Worksheet Solutions: Fractions - 1

Fill in the Blanks

Q1: When 4 children share 1 roti equally, each child gets ______ roti. 
Ans: 1/4 

When a whole item (roti) is divided into 4 equal parts, each part is 1/4 of the whole.

Q2: A whole roti is divided into 3 equal pieces. Each piece is ______ of the roti. 
Ans: 1/3 

When something is divided into 3 equal parts, each part is represented as 1/3 of the whole.

Q3: If 2 chikkis are divided equally among 6 children, each child gets ______ chikki
Ans: 1/3 

 Two chikkis divided among 6 children means each child gets a fraction 2/6, which simplifies to 1/3 of a chikki.

Q4:If 1 glass of juice is equally shared between 3 children, each child gets ______ glass of juice. 

Ans: 1/3 

Sharing 1 glass equally among 3 children results in each child receiving 1/3 of the glass.

Q5: To compare fractions with different denominators, we convert them to have the same ______. 
Ans: denominator 

Fractions need to be converted to have the same denominator so that their sizes can be compared directly.

True or False

Q1: The fraction 1/2 is smaller than 1/4. 
Ans: False 

Explanation: 1/2 is equal to one part out of two, which is larger than 1/4 (one part out of four). Therefore 1/2 > 1/4.

Q2: When 5 children share 2 cakes equally, each child's share is 2/5 of a cake. 
Ans: True 

Explanation: Dividing 2 cakes equally among 5 children gives each child 2/5 of a cake.

Q3: The fraction 3/6 is equivalent to 1/2. 
Ans: True 

Explanation: 3/6 can be simplified by dividing numerator and denominator by 3: 3/6 = (3÷3)/(6÷3) = 1/2, so they are equivalent.

Q4: The number line can only represent whole numbers, not fractions. 
Ans: False 

Explanation: Fractions can be placed on a number line between whole numbers. For example, 1/2 lies halfway between 0 and 1.

Q5: Adding 1/4 and 2/4 results in 3/4. 
Ans: True 

Explanation: When fractions have the same denominator, add the numerators: 1/4 + 2/4 = (1+2)/4 = 3/4.

Match the Following

Ans:

Answer the following Questions

Q1. Are equivalent fractions? Why?

Sol: Here, the simplest form of $\frac{6}{9}\backslash frac\{6\}\{9\}$ is:

The simplest form of $\frac{12}{18}\backslash frac\{12\}\{18\}$ is:

The simplest form of $\frac{15}{25}\backslash frac\{15\}\{25\}$ is:

Since the simplest forms of $\frac{6}{9}\backslash frac\{6\}\{9\}$ and $\frac{12}{18}\backslash frac\{12\}\{18\}$ are the same, they are equivalent fractions.
But the simplest form of $\frac{15}{25}\backslash frac\{15\}\{25\}$ is different, so it is not equivalent to the other two.

Q2. Add the following fractions and express the result as a mixed fraction:

Sol: Given,

Here, the LCM of 4, 6, and 3 is 12.

Now, expressing the fractions with denominator 12, we get:

Now, convert $\frac{63}{12}\backslash frac\{63\}\{12\}$ into a mixed fraction:

$\frac{63}{12}=5\frac{3}{12}\backslash frac\{63\}\{12\}\; =\; 5\; \backslash frac\{3\}\{12\}$

Simplifying $\frac{3}{12}\backslash frac\{3\}\{12\}$:

$\frac{3}{12}=\frac{1}{4}\backslash frac\{3\}\{12\}\; =\; \backslash frac\{1\}\{4\}$

Therefore,  is the correct answer.

Q3. Subtract as indicated:

Q4. Compare the following fraction and justify your answer:

Given fractions are $\frac{7}{4}\backslash frac\{7\}\{4\}$ and $\frac{5}{3}\backslash frac\{5\}\{3\}$.

Here, the LCM of denominators 4 and 3 is 12.

Now, converting both fractions to like fractions:

Since $\frac{21}{12}>\frac{20}{12}\backslash frac\{21\}\{12\}\; >\; \backslash frac\{20\}\{12\}$,

$\frac{7}{4}>\frac{5}{3}\backslash frac\{7\}\{4\}\; >\; \backslash frac\{5\}\{3\}$

Word Problems 

Q1: Aman mixes 7/9 liters of lemon juice with 5/6 liters of orange juice to make fruit punch. What is the total volume of fruit punch he has made?

Sol: Given:
Lemon juice = $\frac{7}{9}\backslash frac\{7\}\{9\}$ L
Orange juice = $\frac{5}{6}\backslash frac\{5\}\{6\}$ L

Total volume of fruit punch

$=\frac{7}{9}+\frac{5}{6}=\; \backslash frac\{7\}\{9\}\; +\; \backslash frac\{5\}\{6\}$

First, find the LCM of 9 and 6.
LCM of 9 and 6 = 18

Convert the fractions into like fractions:

Now, add

Converting into a mixed fraction,

Therefore, The total volume of fruit punch is $1\frac{11}{18}1\; \backslash frac\{11\}\{18\}$ liters.

Q2: Rina's school is $\backslash \backslash frac\{11\}\{15\}$11/15 km from her home. She rides her bicycle for $\backslash \backslash frac\{2\}\{5\}$2/5 km from her home daily and then walks the remaining distance to reach her school. How much distance does she walk daily?

Sol: Given:
Total distance from home to school = $\frac{11}{15}\backslash frac\{11\}\{15\}$ km
Distance covered by bicycle = $\frac{2}{5}\backslash frac\{2\}\{5\}$ km

Distance walked

$=\frac{11}{15}-\frac{2}{5}=\; \backslash frac\{11\}\{15\}\; -\; \backslash frac\{2\}\{5\}$

Find the LCM of 15 and 5.
LCM = 15

Convert $\frac{2}{5}\backslash frac\{2\}\{5\}$ into denominator 15:

Now subtract:

$\frac{11}{15}-\frac{6}{15}=\frac{5}{15}\backslash frac\{11\}\{15\}\; -\; \backslash frac\{6\}\{15\}\; =\; \backslash frac\{5\}\{15\}$

Simplify:

$\frac{5}{15}=\frac{1}{3}\backslash frac\{5\}\{15\}\; =\; \backslash frac\{1\}\{3\}$

Therefore, Rina walks $\frac{1}{3}\backslash frac\{1\}\{3\}$ km daily.

Q3: Mohan takes $\backslash \backslash frac\{5\}\{3\}$5/3 minutes to complete a swimming lap, while his friend Sohan takes 8/5 minutes to do the same. Who completes the lap faster and by how much?

Sol: Given:
Time taken by Mohan = $\frac{5}{3}$ minutes
Time taken by Sohan = $\frac{8}{5}\backslash frac\{8\}\{5\}$ minutes

To compare, convert both fractions to like denominators.

LCM of 3 and 5 = 15

Since

Sohan completes the lap faster by $\frac{1}{15}\backslash frac\{1\}\{15\}$ minute.