# AP Board 6th Class Maths Solutions Chapter 5 Fractions and Decimals Unit Exercise

AP State Syllabus AP Board 6th Class Maths Solutions Chapter 5 Fractions and Decimals Unit Exercise Textbook Questions and Answers.

## AP State Syllabus 6th Class Maths Solutions 5th Lesson Fractions and Decimals Unit Exercise

Question 1.
The sum of two fractions is 5$$\frac{3}{9}$$. If one fraction is 2$$\frac{3}{4}$$, then find the other fraction.
Answer:
Given one fraction = 2$$\frac{3}{4}$$ = $$\frac{11}{4}$$
Sum of two fractions = 5$$\frac{3}{9}$$ = $$\frac{48}{9}$$
Now, $$\frac{11}{4}$$ + second fraction = $$\frac{48}{9}$$
Second fraction = $$\frac{48}{9}$$ – $$\frac{11}{4}$$
LCM of 9 and 4 is 36

Question 2.
A rectangle sheet of paper is of length 12$$\frac{1}{2}$$ and breadth 10$$\frac{2}{3}$$. Find its perimeter.
Answer:
Length of rectangular sheet = l = 12$$\frac{1}{2}$$ = $$\frac{25}{2}$$ m
Breadth of rectangular sheet = b = 10$$\frac{2}{3}$$ = $$\frac{32}{3}$$ m
Perimeter of rectangular sheet = 2(1 + b)

Question 3.
Simplify: $$\left(3 \frac{1}{6}-1 \frac{1}{3}\right)+\left(4 \frac{1}{6}-2 \frac{1}{3}\right)$$
Answer:
$$\left(3 \frac{1}{6}-1 \frac{1}{3}\right)+\left(4 \frac{1}{6}-2 \frac{1}{3}\right)$$
First convert the given mixed fractions into improper fractions.
$$\left(\frac{19}{6}-\frac{4}{3}\right)$$ + $$\left(\frac{25}{6}-\frac{7}{3}\right)$$
Then subtract the fractions which are in brackets by making them like fractions.

Now add the fractions = $$\frac{11+11}{6}$$ = $$\frac{22}{6}$$ = 3$$\frac{4}{6}$$

Question 4.
By what number should 3$$\frac{1}{16}$$ be multiplied to get 9$$\frac{3}{16}$$?
Answer:
Given fraction = 3$$\frac{1}{16}$$ = $$\frac{49}{16}$$
Product = 9$$\frac{3}{16}$$ = $$\frac{147}{16}$$
Fraction × fraction to be multiplied = $$\frac{147}{16}$$
$$\frac{49}{16}$$ × other number = $$\frac{147}{16}$$
other number = $$\frac{147}{16}$$ ÷ $$\frac{49}{16}$$ = $$\frac{147}{16}$$ × $$\frac{16}{49}$$
Other number = 3
∴ Number to be multiplied = 3.

Question 5.
The length of the staircase is 5$$\frac{1}{2}$$ m. If one step is set at $$\frac{1}{4}$$ m. then, how many steps will be there in the staircase?
Answer:
Given length of staircase = 5$$\frac{1}{2}$$ m = $$\frac{11}{2}$$ m
Length of each step = $$\frac{1}{4}$$ m
Length of each step × number of steps = length of staircase
$$\frac{1}{4}$$ × Number of steps = $$\frac{11}{2}$$
Number of steps = $$\frac{11}{2}$$ ÷ $$\frac{1}{4}$$ = $$\frac{11}{2}$$ × $$\frac{4}{1}$$ = 11 × 2 = 22
∴ Number of steps in the staircase = 22

Question 6.
Simplify: 23.5 – 27 + 35.4 – 17
Answer:
Given 23.5 – 27 + 35.4 – 17
First make them like decimals.
= 23.5 – 27.0 + 35.4 – 17.0
Add the positive numbers
= (+23.5 + 35.4) + (-27.0 – 17.0)
= 58.9 + (-44.0)
= 58.9 – 44.0
= 14.9

Question 7.
Sailaja bought 3.350kg of potatoes, 2.250kg of tomatoes and some onions. If the weight of the total items are 10.250 kg. Then, find the weight of onions.
Answer:
Weight of potatoes = 3.350 kg
Weight of tomatoes = 2.250 kg
Weight of total items = 10.250 kg
Weight of onions = ?
Weight of (potatoes + tomatoes + onions) = 10.250 kg
(3.350 + 2.250) + onions weight = 10.250
5.600 + onions weight = 10.250
Onions weight = 10.250 – 5.600
∴ Weight of onions = 4.650 kg.

Question 8.
What should be subtracted from 7.1 to get 0.713?
Answer:
Given number = 7.1
Difference = 0.713
Number to be subtracted = Number – difference
= 7.1 – 0.713
= 7.100 – 0.713
∴ Number to be subtracted = 6.387.