Important Formulas: Far and Near | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Basic Units of Length

• Millimetre (mm): Used for very small things (screws, sprouts, nails).

• Centimetre (cm): Used for small objects (mobile phone, handkerchief).

• Metre (m): Used for medium/large objects (door height, elephant’s trunk, depth of well).

• Kilometre (km): Used for very large distances (roads, races, distance between cities).

• Feet (ft) and Inches (in): Common in daily life, especially for height.

Conversion Rules

• 10 mm = 1 cm

• 100 cm = 1 m

• 1000 m = 1 km

• 1 inch = approx. 2.5 cm

• 1 foot = 12 inches ≈ 30 cm

Comparing Lengths

• Always convert to the same unit before comparing.

Example:

• 5 m = 500 cm

• So, 456 cm < 500 cm

Rule:

• Use < (less than), > (greater than), = (equal to)

Addition & Subtraction of Lengths

• Method 1: Add/Subtract metres and centimetres separately (borrow if needed).

• Method 2: Convert everything into a single unit (cm or m), then add/subtract.

Example 1: A rope is 2 m 45 cm long. Another piece of rope is 1 m 60 cm long. What is the total length of the two ropes?

Solution:
Length of first rope = 2 m 45 cm = (2 × 100 + 45) cm = 245 cm
Length of second rope = 1 m 60 cm = (1 × 100 + 60) cm = 160 cm
Total length = 245 + 160 = 405 cm
Convert back to meters: 405 cm = 4 m 5 cm
Total length = 4 m 5 cm

Example 2:  A ribbon is 3 m 25 cm long. A piece of 1 m 78 cm is cut from it. How much ribbon is left?

Solution:

Method 1: (convert to cm)
Length of ribbon = 3 m 25 cm = (3 × 100 + 25) cm = 325 cm
Length cut = 1 m 78 cm = (1 × 100 + 78) cm = 178 cm

Remaining length = 325 − 178 = 147 cm

Convert back to meters: 147 cm = 1 m 47 cm

Answer: 1 m 47 cm

Method 2: Quick regrouping method (optional):
3 m 25 cm − 1 m 78 cm
→ Borrow 1 m: (2 m 125 cm) − (1 m 78 cm)
Centimetres: 125 − 78 = 47 cm
Metres: 2 − 1 = 1 m
→ 1 m 47 cm

Multiplication of Lengths

• Method 1: Multiply metres and centimetres separately, then convert.

• Method 2: Convert to cm first, multiply, then convert back.

Example 3: A rope is 2 m 15 cm long. If 3 such ropes are joined together, what is the total length?

Solution (convert to cm):
Length of one rope = 2 m 15 cm = (2 × 100 + 15) cm = 215 cm
Total length = 215 × 3 = 645 cm

Convert back to meters: 645 cm = 6 m 45 cm

Answer: 6 m 45 cm

Division of Lengths

• Convert everything into a single unit (usually metres), then divide.

Example 4: A rope is 5 m 20 cm long. It is cut into 4 equal pieces. What is the length of each piece?

Solution (convert to cm):
Total length of rope = 5 m 20 cm = (5 × 100 + 20) cm = 520 cm
Length of one piece = 520 ÷ 4 = 130 cm

Convert back to meters: 130 cm = 1 m 30 cm

Answer: 1 m 30 cm

Estimation in Measurement

Use known references to make good guesses:

• House height ≈ 3–4 m

• Electric pole ≈ 8–10 m

• 2-storey house ≈ 6 m → can be used to estimate taller buildings

Measurement Tools for Long Distances

• Long Tape – large measuring tape

• Rangefinder – measures distance to a target

• Laser Distance Meter – measures using light beams

• Rodo-meter (Measuring Wheel) – distance measured as wheel rolls