Balbharti Maharashtra Board Class 5 Maths Solutions Chapter 5 Fractions Problem Set 18 Textbook Exercise Important Questions and Answers.

## Maharashtra State Board Class 5 Maths Solutions Chapter 5 Fractions Problem Set 18

Convert the given fractions into like fractions. Solution :
8 is the multiple of 4 So, make 8, the common denominator $$\frac{3}{4}=\frac{3 \times 2}{4 \times 2}=\frac{6}{8}$$.Thus 6/8 and 5/8are the required like fractions.  Solution :
The number 35 is a multiple of both 5 and 7 So, making 35 as the common denominater $$\frac{3}{5}=\frac{3 \times 7}{5 \times 7}=\frac{21}{35}, \frac{3}{7}=\frac{3 \times 5}{7 \times 5}=\frac{15}{35}$$ Therefore, 21/35 and 15/35 are required like fractions. Solution :
Here 10 is the multiples of 5. So make 10 as the common denominator $$\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}$$. Thus 8/10 and 3/10 are required like fractions. Solution :
Least common multiple of 9 and 6 is 18. So, make, 18 as the common denominator. $$\frac{2}{9}=\frac{2 \times 2}{9 \times 2}=\frac{4}{18}, \frac{1}{6}=\frac{1 \times 3}{6 \times 3}=\frac{3}{18}$$. Thus, 4/18 and 3/18 are the required like fractions. Solution :
Least common multiple of 4 and 3 is 12 So, make 12 as common denominator $$\frac{1}{4}=\frac{1 \times 3}{4 \times 3}=\frac{3}{12}, \frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}$$. so, $$\frac{3}{12}, \frac{8}{12}$$ are required like fractions.  Solution :
Least common multiple of 6 and 5 is 30 So, make 30 as common denominator $$\frac{5}{6}=\frac{5 \times 5}{6 \times 5}=\frac{25}{30}, \frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$$ So, $$\frac{25}{30}, \frac{24}{30}$$ are required like fractions. Solution :
Least common multiple of 8 and 6 is 24 So, make 24 as common denominator $$\frac{3}{8}=\frac{3 \times 3}{8 \times 3}=\frac{9}{24}, \frac{1}{6}=\frac{1 \times 4}{6 \times 4}=\frac{4}{24}$$ So, $$\frac{9}{24}, \frac{4}{24}$$ are required like fractions. Solution :
Least common multiple of 6 and 9 is 18 So, make 18 as common denominator $$\frac{1}{6}=\frac{1 \times 3}{6 \times 3}=\frac{3}{18}, \frac{4}{9}=\frac{4 \times 2}{9 \times 2}=\frac{8}{18}$$ So, 3/18 and 8/18 are the required like fractions. Comparing like fractions
Example (1) A strip was divided into 5 equal parts. It means that each part is 1/5 . The coloured part is $$\frac{3}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$$. The white part is $$\frac{2}{5}=\frac{1}{5}+\frac{1}{5}$$. The coloured part is bigger than the white part. This tells us that 3/5 is greater than 2/5. This is written as 3/5 > 2/5.

Example (2) This strip is divided into 8 equal parts. 3 of the parts have one colour and 4 have another colour. Here, 3/8 < 8/4. In like fractions, the fraction with the greater numerator is the greater fraction.

Comparing fractions with equal numerators
You have learnt that the value of fractions with numerator 1 decreases as the denominator increases.

Even if the numerator is not 1, the same rule applies so long as all the fractions have a common numerator. For example, look at the figures below. All the strips in the figure are alike.
2 of the 3 equal parts of the strip 2 of the 4 equal parts of the strip 2 of the 5 equal parts of the strip The figure shows that 2/3 > 2/4 > 5/2. Of two fractions with equal numerators, the fraction with the greater denominator is the smaller fraction.

Comparing unlike fractions
Teacher : Suppose we have to compare the unlike fractions 3/5 and 4/7. Let us take an example to see how this is done. These two boys are standing on two blocks. How do we decide who is taller?

Sonu : But the height of the blocks is not the same. If both blocks are of the same height, it is easy to tell who is taller.

Nandu : Now that they are on blocks of equal height, we see that the boy on the right is taller.

Teacher : The height of the boys can be compared when they stand at the same height. Similarly, if fractions have the same denominators, their numerators decide which fraction is bigger.

Nandu : Got it! Let’s obtain the same denominators for both fractions.

Sonu : 5 × 7 can be divided by both 5 and 7. So, 35 can be the common denominator. To compare unlike fractions, we convert them into their equivalent fractions so that their denominators are the same. Question 1.
$$\frac{5}{9}, \frac{17}{36}$$
Solution :
36 is the multiple of 9 So, make 36 the common denominator $$\frac{5}{9}=\frac{5 \times 4}{9 \times 4}=\frac{20}{36}$$, Thus 20/36 and 17/36 are the required like fractions.

Question 2.
$$\frac{5}{6}, \frac{7}{9}$$
Solution:
Least common multiple of 6 and 9 is 18 So, make 18 as the common denominator $$\frac{5}{6}=\frac{5 \times 3}{6 \times 3}=\frac{15}{18}, \quad \frac{7}{9}=\frac{7 \times 2}{9 \times 2}=\frac{14}{18}$$ So, 15/18 and 14/18 are the required like fractions. Question 3.
$$\frac{7}{11}, \frac{3}{5}$$
Solution:
Least common multiple of 11 and 5 is 55 So, make 55 as the common denominator. $$\frac{7}{11}=\frac{7 \times 5}{11 \times 5}=\frac{35}{55}, \frac{3}{5}=\frac{3 \times 11}{5 \times 11}=\frac{33}{55}$$. Thus 35/55 and 33/55 are required like fractions.