Chapter 7: Fractions class 6 ganita prakash

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Chapter 7: Fractions class 6 ganita prakash

FRACTIONS

7.1 Fractional Units and Equal Shares

Fractions class 6 : A fraction represents a part of a whole or, more generally, any number of equal parts. When we share things equally, fractions tell us the size of each person’s share.

Comparing Unit Fractions

A unit fraction is a fraction with 1 as its numerator, like 12 or 14.

When comparing unit fractions, remember: the larger the denominator (the number of people sharing), the smaller the share.

Therefore, 12 > 14 and 15 > 19.

Figure it Out (Page 152-153)

Fill in the blanks:

1. Three guavas weigh 1 kg. Each guava weighs 13 kg. (1 kg divided among 3 guavas)

2. 1 kg of rice in 4 packets. Each packet weighs 14 kg. (1 kg divided among 4 packets)

3. 3 glasses of juice for 4 friends. Each one drank 34 of a glass. (3 wholes divided among 4 people)

4. The big fish weighs 12 kg and the small one weighs 14 kg. Together they weigh:
12 + 14 = 24 + 14 = 34 kg.

5. Arrange from smallest to biggest:

The words are: One and a half (112), three quarters (34), one and a quarter (114), half (12), quarter (14), two and a half (212).

In order: Quarter, Half, Three quarters, One and a quarter, One and a half, Two and a half.

( 14, 12, 34, 114, 112, 212 )

7.2 & 7.3 Fractional Units as Parts of a Whole

Any fraction can be understood as a collection of unit fractions. For example, the fraction 34 simply means “3 times the unit fraction 14“.

Figure it Out (Page 155, 158)

1. How much of a whole chikki is each piece? (Page 155)

By visualizing how many of each piece would make a whole square:

  • a. 16
  • b. 14
  • c. 12
  • d. 13
  • e. 13 (It’s made of two 16 pieces)
  • f. 13
  • g. 18
  • h. 18

2. Match each fractional unit with the correct picture: (Page 158)

  • 13 matches the circle divided into 3 parts.
  • 15 matches the circle divided into 5 parts.
  • 18 matches the circle divided into 8 parts.
  • 16 matches the circle divided into 6 parts.

7.4 Fractions on the Number Line

Fractions are numbers and can be placed on a number line. To mark 35, you divide the space between 0 and 1 into 5 equal parts, and then count 3 parts from 0.

Figure it Out (Page 159-160)

1. & 2. (Page 159): The boxes should be filled as:
First line: 13
Second line: 25 and 45

3. (Page 160): How many fractions lie between 0 and 1?
There are infinitely many fractions between 0 and 1. You can always make the denominator larger to find more fractions in between any two existing ones.

5. (Page 160): Write the fraction for each black line.
The marks are at 65, 75, 85, 95.

7.5 Mixed Fractions

When a fraction’s numerator is larger than its denominator (an improper fraction), it represents a value greater than 1. These can be written as a mixed number, which has a whole number part and a fractional part.

Figure it Out (Page 162-163)

1. Write as mixed fractions:

  • a. 92 = 412
  • b. 95 = 145
  • c. 2119 = 1219
  • d. 479 = 529
  • e. 1211 = 1111
  • f. 196 = 316

2. Write as improper fractions:

  • a. 314 = (3×4)+14 = 134
  • b. 723 = (7×3)+23 = 233
  • c. 949 = (9×9)+49 = 859
  • d. 316 = (3×6)+16 = 196
  • e. 2311 = (2×11)+311 = 2511
  • f. 3910 = (3×10)+910 = 3910

7.6 Equivalent Fractions

Equivalent fractions are fractions that represent the same value, even though they have different numerators and denominators. You can create an equivalent fraction by multiplying (or dividing) both the numerator and denominator by the same non-zero number.

Example: 12 = 24 = 36. In each case, the share per person is the same.

Figure it Out (Page 168)

a. 5 glasses for 4 friends is the same as 10 glasses for 8 friends. (54 = 108)

b. 4 kg of potatoes in 3 bags is the same as 12 kgs in 9 bags. (43 = 129)

c. 7 rotis for 5 children is the same as 14 rotis for 10 children. (75 = 1410)

7.7 Comparing, Adding, and Subtracting Fractions

The Golden Rule

To compare, add, or subtract fractions with different denominators, you must first convert them into equivalent fractions with a common denominator.

The easiest common denominator to find is the Lowest Common Multiple (LCM) of the original denominators.

Figure it Out (Page 172-174)

1. Express in lowest terms: (Page 173)

  • a. 1751 (divide by 17) = 13
  • b. 64144 (divide by 8, then 2) = 818 = 49
  • c. 126147 (divide by 7, then 3) = 1821 = 67

2. Write in ascending order: (Page 174)

a. 710, 1115, 25. LCM of 10, 15, 5 is 30.
Fractions become: 2130, 2230, 1230.
Ascending order: 1230, 2130, 2230 → 25, 710, 1115.

3. Write in descending order: (Page 174)

a. 2516, 78, 134, 1732. LCM is 32.
Fractions become: 5032, 2832, 10432, 1732.
Descending order: 134, 2516, 78, 1732.

Addition & Subtraction Word Problems (Page 179, 182)

1. Rahim’s paint (Page 179)

212 + 314 = 52 + 134 = 104 + 134 = 234 = 534 litres.

2. Geeta and Shamim’s lace (Page 179)

Total lace bought: 25 + 34 = 820 + 1520 = 2320 = 1320 metres.
Since 1320 m is more than the required 1 m, yes, the lace will be sufficient.

3. Jaya’s walk (Page 182)

Total distance is 710 km. Auto distance is 12 km.
Walking distance = 710 – 12 = 710 – 510 = 210 = 15 km.

Puzzle! (Page 184-185)

Find different unit fractions that add up to 1.

1. Three different unit fractions:
The only solution is 12 + 13 + 16 = 1.
(36 + 26 + 16 = 66 = 1)

2. Four different unit fractions:
There are six solutions. One of them is 12 + 14 + 16 + 112 = 1.
(612 + 312 + 212 + 112 = 1212 = 1)

SUMMARY

  • A fraction represents equal shares of a whole. The top number is the numerator, the bottom is the denominator.
  • Unit fractions have a numerator of 1. A larger denominator means a smaller unit fraction.
  • Equivalent fractions represent the same value (e.g., 12 and 24).
  • A fraction is in its simplest form (or lowest terms) when the numerator and denominator have no common factors other than 1.
  • Mixed numbers (e.g., 213) represent values greater than 1 and can be converted to/from improper fractions (e.g., 73).
  • The Golden Rule: To compare, add, or subtract fractions, you must first find a common denominator.