Addition and Subtraction of Fractions - Class 5 - Mathematics
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Exercise 26 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
$\frac{5}{7}+\frac{2}{7}$
To solve $\frac{5}{7}+\frac{2}{7}$:
Since the denominators are the same, you simply add the numerators and keep the same denominator:
$$ \frac{5}{7}+\frac{2}{7} = \frac{5+2}{7} = \frac{7}{7} = 1 $$
So, $\frac{5}{7}+\frac{2}{7} = 1$.
$\frac{2}{9}+\frac{5}{9}$
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Sign up now$\frac{3}{11}+\frac{9}{11}$
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Sign up now$\frac{6}{7}+\frac{3}{7}$
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Sign up now$\frac{5}{8}+\frac{5}{8}$
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Sign up now$\frac{5}{12}+\frac{11}{12}$
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Sign up now$\frac{1}{4}+\frac{1}{4}+\frac{3}{4}$
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Sign up now$\frac{4}{15}+\frac{7}{15}+\frac{8}{15}$
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Sign up now$\frac{1}{10}+\frac{7}{10}+\frac{3}{10}$
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Sign up now$\frac{9}{16}+\frac{7}{16}+\frac{3}{16}$
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Sign up now$\frac{16}{21}+\frac{4}{21}+\frac{1}{21}$
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Sign up now$\frac{12}{19}+\frac{8}{19}+\frac{6}{19}$
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Sign up nowExercise 27 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
Add $\frac{2}{5}$ and $\frac{3}{10}$
To add the fractions $\frac{2}{5}$ and $\frac{3}{10}$, we need to find a common denominator, which in this case is $10$. Once we have a common denominator, we can add the numerators.
First, convert $\frac{2}{5}$ to a fraction with a denominator of $10$: $$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$
Now, we can add $\frac{4}{10}$ and $\frac{3}{10}$: $$\frac{4}{10} + \frac{3}{10} = \frac{4 + 3}{10} = \frac{7}{10}$$
Therefore, $\frac{2}{5} + \frac{3}{10} = \frac{7}{10}$.
Add $\frac{4}{7}$ and $\frac{2}{3}$
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Sign up nowAdd $\frac{4}{9}$ and $\frac{5}{6}$
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Sign up nowAdd $\frac{3}{4}$ and $\frac{11}{12}$
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Sign up nowFind the sum.
5. $\frac{5}{12}+\frac{7}{16}$
6. $\frac{5}{8}+\frac{7}{12}$
7. $\frac{1}{6}+\frac{7}{10}$
8. $\frac{8}{15}+\frac{9}{20}$
9. $\frac{11}{12} + \frac{13}{18}$
10. $\frac{1}{2}+\frac{2}{3}+\frac{3}{4}$
11. $\frac{1}{6}+\frac{3}{8}+3$
12. $\frac{5}{7}+\frac{9}{14}+\frac{1}{2}$
13. $\frac{5}{9}+\frac{7}{12}+\frac{1}{3}$
14. $\frac{3}{4}+\frac{5}{8}+\frac{7}{12}$
15. $\frac{3}{8}+\frac{5}{16}+\frac{13}{24}$
16. $\frac{5}{6} + \frac{7}{12} + \frac{11}{18}$
17. $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}$
18. $\frac{1}{1}+\frac{2}{3}+\frac{3}{4}+\frac{5}{8}$
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Sign up nowExercise 28 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
Find the following sums.
1. $4 \frac{2}{5}+3 \frac{1}{5}$
2. $3 \frac{4}{7}+5 \frac{2}{7}$
3. $6 \frac{1}{4}+3 \frac{3}{8}$
4. $4 \frac{1}{6}+5 \frac{7}{12}$
5. $2 \frac{3}{7}+\frac{9}{14}$
6. $2 \frac{4}{9}+\frac{2}{3}$
7. $1 \frac{3}{4}+2 \frac{2}{3}+3 \frac{1}{6}$
8. $2 \frac{4}{5}+1 \frac{3}{10}+2 \frac{1}{2}$
9. $2 \frac{5}{9}+3 \frac{1}{3}+1 \frac{5}{6}$
10. $3 \frac{2}{5}+1 \frac{1}{10}+\frac{4}{15}$
11. $2 \frac{3}{5}+8+\frac{7}{10}$
12. $7 \frac{1}{2}+\frac{5}{9}+\frac{2}{3}$
The sum of $4 \frac{2}{5}+3 \frac{1}{5}$ is $\frac{38}{5}$, which equals $7.6$ or as a mixed fraction, $7 \frac{3}{5}$.
$3 \frac{4}{7}+5 \frac{2}{7} = 8 \frac{6}{7}$
$6 \frac{1}{4}+3 \frac{3}{8} = 9 \frac{5}{8}$
$4 \frac{1}{6}+5 \frac{7}{12} = 9 \frac{3}{4}$
$2 \frac{3}{7}+\frac{9}{14} = 3 \frac{1}{14}$
$2 \frac{4}{9}+\frac{2}{3} = 3 \frac{1}{9}$
$1 \frac{3}{4}+2 \frac{2}{3}+3 \frac{1}{6} = 7 \frac{7}{12}$
$2 \frac{4}{5}+1 \frac{3}{10}+2 \frac{1}{2} = 6 \frac{3}{5}$
$2 \frac{5}{9}+3 \frac{1}{3}+1 \frac{5}{6} = 7 \frac{13}{18}$
$3 \frac{2}{5}+1 \frac{1}{10}+\frac{4}{15} = 4 \frac{23}{30}$
$2 \frac{3}{5}+8+\frac{7}{10} = 11 \frac{3}{10}$
$7 \frac{1}{2}+\frac{5}{9}+\frac{2}{3} = 8 \frac{13}{18}$
Exercise 29 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
Find the difference.
1. $\frac{9}{4}-\frac{1}{4}$
2. $\frac{3}{8}-\frac{1}{8}$
3. $\frac{7}{10}-\frac{3}{10}$
4. $\frac{11}{15}-\frac{8}{15}$
5. $\frac{7}{20}-\frac{3}{20}$
6. $\frac{5}{6}-\frac{1}{6}$
7. $\frac{3}{2}-\frac{1}{2}$
8. $\frac{5}{18}-\frac{1}{18}$
9. $\frac{9}{28}-\frac{5}{28}$
Here are the differences for the given fractions:
1. $\frac{9}{4} - \frac{1}{4} = 2$
2. $\frac{3}{8} - \frac{1}{8} = \frac{1}{4}$
3. $\frac{7}{10} - \frac{3}{10} = \frac{2}{5}$
4. $\frac{11}{15} - \frac{8}{15} = \frac{1}{5}$
5. $\frac{7}{20} - \frac{3}{20} = \frac{1}{5}$
6. $\frac{5}{6} - \frac{1}{6} = \frac{2}{3}$
7. $\frac{3}{2} - \frac{1}{2} = 1$
8. $\frac{5}{18} - \frac{1}{18} = \frac{2}{9}$
9. $\frac{9}{28} - \frac{5}{28} = \frac{1}{7}$
Exercise 30 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
Find the difference of:
1. $\frac{1}{2}$ and $\frac{1}{3}$
2. $\frac{1}{6}$ and $\frac{2}{3}$
3. $\frac{3}{4}$ and $\frac{5}{6}$
4. $\frac{3}{8}$ and $\frac{5}{12}$
5. $\frac{7}{10}$ and $\frac{8}{15}$
6. $\frac{7}{20}$ and $\frac{19}{15}$
Here are the differences for the specified fractions:
$\frac{1}{2} - \frac{1}{3} = \frac{1}{6}$
$\frac{1}{6} - \frac{2}{3} = -\frac{1}{2}$
$\frac{3}{4} - \frac{5}{6} = -\frac{1}{12}$
$\frac{3}{8} - \frac{5}{12} = -\frac{1}{24}$
$\frac{7}{10} - \frac{8}{15} = \frac{1}{6}$
$\frac{7}{20} - \frac{19}{15} = -\frac{11}{12}$
Subtract:
7. $\frac{4}{5}-\frac{3}{10}$
8. $6-\frac{3}{5}$
9. $\frac{17}{16}-\frac{11}{24}$
10. $1-\frac{8}{15}$
11. $5-\frac{5}{8}$
12. $\frac{53}{6}-7$
13. $3 \frac{3}{4}-2 \frac{1}{2}$
14. $6 \frac{2}{3}-4 \frac{1}{9}$
15. $5 \frac{2}{3}-2 \frac{3}{4}$
16. $5 \frac{5}{12}-4 \frac{1}{6}$
17. $5 \frac{1}{8}-3 \frac{1}{12}$
18. $5 \frac{3}{10}-3 \frac{7}{15}$
19. $7 \frac{4}{9}-3 \frac{5}{12}$
20. $5 \frac{1}{6}-1 \frac{7}{10}$
21. $3-2 \frac{1}{8}$
22. $5-1 \frac{6}{7}$
23. $3 \frac{3}{4}-\frac{7}{10}$
24. $1 \frac{11}{24}-\frac{7}{8}$
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Sign up nowExercise 31 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
1. $\frac{1}{2}+\frac{3}{4}-\frac{5}{8}$
The result of the calculation $$\frac{1}{2}+\frac{3}{4}-\frac{5}{8}$$ is $$\frac{5}{8}$$, which is equivalent to 0.625 in decimal form.
Here's a visual representation on a number line:
Additionally, you can view it as a pie chart:
And as a tape diagram:
2. $\frac{7}{8}-\frac{1}{6}+\frac{5}{12}$
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Sign up now3. $\frac{1}{4}-\frac{5}{9}+\frac{7}{12}$
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Sign up now4. $\frac{3}{5}+\frac{7}{10}-\frac{1}{2}$
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Sign up now5. $\frac{3}{10}-\frac{8}{15}+\frac{2}{5}$
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Sign up now6. $\frac{4}{9}-\frac{5}{12}+\frac{1}{4}$
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Sign up now7. $2 \frac{1}{3}+3 \frac{1}{6}-1 \frac{5}{12}$
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Sign up now8. $4 \frac{1}{4}-2 \frac{3}{8}+3 \frac{1}{3}$
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Sign up now9. $6 \frac{5}{9}-4 \frac{1}{3}-2 \frac{1}{6}$
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Sign up now10. $10-3 \frac{1}{5}-5 \frac{3}{10}$
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Sign up now11. Subtract the sum of $5 \frac{1}{2}$ and $6 \frac{3}{8}$ from the sum of $7 \frac{3}{4}$ and $6 \frac{1}{2}$.
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Sign up now12. Subtract the difference of $6 \frac{2}{3}$ and $5 \frac{1}{6}$ from the difference of 4 and $2 \frac{1}{3}$.
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Sign up nowExercise 32 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
A frog took three jumps. The first jump was $\frac{3}{5} \mathrm{~m}$ long, the second was $\frac{3}{4} \mathrm{~m}$ long and the third was $\frac{7}{10} \mathrm{~m}$ long. How far did the frog jump in all?
To find the total distance the frog jumped, we sum up the lengths of all three jumps:
$$ \frac{3}{5} , \mathrm{m} + \frac{3}{4} \mathrm{m} + \frac{7}{10} \mathrm{m} $$
Calculating this, we get:
$$ = \frac{3 \times 8}{5 \times 8} + \frac{3 \times 5}{4 \times 5} + \frac{7 \times 4}{10 \times 4} $$
$$ = \frac{24}{40} + \frac{15}{20} + \frac{28}{40} $$
Since $\frac{15}{20}$ equals $\frac{30}{40}$, we have:
$$ = \frac{24 + 30 + 28}{40} $$
$$ = \frac{82}{40} $$
$$ = \frac{41}{20} $$
Therefore, the frog jumped a total of $\frac{41}{20} , \mathrm{m}$ or $2.05 , \mathrm{m}$.
Renu took $2 \frac{3}{4}$ hours to paint a table and $1 \frac{1}{3}$ hours to paint a chair. How much time did she take in all?
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Sign up nowRohit purchased $4 \frac{1}{2} \mathrm{~kg}$ of potatoes, $3 \frac{1}{4} \mathrm{~kg}$ of onions, $\frac{3}{4} \mathrm{~kg}$ of tomatoes and $1 \frac{1}{8} \mathrm{~kg}$ of peas. What is the total quantity of vegetables purchased by Rohit?
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Sign up nowA piece of length $3 \frac{4}{5}$ metres is cut off from a rope $7 \frac{1}{4}$ metres long. What is the length of the remaining piece?
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Sign up nowA gas cylinder contained 35 litres of gas. $23 \frac{3}{5}$ litres of gas is used. How much gas is left in the cylinder?
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Sign up nowA drum full of rice weighs $40 \frac{1}{6} \mathrm{~kg}$. If the empty drum weighs $13 \frac{3}{4} \mathrm{~kg}$, find the weight of rice in the drum.
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Sign up nowThe heights of Deepak and Vikas are $148 \frac{5}{6} \mathrm{~cm}$ and $153 \frac{3}{4} \mathrm{~cm}$ respectively. Who is taller, and by how much?
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Sign up nowWhat must be subtracted from $6 \frac{4}{5}$ to get $2 \frac{7}{10}$ ?
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Sign up nowWhat must be added to $7 \frac{1}{6}$ to get $9 \frac{1}{9}$ ?
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Sign up nowA man travelled $47 \frac{1}{2} \mathrm{~km}$ in one day. He covered $29 \frac{1}{3} \mathrm{~km}$ by scooter, $8 \frac{5}{6} \mathrm{~km}$ on bicycle and the remaining distance on foot. How much did he travel on foot?
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Sign up nowA basket contains three types of $19 \frac{1}{3} \mathrm{~kg}$ of fruits. There are $8 \frac{1}{9} \mathrm{~kg}$ of apples, $3 \frac{1}{6} \mathrm{~kg}$ of oranges rest pears. What is the weight of pears in the basket?
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Sign up nowMeena purchased 12 metres of cloth. She used $7 \frac{3}{4}$ metres of it for curtains and $1 \frac{5}{6}$ metres for a be sheet. How much cloth is left?
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Sign up nowWhich is greater?
The difference between $2 \frac{3}{4}$ and $5 \frac{1}{6}$.
$$
\text { Or }
$$
The sum of $1 \frac{3}{12}$ and $1 \frac{1}{3}$.
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Sign up nowQuestion Bag 1 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
$\frac{1}{3}+\frac{1}{6}=$
(a) $\frac{2}{9}$
(b) $\frac{1}{18}$
(c) $\frac{1}{2}$
(d) 1
To add the fractions $\frac{1}{3}$ and $\frac{1}{6}$, we find a common denominator and add the numerators:
$$ \frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2} $$
Hence, the correct option is:
(c) $\frac{1}{2}$
$2 \frac{1}{3}+4 \frac{1}{2}=$
(a) $6 \frac{1}{6}$
(b) $6 \frac{1}{5}$
(c) $6 \frac{2}{5}$
(d) $6 \frac{5}{6}$
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Sign up nowQuestion Bag 2 - Addition and Subtraction of Fractions | R.S. Aggarwal | Mathematics | Class 5
State whether the following statement is true or false:
$\frac{3}{4}+\frac{4}{3}=1$
To determine whether the following statement is true or false, let's calculate the sum:
$$\frac{3}{4} + \frac{4}{3}$$
To add these fractions, we'll find a common denominator, which is $12$ in this case. Then we rewrite each fraction with the common denominator and add the numerators:
$$ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $$
$$ \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} $$
Adding these together:
$$ \frac{9}{12} + \frac{16}{12} = \frac{25}{12} $$
Given that $\frac{25}{12} \neq 1$, the statement $\frac{3}{4}+\frac{4}{3}=1$ is False.
A recipe needs $\frac{2}{5}$ cup of milk and $\frac{1}{3}$ cup of cream. How much more milk than cream is required?
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