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Measuring Using Fractional Units

Class 6 Maths · Chapter 7: Fractions · NCERT Ganita Prakash section 7.3

Learn

Meher wants to measure her pencil, but her measuring strip is only marked in wholes. The pencil is longer than 0 strips and shorter than 1. So she folds the strip into 4 equal parts: the pencil reaches 3 of them. Her pencil is 3/4 of the strip.

3 × 1/4 = 3/4

Fractional units help us measure between whole numbers. Half a metre, a quarter of a kilogram, three quarters of an hour: all are fractions of a unit.

To find a fraction of a length, find one unit first. 1/4 of 20 cm: share 20 cm into 4 equal parts → 5 cm. Then 3/4 of 20 cm is 3 × 5 = 15 cm.

20 ÷ 4 = 5 → 3 × 5 = 15 cm

Going the other way: how many pieces of 1/4 m come from a 3 m ribbon? Each metre gives 4 pieces, so 3 m gives 12 pieces.

3 × 4 = 12

Explore: this measuring strip is 1 unit long. Choose the number of equal parts and shade the length of each object.

  1. An eraser is 1/2 unit long. Shade its length.
  2. A crayon is 2/3 unit long. Shade it using thirds.
  3. A key is 5/6 unit long. Shade it.

Remember

  • Fractional units measure lengths between whole units.
  • k/d of an amount: divide by d to get one unit, then multiply by k.

Quick check

What is 1/5 of 35 cm?

  1. 7 cm
  2. 5 cm
  3. 30 cm
  4. 175 cm
Answer

7 cm. Share 35 cm into 5 equal parts: 35 ÷ 5 = 7 cm.

Think about it

A rope is 1 m long. Rohan cuts 1/2 of it, then cuts 1/2 of what is left. How long is the last piece?

One answer

Half of 1 m is 1/2 m. Half of that 1/2 m is 1/4 m. So the last piece is 1/4 m (25 cm).

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.