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.