Class 6 Fractions worksheet with questions on adding fractions, solving equations, and identifying fraction types.

Here are the step-by-step solutions for each question on the worksheet.

(1) Add the following fractions and reduce them to the simplest form:

A) $\frac{11}{12} + \frac{4}{9}$
1. Find the Least Common Multiple (LCM) of 12 and 9, which is 36.
2. Convert fractions: $\frac{11 \times 3}{36} + \frac{4 \times 4}{36} = \frac{33}{36} + \frac{16}{36}$.
3. Add numerators: $\frac{33 + 16}{36} = \frac{49}{36}$.
4. This cannot be simplified further. As a mixed number, it is $1 \frac{13}{36}$.

B) $\frac{23}{24} + \frac{17}{37}$
1. The LCM of 24 and 37 is $24 \times 37 = 888$.
2. Convert fractions: $\frac{23 \times 37}{888} + \frac{17 \times 24}{888}$.
3. Calculate numerators: $23 \times 37 = 851$ and $17 \times 24 = 408$.
4. Add: $\frac{851 + 408}{888} = \frac{1259}{888}$.
5. As a mixed number: $1 \frac{371}{888}$.

C) $\frac{23}{27} + \frac{19}{26}$
1. The LCM of 27 and 26 is $27 \times 26 = 702$.
2. Convert fractions: $\frac{23 \times 26}{702} + \frac{19 \times 27}{702}$.
3. Calculate numerators: $23 \times 26 = 598$ and $19 \times 27 = 513$.
4. Add: $\frac{598 + 513}{702} = \frac{1111}{702}$.
5. As a mixed number: $1 \frac{409}{702}$.

D) $\frac{29}{32} + \frac{15}{37}$
1. The LCM of 32 and 37 is $32 \times 37 = 1184$.
2. Convert fractions: $\frac{29 \times 37}{1184} + \frac{15 \times 32}{1184}$.
3. Calculate numerators: $29 \times 37 = 1073$ and $15 \times 32 = 480$.
4. Add: $\frac{1073 + 480}{1184} = \frac{1553}{1184}$.
5. As a mixed number: $1 \frac{369}{1184}$.

E) $\frac{23}{27} + \frac{2}{25}$
1. The LCM of 27 and 25 is $27 \times 25 = 675$.
2. Convert fractions: $\frac{23 \times 25}{675} + \frac{2 \times 27}{675}$.
3. Calculate numerators: $23 \times 25 = 575$ and $2 \times 27 = 54$.
4. Add: $\frac{575 + 54}{675} = \frac{629}{675}$.

F) $\frac{29}{30} + \frac{15}{16}$
1. The LCM of 30 and 16 is 240.
2. Convert fractions: $\frac{29 \times 8}{240} + \frac{15 \times 15}{240}$.
3. Calculate numerators: $29 \times 8 = 232$ and $15 \times 15 = 225$.
4. Add: $\frac{232 + 225}{240} = \frac{457}{240}$.
5. As a mixed number: $1 \frac{217}{240}$.

---

(2) Word Problem

* Total pages: 336
* Pages read per day: $\frac{2}{48}$ of the book.
* Simplify daily fraction: $\frac{2}{48}$ simplifies to $\frac{1}{24}$.
* Calculate pages per day: $\frac{1}{24} \times 336 = 14$ pages.
* Total days: 2 days.
* Total pages read: $14 \text{ pages/day} \times 2 \text{ days} = 28$ pages.

Meenakshi has read 28 pages.

---

(3) Solve for the value of z

Equation: $\frac{6}{100} + \frac{5}{10} + \frac{6}{z} + 3 = 3.62$

1. Convert fractions to decimals:
* $\frac{6}{100} = 0.06$
* $\frac{5}{10} = 0.5$
2. Rewrite the equation:
$0.06 + 0.5 + \frac{6}{z} + 3 = 3.62$
3. Combine the known numbers on the left side:
$0.06 + 0.5 + 3 = 3.56$
So, $3.56 + \frac{6}{z} = 3.62$
4. Subtract 3.56 from both sides:
$\frac{6}{z} = 3.62 - 3.56$
$\frac{6}{z} = 0.06$
5. Solve for $z$:
$z = \frac{6}{0.06}$
$z = 100$

The value of z is 100.

---

(4) What is the LCM?

Find the LCM of $\frac{11}{42}, \frac{11}{28}, \text{and } \frac{8}{35}$.

Rule: $\text{LCM of Fractions} = \frac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$

1. Numerators: 11, 11, 8.
* LCM(11, 11, 8) = $11 \times 8 = 88$.
2. Denominators: 42, 28, 35.
* Factors of 42: $2 \times 3 \times 7$
* Factors of 28: $2 \times 2 \times 7$
* Factors of 35: $5 \times 7$
* The only common factor for all three is 7. So, HCF = 7.
3. Calculate Final LCM:
$\frac{88}{7}$

The LCM is $\frac{88}{7}$ (or $12 \frac{4}{7}$).

---

(5) Choose correct answer

The figure shows a circle divided into 8 equal parts.
* It can represent proper fractions (like $\frac{3}{8}$).
* It can represent improper fractions (like $\frac{9}{8}$, which would require more than one circle).
* It can represent unit fractions (like $\frac{1}{8}$).
* "Unlike fractions" refers to fractions with *different* denominators (e.g., $\frac{1}{2}$ and $\frac{1}{3}$). A single figure with fixed divisions (denominator 8) cannot simultaneously represent fractions with different denominators directly without conversion. Therefore, this type of figure is least suited for representing the concept of "unlike fractions" directly.

Correct Answer: a. Unlike fractions

──────────────────────────────────────

Final Answer:
(1)
A) $\frac{49}{36}$ or $1 \frac{13}{36}$
B) $\frac{1259}{888}$ or $1 \frac{371}{888}$
C) $\frac{1111}{702}$ or $1 \frac{409}{702}$
D) $\frac{1553}{1184}$ or $1 \frac{369}{1184}$
E) $\frac{629}{675}$
F) $\frac{457}{240}$ or $1 \frac{217}{240}$

(2) 28 pages

(3) $z = 100$

(4) $\frac{88}{7}$ or $12 \frac{4}{7}$

(5) a. Unlike fractions