MEASURES OF AREA

100 square millimeters (mm2) = 1 square centimeter (cm2)
100 square centimeters (cm2) = 1 square decimeter (dm2)
100 square decimeters (dm2­) = 1 square meter (m2)
100 square meters (m2) = 1 square decameter (dkm2)
100 square decameters (dkm2) = 1 square hectometer (hm2)
100 square hectometers (hm2) = 1 square kilometer (km2)
10,000 square centimeters (cm2) = 1 square meter (m2)
 1,000,000,000 square meters (m2) = 1 square kilometer (km2)
10,000 square meters (m2) = 1 hectare (ha)

MEASURES OF LENGTH

10 millimeters (mm) = 1 centimeter (cm)
10 centimeters (cm) = 1 decimeter (dm)
10 decimeters (dm) = 1 meter (m)
10 meters (m) = 1 decameter (dkm)
10 decameters (dkm) = 1 hectometer (hm)
10 hectometers (hm) = 1 kilometer (km)
100 centimeters (cm) = 1 meter (m)
 1,000 meters (m) = 1 kilometer (km)

PERIMETER

Perimeter is the measure around a closed figure.
To find the perimeter of a polygon, add the measures of all sides.
Perimeter is measured in linear units such as centimeter, decimeter, meter, kilometer, etc.

Formulas to find the perimeter of:

1. Square
P = S1 + S2 + S3 + S4 or P = 4s

2. Rectangle
a. P = l + w + l + w
b. P = 2l + 2w
c. P = 2(l + w)

3. Triangle
 P = S1 + S2 + S3

4. Rhombus
P = S1 + S2 + S3 = S4 or P = 4s

*P = Perimeter*
*S = Side*
*l = length*
*w = width*

DIVISION OF DENOMINATE NUMBERS

1. Arrange the units, start with the highest unit at the left end.
2. Divide starting from the highest unit.
3. Add the remaining if there is any to the next lower unit.
(Be sure to change the remainder to the lower unit before adding)

Ex. James is going to cut his 20 feet 6 inches in rope into 6 equal pieces. How long will each piece be?

Solution:

Step 1. Arrange the units and write the divisor.
   ________
6 )20 ft 6 in

Step 2. Divide starting from the highest unit.

   _3ft_____
6 )20 ft 6 in
    18__
     2 ft

Step 3. Add the remainder to the lower unit. (Be sure to change the remainder to the lower unit before adding)

2 ft = 24 inches. So, 24 inches + 6 inches = 30 inches

Step 4. Divide the lower unit.

    _3ft  5 in_
6 )20 ft 6 in
    18__
     2 ft
            30 in ( step 3)
     -     30 in
             0

ANSWER: 3 feet 5 inches

MULTIPLICATION OF DENOMINATE NUMBERS

1. Arrange the units, start with the higher unit at the left end.
2. Write the multiplier in column with the smallest unit.
3. Multiply the numbers.
4. Reduce the answer to the higher denominations if necessary.
 
Ex. Chris studies his lessons everyday on the average of 2 hours 40 minutes. How long is it in 5 days?
 
Solution no. 1:
 
Step 1. Arrange the units and write the multiplier.
 
2 hrs 40 min
   x                 5
 
Step 2. Multiply starting from right.
 
40 min x 5 = 200 min
200 min = 3 hrs 20 min. So, write down 20 min and carry 3hrs.
 
3hrs
2hrs 30 min
    x               5
 
ANSWER: 13 hrs 20 min
 
Solution no. 2:
 
Step 1. Multiply.
 
2 hrs 40 min
    x                 5
10 hrs 200 min
 
Step 2. Reduce the answer to the higher term. 

200 min = 3 hrs 20 min So,
10 hrs 200 min = 13 hrs 20 min
 
ANSWER: 12 hours 30 minutes

SUBTRACTION OF DENOMINATE NUMBERS

1. Arrange the units in column, start with the highest unit at the left end.
2. Subtract starting at the smallest unit at the right.
3. Take one unit of the next higher order if you cannot deduct.
4. Reduce the answer to the higher denominations if necessary.

Ex. Find the difference of 24 yards 5 feet 7 inches and 21 yards 5 feet 10 inches.

Solution:

Step 1. Arrange the units in column.

          24 yd 5 ft 7 in
-        21 yd 5 ft 10 in

Step 2. Subtract starting from the lowest unit.

7 in - 10 in (cannot be done for being whole numbers)
So, take 1 ft from 5 ft leaving 4 ft.

Step 3. Change the foot borrowed to inches.

1 ft = 12 inches

Step 4. Regroup the inches in the minuend.

12 inches + 7 inches = 19 inches

Step 5. Subtract the inches.

      24 yd 4 ft 19 in
-    21 yd 5 ft 10 in
                       9 in

Step 6. Subtract the feet.

4ft - 5ft (cannot be done for being a whole numbers).
So, take 1 yard from 24 yards leaving 23 yards.

Step 7. Change the yard borrowed to feet.

1 yard = 3 ft

Step 8. Regroup the feet in the minuend.

4 ft + 3 ft = 7 ft

Step 9. Subtract the feet and yard.

         23 yd 7 ft 19 in
-       21 yd 5 ft 10 in

ANSWER: 2 yd 2ft 9 in

ADDITION OF DENOMINATE NUMBERS

1. Arrange the units in column, start with the highest unit at the left end.

2. Add all columns.
3. Reduce the answer to the higher denomination if necessary.

Ex. Combine 8hrs 44 min 31 sec and 9 hrs 47 min 53 sec.

Solution:

Step 1. Arrange the units and add:
           8hrs 44 min 31 sec
+         9 hrs 47 min 53 sec
         17 hrs 91 min 84 sec

Step 2. Reduce the answer.

There are 60 sec in 1 min. So, 84 sec = 1 min 24 sec.
There are 60 min in 1 hr. So, 92 min = 1 hr 32 min.

           8hrs 44 min 31 sec
+         9 hrs 47 min 53 sec
        17 hrs 91 min 84 sec

= 17 hrs 91 min 1 min + 24 sec

= 17 hrs 91 min + 1 min 24 sec

= 17 hrs 92 min 24 sec
 
= 17 hrs 1hr + 32 min 24 sec

= 17 hrs 1hr + 32 min 24 sec

Answer: 18 hrs 32 min 24 sec