This MCQ module is based on: Fractional Units and Equal Shares
TOPIC 24 OF 41
Fractional Units and Equal Shares
🎓 Class 6
Mathematics
CBSE
Theory
Ch 7 — Fractions
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Fractional Units and Equal Shares
Targeting Class 6 level in Fractions, with Basic difficulty.
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7.1 Fractional Units and Equal Shares
Imagine some friends sharing food equally. When one whole roti is split equally among 2 children, each child gets one-half, written as \(\frac{1}{2}\). If it is split among 4 children, each gets one-fourth, written as \(\frac{1}{4}\). As the number of children grows, each share shrinks.
When 4 children share 3 rotis equally, each child gets \(\frac{3}{4}\) of a roti. When 5 children share 2 rotis equally, each gets \(\frac{2}{5}\) of a roti.
Key Idea
When a whole is divided into equal parts, the number of parts tells us the fractional unit?. Fractions such as \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \dots, \frac{1}{10}, \dots, \frac{1}{100}, \dots\) are called unit fractions because each is one part of an equal division.
Splitting one roti into 2, 4, or 8 equal parts. More parts → smaller share.
In-text Q: Which fraction is greater — \(\frac{1}{2}\) or \(\frac{1}{3}\)?
Answer: \(\frac{1}{2}\), because splitting a whole into 2 pieces gives bigger pieces than splitting into 3.
Answer: \(\frac{1}{2}\), because splitting a whole into 2 pieces gives bigger pieces than splitting into 3.
In general, among two unit fractions, the one with the bigger denominator is smaller. For example, \(\frac{1}{5} < \frac{1}{3}\), and \(\frac{1}{100}\) is much smaller than \(\frac{1}{10}\).
Figure it Out (p.152)
Q1. Three guavas together weigh 1 kg. If they are roughly the same size, each guava will roughly weigh ___ kg.
\(\frac{1}{3}\) kg.
Q2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.
\(\frac{1}{4}\) kg.
Q3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ___ glasses of sugarcane juice.
\(\frac{3}{4}\) glass each.
Q4. The big fish weighs \(\frac{1}{2}\) kg. The small one weighs \(\frac{1}{4}\) kg. Together they weigh ___ kg.
\(\frac{1}{2} + \frac{1}{4} = \frac{2}{4}+\frac{1}{4} = \frac{3}{4}\) kg.
Knowledge from the Past
Fractions have been used and named in India since ancient times. In the Rig Veda, the fraction \(\frac{1}{3}\) is referred to as tri-pada. The same meaning as the words 'teen paav' in colloquial Hindi and 'mukkaal' in Tamil! Words for fractions used today in many Indian languages go back to ancient times.
7.2 Fractional Units as Parts of a Whole
Consider a whole chikki (a flat sweet). If the chikki is cut into 2 equal pieces, each piece is \(\frac{1}{2}\) of the original. If it is cut into 6 equal pieces, each piece is \(\frac{1}{6}\). A bigger piece made of 3 of these sixths is \(\frac{3}{6}\) of the whole chikki.
Fractional units as equal parts of a whole chikki.
In-text Q (Math Talk): By dividing the whole chikki into 6 equal parts in different ways, we get \(\frac{1}{6}\) pieces of different shapes. Are they of the same size?
Answer: Yes — shape may differ, but each piece has the same area because the whole is split into 6 equal parts.
Answer: Yes — shape may differ, but each piece has the same area because the whole is split into 6 equal parts.
Activity: Paper-Folding Fractions
L3 ApplyMaterials: Square paper sheets, scissors, sketch pens
Predict: If you fold a square three times, into how many equal parts will it be divided? What unit fraction is each part?
- Fold the square in half. Open it. Count parts.
- Fold it in half again (perpendicular to the first fold). Count parts.
- Fold it once more. Count and label each part with its fractional unit.
- Shade 3 parts. Write the fraction represented.
After 1 fold → 2 parts (\(\frac{1}{2}\)). After 2 folds → 4 parts (\(\frac{1}{4}\)). After 3 folds → 8 parts (\(\frac{1}{8}\)). Each fold doubles the number of equal parts. Shading 3 of 8 parts represents \(\frac{3}{8}\) of the whole.
Figure it Out (p.155) — Identify the fraction
Q. Eight pictures show different fractional units of a whole chikki (a square or rectangle cut into equal pieces). Identify each.
(a) whole split into 2 equal halves, one shown → (b) whole split into 4, one shown → (c) whole split into 3, one shown → (d) whole split into 6, one shown → (e) whole split into 8, one shown → (f) whole split into 4, one shown → (g) whole split into 8, one shown → (h) whole split into 9, one shown.
(a) whole split into 2 equal halves, one shown → (b) whole split into 4, one shown → (c) whole split into 3, one shown → (d) whole split into 6, one shown → (e) whole split into 8, one shown → (f) whole split into 4, one shown → (g) whole split into 8, one shown → (h) whole split into 9, one shown.
(a) \(\frac{1}{2}\) (b) \(\frac{1}{4}\) (c) \(\frac{1}{3}\) (d) \(\frac{1}{6}\) (e) \(\frac{1}{8}\) (f) \(\frac{1}{4}\) (g) \(\frac{1}{8}\) (h) \(\frac{1}{9}\).
Competency-Based Questions
Scenario: A family orders 2 large pizzas. Each pizza is cut into 8 equal slices. Four family members — Meena, Arjun, Rina, and Kabir — share the 16 slices so that each person gets an equal number of slices.
Q1. How many slices does each person receive, and what fraction of one pizza does this represent?
L3 Apply\(16 \div 4 = 4\) slices each. Each slice is \(\frac{1}{8}\) of a pizza, so 4 slices = \(\frac{4}{8} = \frac{1}{2}\) of a pizza.
Q2. Kabir has eaten his slices. If he had instead shared them equally with his younger sister, analyse how much of one pizza each would have had.
L4 AnalyseKabir's 4 slices split 2 ways = 2 slices each = \(\frac{2}{8} = \frac{1}{4}\) of a pizza each.
Q3. Rina says: "Cutting a pizza into 16 pieces instead of 8 means each person gets more pizza." Evaluate her claim.
L5 EvaluateRina is wrong. Cutting a whole into more parts makes each part smaller, but the total pizza stays the same. Each person still receives \(\frac{1}{2}\) of a pizza (now 8 tiny slices instead of 4 bigger ones).
Q4. Design a sharing plan so that an extra guest (5 people in total) can share the 16 slices equally. Create your plan and give the fractional share per person.
L6 Create\(16 \div 5 = 3\) slices each with 1 slice left. Cut that remaining slice into 5 equal parts (each \(\frac{1}{40}\) of a pizza) — one tiny piece for each guest. Total share per person = \(\frac{3}{8}+\frac{1}{40} = \frac{15}{40}+\frac{1}{40}=\frac{16}{40}=\frac{2}{5}\) of a pizza.
Assertion–Reason Questions
Assertion (A): \(\frac{1}{8} < \frac{1}{5}\).
Reason (R): Among unit fractions, the one with a bigger denominator is smaller.
Reason (R): Among unit fractions, the one with a bigger denominator is smaller.
(a) — Both true and R correctly explains A.
Assertion (A): When 1 roti is shared among 3 children, each gets \(\frac{1}{3}\) roti.
Reason (R): \(\frac{1}{3}\) means 1 part out of 3 equal parts.
Reason (R): \(\frac{1}{3}\) means 1 part out of 3 equal parts.
(a) — Both true, and R gives the defining reason for A.
Assertion (A): Cutting a chikki into 6 equal parts of different shapes gives pieces of different sizes.
Reason (R): Equal fractional units must always have the same shape.
Reason (R): Equal fractional units must always have the same shape.
A is false, R is false. Equal parts must have equal area, not the same shape. Correct option: neither (c) nor (d) — actually closest to the given options is that both statements are false. (Exam-style: pick (c) only if R were true; here both are wrong.)
Frequently Asked Questions
What is a fractional unit in Class 6 Maths Chapter 7?
A fractional unit is one equal part of a whole object. If a roti is divided into 4 equal pieces, each piece is the fractional unit 1/4. Fractional units are always written with 1 on top and the number of equal parts below.
What are unit fractions with examples?
Unit fractions are fractions with 1 as the numerator such as 1/2, 1/3, 1/4, 1/5 and 1/100. Each tells us one equal share of a whole divided into that many parts. As the denominator grows, the unit fraction becomes smaller.
How do equal shares relate to fractions?
When an object is shared equally among a group, each person gets the same size piece. If 4 children share 3 rotis equally, each gets 3/4 of a roti. Equal shares always produce fractions where all parts are exactly the same size.
Which fraction is bigger, 1/2 or 1/3?
1/2 is larger than 1/3. When you divide a whole into fewer equal parts, each part is bigger, so 1/2 (two parts) gives larger pieces than 1/3 (three parts).
Why do we need fractions in daily life?
Fractions help us describe amounts smaller than one whole such as half a glass of water, a quarter kilogram of sugar or one-third of a cake. They are essential in measurement, money, cooking and sharing.
How are fractions introduced in Ganita Prakash Chapter 7?
NCERT Class 6 Ganita Prakash Chapter 7 introduces fractions through real sharing situations, then builds fractional units, measurement with fractions, equivalent fractions and basic addition and subtraction.
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