CBSE Class 6 Mental Maths Fractions Worksheet - Free Printable

Let's solve the problems step by step.

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Section 1: Missing Fractions

#### Problem 40
$$
\frac{8}{9} - \square = \frac{3}{9}
$$

To find the missing fraction, we rearrange the equation:
$$
\square = \frac{8}{9} - \frac{3}{9}
$$

Since the denominators are the same, we subtract the numerators:
$$
\square = \frac{8 - 3}{9} = \frac{5}{9}
$$

Answer:
$$
\boxed{\frac{5}{9}}
$$

#### Problem 41
$$
\frac{7}{11} - \square = \frac{4}{11}
$$

Rearrange the equation:
$$
\square = \frac{7}{11} - \frac{4}{11}
$$

Subtract the numerators:
$$
\square = \frac{7 - 4}{11} = \frac{3}{11}
$$

Answer:
$$
\boxed{\frac{3}{11}}
$$

---

Section 2: Addition and Subtraction of Fractions

#### Problem 42
Add $\frac{2}{5}$ and $\frac{3}{4}$.

First, find a common denominator. The least common multiple (LCM) of 5 and 4 is 20. Rewrite each fraction with the common denominator:
$$
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
$$
$$
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
$$

Now add the fractions:
$$
\frac{2}{5} + \frac{3}{4} = \frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}
$$

Answer:
$$
\boxed{\frac{23}{20}}
$$

#### Problem 43
Add $\frac{3}{10}$ and $\frac{1}{2}$.

The LCM of 10 and 2 is 10. Rewrite each fraction with the common denominator:
$$
\frac{3}{10} = \frac{3}{10}
$$
$$
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
$$

Now add the fractions:
$$
\frac{3}{10} + \frac{1}{2} = \frac{3}{10} + \frac{5}{10} = \frac{3 + 5}{10} = \frac{8}{10} = \frac{4}{5}
$$

Answer:
$$
\boxed{\frac{4}{5}}
$$

#### Problem 44
Add $\frac{4}{5}$ and $\frac{3}{25}$.

The LCM of 5 and 25 is 25. Rewrite each fraction with the common denominator:
$$
\frac{4}{5} = \frac{4 \times 5}{5 \times 5} = \frac{20}{25}
$$
$$
\frac{3}{25} = \frac{3}{25}
$$

Now add the fractions:
$$
\frac{4}{5} + \frac{3}{25} = \frac{20}{25} + \frac{3}{25} = \frac{20 + 3}{25} = \frac{23}{25}
$$

Answer:
$$
\boxed{\frac{23}{25}}
$$

#### Problem 45
Add $2\frac{4}{5}$ and $3\frac{1}{5}$.

Convert mixed numbers to improper fractions:
$$
2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}
$$
$$
3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}
$$

Now add the fractions:
$$
2\frac{4}{5} + 3\frac{1}{5} = \frac{14}{5} + \frac{16}{5} = \frac{14 + 16}{5} = \frac{30}{5} = 6
$$

Answer:
$$
\boxed{6}
$$

#### Problem 46
Add $3\frac{4}{9}$ and $5\frac{5}{9}$.

Convert mixed numbers to improper fractions:
$$
3\frac{4}{9} = \frac{3 \times 9 + 4}{9} = \frac{27 + 4}{9} = \frac{31}{9}
$$
$$
5\frac{5}{9} = \frac{5 \times 9 + 5}{9} = \frac{45 + 5}{9} = \frac{50}{9}
$$

Now add the fractions:
$$
3\frac{4}{9} + 5\frac{5}{9} = \frac{31}{9} + \frac{50}{9} = \frac{31 + 50}{9} = \frac{81}{9} = 9
$$

Answer:
$$
\boxed{9}
$$

#### Problem 47
Subtract $\frac{5}{10}$ from $\frac{13}{10}$.

Since the denominators are the same, subtract the numerators:
$$
\frac{13}{10} - \frac{5}{10} = \frac{13 - 5}{10} = \frac{8}{10} = \frac{4}{5}
$$

Answer:
$$
\boxed{\frac{4}{5}}
$$

#### Problem 48
Subtract $2\frac{3}{5}$ from $8\frac{2}{5}$.

Convert mixed numbers to improper fractions:
$$
2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}
$$
$$
8\frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5}
$$

Now subtract the fractions:
$$
8\frac{2}{5} - 2\frac{3}{5} = \frac{42}{5} - \frac{13}{5} = \frac{42 - 13}{5} = \frac{29}{5} = 5\frac{4}{5}
$$

Answer:
$$
\boxed{5\frac{4}{5}}
$$

---

Section 3: Word Problems

#### Problem 49
What fraction was left in the bag if Ravi was given $\frac{3}{5}$ of marbles from it?

If Ravi was given $\frac{3}{5}$ of the marbles, the remaining fraction is:
$$
1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}
$$

Answer:
$$
\boxed{\frac{2}{5}}
$$

#### Problem 50
Ashok has $1\frac{1}{2}$ m of cloth and Hari has $1\frac{1}{3}$ m of cloth. What is the total length of cloth?

Convert mixed numbers to improper fractions:
$$
1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}
$$
$$
1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}
$$

Find a common denominator. The LCM of 2 and 3 is 6. Rewrite each fraction with the common denominator:
$$
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
$$
$$
\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
$$

Now add the fractions:
$$
1\frac{1}{2} + 1\frac{1}{3} = \frac{9}{6} + \frac{8}{6} = \frac{9 + 8}{6} = \frac{17}{6} = 2\frac{5}{6}
$$

Answer:
$$
\boxed{2\frac{5}{6}}
$$

---

Test Your Self

#### Problem 1
What fraction of a day is 6 hours?

A day has 24 hours. Therefore:
$$
\text{Fraction} = \frac{6}{24} = \frac{1}{4}
$$

Answer:
$$
\boxed{\frac{1}{4}}
$$

#### Problem 2
What fraction of the numbers 1 to 30 is prime?

The prime numbers between 1 and 30 are:
$$
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
$$
There are 10 prime numbers. The total numbers from 1 to 30 is 30. Therefore:
$$
\text{Fraction} = \frac{10}{30} = \frac{1}{3}
$$

Answer:
$$
\boxed{\frac{1}{3}}
$$

#### Problem 3
Express the mixed fraction $9\frac{3}{21}$ as an improper fraction.

Convert the mixed number to an improper fraction:
$$
9\frac{3}{21} = \frac{9 \times 21 + 3}{21} = \frac{189 + 3}{21} = \frac{192}{21}
$$

Simplify the fraction:
$$
\frac{192}{21} = \frac{64}{7}
$$

Answer:
$$
\boxed{\frac{64}{7}}
$$

#### Problem 4
Express $\frac{231}{9}$ as a mixed fraction.

Divide 231 by 9:
$$
231 \div 9 = 25 \text{ remainder } 6
$$
So:
$$
\frac{231}{9} = 25\frac{6}{9} = 25\frac{2}{3}
$$

Answer:
$$
\boxed{25\frac{2}{3}}
$$

#### Problem 5
What is the equivalent fraction of $\frac{5}{11}$ having numerator 75?

Let the equivalent fraction be $\frac{75}{x}$. Since the fractions are equivalent:
$$
\frac{5}{11} = \frac{75}{x}
$$
Cross-multiply:
$$
5x = 75 \times 11
$$
$$
5x = 825
$$
$$
x = \frac{825}{5} = 165
$$
So the equivalent fraction is:
$$
\frac{75}{165}
$$

Answer:
$$
\boxed{\frac{75}{165}}
$$

#### Problem 6
What is the equivalent fraction of $\frac{13}{15}$ having denominator 60?

Let the equivalent fraction be $\frac{y}{60}$. Since the fractions are equivalent:
$$
\frac{13}{15} = \frac{y}{60}
$$
Cross-multiply:
$$
15y = 13 \times 60
$$
$$
15y = 780
$$
$$
y = \frac{780}{15} = 52
$$
So the equivalent fraction is:
$$
\frac{52}{60}
$$

Answer:
$$
\boxed{\frac{52}{60}}
$$

#### Problem 7
Reduce $\frac{112}{154}$ to its simplest form.

Find the greatest common divisor (GCD) of 112 and 154. The GCD is 14. Divide both the numerator and the denominator by 14:
$$
\frac{112}{154} = \frac{112 \div 14}{154 \div 14} = \frac{8}{11}
$$

Answer:
$$
\boxed{\frac{8}{11}}
$$

#### Problem 8
Fill with the missing fraction:
$$
\frac{5}{7} - \square = \frac{1}{7}
$$

Rearrange the equation:
$$
\square = \frac{5}{7} - \frac{1}{7}
$$

Subtract the numerators:
$$
\square = \frac{5 - 1}{7} = \frac{4}{7}
$$

Answer:
$$
\boxed{\frac{4}{7}}
$$

#### Problem 9
Add $3\frac{2}{5}$ and $2\frac{3}{5}$.

Convert mixed numbers to improper fractions:
$$
3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
$$
$$
2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}
$$

Now add the fractions:
$$
3\frac{2}{5} + 2\frac{3}{5} = \frac{17}{5} + \frac{13}{5} = \frac{17 + 13}{5} = \frac{30}{5} = 6
$$

Answer:
$$
\boxed{6}
$$

#### Problem 10
Meena bought two pieces of ribbon of length $\frac{2}{7}$ metre and $\frac{1}{2}$ metre. What is the total length of the ribbon bought by her?

Find a common denominator. The LCM of 7 and 2 is 14. Rewrite each fraction with the common denominator:
$$
\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}
$$
$$
\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
$$

Now add the fractions:
$$
\frac{2}{7} + \frac{1}{2} = \frac{4}{14} + \frac{7}{14} = \frac{4 + 7}{14} = \frac{11}{14}
$$

Answer:
$$
\boxed{\frac{11}{14}}
$$

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Final Answer

$$
\boxed{\frac{5}{9}, \frac{3}{11}, \frac{23}{20}, \frac{4}{5}, \frac{23}{25}, 6, 9, \frac{4}{5}, 5\frac{4}{5}, \frac{2}{5}, 2\frac{5}{6}, \frac{1}{4}, \frac{1}{3}, \frac{64}{7}, 25\frac{2}{3}, \frac{75}{165}, \frac{52}{60}, \frac{8}{11}, \frac{4}{7}, 6, \frac{11}{14}}
$$