# Fractions - Class 5 - Mathematics

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## Exercise 22 - Fractions | R.S. Aggarwal | Mathematics | Class 5

(a)

Shaded $=$

Unshaded $=$

(b)

Shaded $=$

Unshaded $=$

(c)

Shaded $=$

Unshaded $=$

(a)

Shaded $=$ 2

Unshaded $=$ 1

(b)

Shaded $=$ 1

Unshaded $=$ 5

(c)

Shaded $=$ 4

Unshaded $=$ 9

Circle each one of the unit fractions given below.

$\frac{6}{1}, \frac{1}{4}, \frac{3}{6}, \frac{1}{7}, \frac{9}{1}, \frac{1}{10}, \frac{5}{5}, \frac{1}{11}$

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Sign up nowCircle each pair of like fractions given below.

(a) $\frac{3}{5}, \frac{4}{5}$

(b) $\frac{2}{5}, \frac{2}{7}$

(c) $\frac{5}{9}, \frac{7}{9}$

(d) $\frac{6}{7}, \frac{6}{11}$

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Sign up nowCircle each pair of unlike fractions given below.

(a) $\frac{1}{4}, \frac{1}{7}$

(b) $\frac{3}{4}, \frac{3}{5}$

(c) $\frac{4}{9}, \frac{7}{9}$

(d) $\frac{5}{11}, \frac{7}{11}$

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Sign up nowCircle each one of the proper fractions given below.

(a) $\frac{5}{3}$

(b) $\frac{6}{7}$

(c) $\frac{3}{3}$

(d) $\frac{8}{11}$

(e) $\frac{6}{1}$

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Circle each one of the improper fractions given below.

(a) $\frac{7}{8}$

(b) $\frac{4}{4}$

(c) $\frac{11}{6}$

(d) $\frac{8}{1}$

(e) $\frac{1}{1}$

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Convert each of the following into an improper fraction.

(a) $3 \frac{3}{5}$

(b) $2 \frac{5}{7}$

(c) $6 \frac{2}{3}$

(d) $4 \frac{5}{6}$

(e) $7 \frac{1}{7}$

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Convert each of the following into a mixed number.

(a) $\frac{11}{4}$

(b) $\frac{17}{8}$

(c) $\frac{23}{6}$

(d) $\frac{19}{5}$

(e) $\frac{15}{7}$

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Write four fractions equivalent to each of the following.

(a) $\frac{2}{3}$

(b) $\frac{5}{6}$

(c) $\frac{4}{7}$

(d) $\frac{3}{5}$

(e) $\frac{8}{11}$

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Replace $\square$ in each of the following by the correct numeral.

(a) $\frac{3}{5}=\frac{12}{\square}$

(b) $\frac{6}{13}=\frac{\square}{52}$

(c) $\frac{7}{17}=\frac{\square}{85}$

(d) $\frac{11}{27}=\frac{33}{\square}$

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Find an equivalent fraction of $\frac{7}{11}$ having denominator 33 .

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Find an equivalent fraction of $\frac{5}{6}$ having numerator 35 .

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Find an equivalent fraction of $\frac{45}{54}$ having numerator 5 .

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Find an equivalent fraction of $\frac{35}{40}$ having denominator 8 .

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Check whether the given fractions are equivalent or not.

(a) $\frac{3}{4}$ and $\frac{15}{20}$

(b) $\frac{4}{5}$ and $\frac{12}{20}$

(c) $\frac{2}{3}$ and $\frac{10}{15}$

(d) $\frac{5}{8}$ and $\frac{15}{24}$

(e) $\frac{7}{11}$ and $\frac{28}{44}$

(f) $\frac{3}{10}$ and $\frac{12}{50}$

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## Exercise 23 - Fractions | R.S. Aggarwal | Mathematics | Class 5

Which of the following fractions are in simplest form?

1. $\frac{21}{40}$

2. $\frac{24}{35}$

3. $\frac{15}{20}$

4. $\frac{36}{81}$

5. $\frac{24}{57}$

6. $\frac{28}{39}$

The fractions in their simplest form are:

- $\frac{21}{40}$: Already in simplest form.
- $\frac{24}{35}$: Already in simplest form.
- $\frac{15}{20}$: Simplifies to $\frac{3}{4}$.
- $\frac{36}{81}$: Simplifies to $\frac{4}{9}$.
- $\frac{24}{57}$: Simplifies to $\frac{8}{19}$.
- $\frac{28}{39}$: Already in simplest form.

Thus, the fractions already in simplest form are $\frac{21}{40}$, $\frac{24}{35}$, and $\frac{28}{39}$.

Reduce each of the following fractions to the simplest form.

7. $\frac{9}{27}$

8. $\frac{16}{24}$

9. $\frac{42}{48}$

10. $\frac{45}{54}$

11. $\frac{40}{72}$

12. $\frac{38}{95}$

13. $\frac{35}{63}$

14. $\frac{56}{70}$

15. $\frac{64}{80}$

16. $\frac{44}{66}$

17. $\frac{72}{80}$

18. $\frac{51}{68}$

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## Exercise 24 - Fractions | R.S. Aggarwal | Mathematics | Class 5

Which is the greater fraction in each of the following pairs?

(a) $\frac{3}{4}, \frac{1}{4}$

(b) $\frac{4}{7}, \frac{6}{7}$

(c) $\frac{7}{9}, \frac{5}{9}$

(d) $\frac{8}{13}, \frac{11}{13}$

(e) $\frac{13}{27}, \frac{23}{27}$

(f) $\frac{17}{21}, \frac{20}{21}$

Here are the greater fractions for each pair:

(a) $\frac{3}{4}$ is greater than $\frac{1}{4}$.

(b) $\frac{6}{7}$ is greater than $\frac{4}{7}$.

(c) $\frac{7}{9}$ is greater than $\frac{5}{9}$.

(d) $\frac{11}{13}$ is greater than $\frac{8}{13}$.

(e) $\frac{23}{27}$ is greater than $\frac{13}{27}$.

(f) $\frac{20}{21}$ is greater than $\frac{17}{21}$.

Which is the smaller fraction in each of the following pairs?

(a) $\frac{1}{3}, \frac{1}{5}$

(b) $\frac{5}{6}, \frac{5}{7}$

(c) $\frac{4}{9}, \frac{4}{7}$

(d) $\frac{7}{10}, \frac{7}{13}$

(e) $\frac{8}{9}, \frac{8}{11}$

(f) $\frac{6}{7}, \frac{6}{5}$

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Arrange the following fractions in ascending order.

(a) $\frac{9}{11}, \frac{3}{11}, \frac{7}{11}, \frac{6}{11}, \frac{10}{11}$

(b) $\frac{8}{15}, \frac{2}{15}, \frac{11}{15}, \frac{7}{15}, \frac{13}{15}$

(c) $\frac{5}{19}, \frac{13}{19}, \frac{7}{19}, \frac{3}{19}, \frac{11}{19}$

(d) $\frac{12}{25}, \frac{23}{25}, \frac{9}{25}, \frac{13}{25}, \frac{11}{25}$

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Arrange the following fractions in descending order.

(a) $\frac{3}{7}, \frac{3}{5}, \frac{3}{11}, \frac{3}{8}, \frac{3}{14}$

(b) $\frac{8}{9}, \frac{8}{15}, \frac{8}{11}, \frac{8}{17}, \frac{8}{13}$

(c) $\frac{5}{8}, \frac{5}{6}, \frac{5}{11}, \frac{5}{14}, \frac{5}{12}$

(d) $\frac{10}{21}, \frac{10}{17}, \frac{10}{19}, \frac{10}{23}, \frac{10}{11}$

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## Exercise 25 - Fractions | R.S. Aggarwal | Mathematics | Class 5

Fill in each placeholder with the symbol $>,<$ or $=$ to make the statement true.

(a) $\frac{2}{5} \bigcirc \frac{7}{8}$

(b) $\frac{3}{4} \bigcirc \frac{2}{5}$

(c) $\frac{17}{4} \bigcirc \frac{13}{3}$

(d) $\frac{5}{8} \bigcirc \frac{4}{7}$

(e) $\frac{4}{6} \bigcirc \frac{6}{9}$

(f) $\frac{13}{6} \bigcirc \frac{11}{5}$

(g) $\frac{7}{10} \bigcirc \frac{5}{9}$

(h) $\frac{3}{10} \bigcirc \frac{7}{25}$

(i) $\frac{3}{8} \bigcirc \frac{2}{9}$

Here are the correct symbols to make each statement true:

(a) $\frac{2}{5} < \frac{7}{8}$

(b) $\frac{3}{4} > \frac{2}{5}$

(c) $\frac{17}{4} < \frac{13}{3}$

(d) $\frac{5}{8} > \frac{4}{7}$

(e) $\frac{4}{6} = \frac{6}{9}$

(f) $\frac{13}{6} < \frac{11}{5}$

(g) $\frac{7}{10} > \frac{5}{9}$

(h) $\frac{3}{10} > \frac{7}{25}$

(i) $\frac{3}{8} > \frac{2}{9}$

Compare the following.

(a) $2 \frac{3}{5}, 2 \frac{3}{4}$

(b) $3 \frac{1}{3}, 3 \frac{3}{10}$

(c) $2 \frac{1}{7}, 1 \frac{7}{9}$

(d) $4 \frac{2}{7}, 4 \frac{1}{3}$

(e) $5 \frac{1}{6}, 5 \frac{1}{4}$

(f) $\frac{2}{1}, 2 \frac{1}{10}$

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Arrange the following fractions in an ascending order.

(a) $\frac{5}{6}, \frac{7}{9}, \frac{2}{3}, \frac{11}{12}$

(b) $\frac{4}{5}, \frac{7}{10}, \frac{8}{15}, \frac{1}{2}$

(c) $\frac{1}{3}, \frac{3}{10}, \frac{5}{6}, \frac{2}{5}$

(d) $\frac{7}{8}, \frac{5}{12}, \frac{15}{16}, \frac{17}{24}$

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Arrange the following fractions in a descending order.

(a) $\frac{1}{2}, \frac{3}{4}, \frac{5}{8}, \frac{9}{16}$

(b) $\frac{2}{7}, \frac{11}{35}, \frac{9}{14}, \frac{13}{28}$

(c) $\frac{3}{4}, \frac{7}{8}, \frac{7}{12}, \frac{17}{24}$

(d) $\frac{2}{5}, \frac{3}{10}, \frac{7}{15}, \frac{1}{2}$

(e) $\frac{5}{9}, \frac{3}{12}, \frac{1}{3}, \frac{4}{15}$

(f) $\frac{3}{8}, \frac{1}{2}, \frac{5}{6}, \frac{2}{3}$

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## Question Bag 1 - Fractions | R.S. Aggarwal | Mathematics | Class 5

Which of the following is an improper fraction?

(a) $\frac{2}{3}$

(b) $\frac{16}{17}$

(c) $\frac{5}{4}$

(d) $\frac{19}{50}$

An improper fraction is defined as a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Let's examine the options:

(a) $\frac{2}{3}$: The numerator (2) is less than the denominator (3), so it's a proper fraction.

(b) $\frac{16}{17}$: The numerator (16) is less than the denominator (17), so it's a proper fraction.

(c) $\frac{5}{4}$: The numerator (5) is greater than the denominator (4), making it an improper fraction.

(d) $\frac{19}{50}$: The numerator (19) is less than the denominator (50), so it's a proper fraction.

Therefore, the improper fraction among the options is:

(c) $\frac{5}{4}$

Which fraction is greater than $\frac{1}{2}$ ?

(a) $\frac{1}{4}$

(b) $\frac{2}{7}$

(c) $\frac{3}{8}$

(d) $\frac{3}{4}$

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## Question Bag 2 - Fractions | R.S. Aggarwal | Mathematics | Class 5

Find the equivalent fraction of $\frac{\mathbf{7 5}}{\mathbf{9 0}}$ having

(a) numerator 15

(b) denominator 42

(c) denominator 270

(d) numerator 30

To find the equivalent fraction of $\frac{75}{90}$ that meets each condition, we’ll first simplify $\frac{75}{90}$ and then scale it accordingly.

### Step 1: Simplify $\frac{75}{90}$

This fraction simplifies by dividing both the numerator and denominator by their greatest common divisor (GCD).

### Step 2: Find Equivalent Fractions

(a) **Numerator 15**: Scale the simplified fraction so its numerator is 15.

(b) **Denominator 42**: Scale the simplified fraction so its denominator is 42.

(c) **Denominator 270**: Scale the simplified fraction so its denominator is 270.

(d) **Numerator 30**: Scale the simplified fraction so its numerator is 30.

Let’s first simplify $\frac{75}{90}$ and then find the equivalent fractions for each condition. Here are the equivalent fractions of $\frac{75}{90}$:

- Simplified, $\frac{75}{90}$ is equal to $\frac{5}{6}$.

For the conditions given, the equivalent fractions are:

(a) With numerator 15, the equivalent fraction is $\frac{5}{2}$.

(b) With denominator 42, the equivalent fraction cannot be directly calculated due to a mistake. Let's correct that.

(c) With denominator 270, the equivalent fraction is $\frac{75}{2}$.

(d) With numerator 30, the equivalent fraction is $\frac{5}{1}$ or simply 5.

There seems to have been an error in calculating the equivalent fraction for the denominator 42 condition. Let me correct this and provide the proper equivalent fraction. Correcting the previous mistake, for the condition with denominator 42, the equivalent fraction is $\frac{35}{6}$.

Summarizing all the conditions:

- Simplified fraction of $\frac{75}{90}$: $\frac{5}{6}$
- (a) For numerator 15: $\frac{5}{2}$
- (b) For denominator 42: $\frac{35}{6}$
- (c) For denominator 270: $\frac{75}{2}$
- (d) For numerator 30: $\frac{5}{1}$ or simply 5

Complete the following table.

Improper Fraction | $\frac{86}{9}$ | $\frac{227}{15}$ | $\frac{120}{21}$ | |||

Mixed Numeral | $5 \frac{6}{7}$ | $8 \frac{11}{13}$ | $7 \frac{17}{54}$ |