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Fractions - Measuring Using Fractional Units

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A fraction represents a part of a whole measurement unit. For example, if 1 metre1 \text{ metre} is divided into 100100 equal parts, each part is 1100\frac{1}{100} of a metre.

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On a standard ruler, the distance between two whole numbers (like 22 and 33) is usually divided into 1010 equal sub-divisions. Each sub-division represents 110\frac{1}{10} of a centimetre (1 mm1 \text{ mm}).

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To measure an object using fractional units, identify the last whole unit passed and then count the number of smaller divisions. Total measurement = Whole number+Sub-divisions countedTotal sub-divisions in one unit\text{Whole number} + \frac{\text{Sub-divisions counted}}{\text{Total sub-divisions in one unit}}.

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Fractional units are frequently used in weight (e.g., 12 kg\frac{1}{2} \text{ kg}), capacity (e.g., 14 L\frac{1}{4} \text{ L}), and length (e.g., 34 m\frac{3}{4} \text{ m}).

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Converting smaller units to larger units often involves fractions. Since 1000 ml=1 L1000 \text{ ml} = 1 \text{ L}, then 500 ml=5001000 L=12 L500 \text{ ml} = \frac{500}{1000} \text{ L} = \frac{1}{2} \text{ L}.

📐Formulae

Measurement=Whole NumberNumeratorDenominator\text{Measurement} = \text{Whole Number} \frac{\text{Numerator}}{\text{Denominator}}

1 mm=110 cm1 \text{ mm} = \frac{1}{10} \text{ cm}

1 cm=1100 m1 \text{ cm} = \frac{1}{100} \text{ m}

1 gram=11000 kg1 \text{ gram} = \frac{1}{1000} \text{ kg}

Value of 1 division=1Total divisions between two whole units\text{Value of 1 division} = \frac{1}{\text{Total divisions between two whole units}}

💡Examples

Problem 1:

A ribbon measures 55 whole centimetres and 77 small divisions on a ruler where 1 cm1 \text{ cm} is divided into 1010 parts. Express this measurement as a mixed fraction.

Solution:

5710 cm5\frac{7}{10} \text{ cm}

Explanation:

The whole number part is 55. Since the centimetre is divided into 1010 parts, the denominator is 1010. The ribbon covers 77 such parts, so the numerator is 77. The measurement is 5+710=5710 cm5 + \frac{7}{10} = 5\frac{7}{10} \text{ cm}.

Problem 2:

Express 750 grams750 \text{ grams} as a fraction of a kilogram in its simplest form.

Solution:

34 kg\frac{3}{4} \text{ kg}

Explanation:

Since 1000 g=1 kg1000 \text{ g} = 1 \text{ kg}, 750 g=7501000 kg750 \text{ g} = \frac{750}{1000} \text{ kg}. Dividing both the numerator and denominator by their greatest common divisor (250250), we get 750÷2501000÷250=34 kg\frac{750 \div 250}{1000 \div 250} = \frac{3}{4} \text{ kg}.

Problem 3:

A glass contains 200 ml200 \text{ ml} of water. If the total capacity of a bottle is 1000 ml1000 \text{ ml}, what fraction of the bottle is filled by the glass? If you add another 300 ml300 \text{ ml}, what is the total fractional measurement in litres?

Solution:

200+300500\begin{array}{r} 200 \\ + 300 \\ \hline 500 \end{array} Total is 12 L\frac{1}{2} \text{ L}.

Explanation:

Initially, the volume is 200 ml200 \text{ ml}. After adding 300 ml300 \text{ ml}, the total volume is 500 ml500 \text{ ml}. To express this in litres, we use the fraction 5001000\frac{500}{1000}, which simplifies to 12 L\frac{1}{2} \text{ L}.