Maharashtra Board Class 5 Maths Chapter 9 Decimal Fractions Set 40 Solutions

Question 1. Two and a half
Answer: \( 2\frac{1}{2} \) = 2.5 = 2.50
In simple words: To convert two and a half to a decimal, express the fraction 1/2 as 0.5 and add it to the whole number 2, resulting in 2.50.

🎯 Exam Tip: Always ensure the fractional part is correctly converted to its decimal equivalent before combining with the whole number.

Question 2. Two and a quarter
Answer: \( 2\frac{1}{4} \) = 2.25
In simple words: Two and a quarter means 2 plus 1/4. Since 1/4 is 0.25 in decimal form, the total is 2.25.

🎯 Exam Tip: Familiarize yourself with common fraction-to-decimal conversions like 1/4 = 0.25 to speed up calculations.

Question 3. Two and three quarters
Answer: \( 2\frac{3}{4} \) = 2.75
In simple words: Two and three quarters is 2 plus 3/4. As 3/4 equals 0.75, the decimal form is 2.75.

🎯 Exam Tip: Practice converting mixed fractions to decimals by first converting the fractional part and then adding it to the whole number.

Question 4. Ten and a half
Answer: \( 10\frac{1}{2} \) = 10.5 = 10.50
In simple words: Ten and a half is 10 plus 1/2. Since 1/2 is 0.5, the decimal value is 10.50.

🎯 Exam Tip: Writing 10.5 as 10.50 can sometimes help with alignment when adding or comparing decimals with more decimal places.

Question 5. Fourteen and three quarters
Answer: \( 14\frac{3}{4} \) = 14.75
In simple words: Fourteen and three quarters translates to 14 plus 3/4, which is 14 plus 0.75, giving 14.75.

🎯 Exam Tip: Understand that the "and" in such phrases signifies addition of the whole number and the fractional part.

Question 6. Sixteen and a quarter
Answer: \( 16\frac{1}{4} \) = 16.25
In simple words: Sixteen and a quarter means the whole number 16 combined with the decimal equivalent of 1/4, which is 0.25, resulting in 16.25.

🎯 Exam Tip: Double-check your decimal place value when converting fractions like 1/4 to avoid errors.

Question 7. Twenty-eight and a half
Answer: \( 28\frac{1}{2} \) = 28.50 = 28.5
In simple words: To convert twenty-eight and a half, add 28 to 0.5 (the decimal for 1/2), which yields 28.5.

🎯 Exam Tip: Remember that trailing zeros after the decimal point (e.g., 28.50 vs 28.5) do not change the value unless they represent significant figures in a specific context.

Adding Decimal Fractions

Sir: If the cost of one pencil is two and a half rupees and the cost of a pen is four and half rupees, what is the total cost?

Sumit : Two and a half rupees means two rupees and one half rupee. Similarly, four and a half rupees means four rupees and one-half rupee. 4 rupees and 2 rupees make 6 rupees and two half rupees make one rupee, so both objects together cost 6 + 1 = 7 rupees.

Sir: Correct! Now, see how this is done using decimals. The sum of the O's in the hundredths place is 0.

\( 0.5 + 0.5 \) is the same as \( \frac{5}{10} + \frac{5}{10} = \frac{5+5}{10} = \frac{10}{10} = 1 \)

This 1 is carried over to the units place. There is nothing in the tenths place, so we put a zero there. In the units place, 2 + 4 = 6 plus the carried over 1 makes 7.

So 2.50 rupees and 4.50 rupees add up to 7 rupees.

We use the decimal system to write whole numbers. We extend the same method to write fractions; therefore, we can add in the same way as we add whole numbers.

I will now show some more additions. Watch carefully.

Sumit : There is no carried over number in the first sum, but there are carried over numbers in the second and third sums.

Rekha : While adding whole numbers, we add units first. Similarly, here, tenths are added first. In the second example, the sum of the tenths place is 13. 13 tenths are 10 tenths + 3 tenths = 1 unit + 3 tenths.

Sumit : That is why, in the sum, 3 stayed in the tenths place and 1 was carried over to the units place. 6 + 5 plus 1 carried over makes 12.

Sir: Your observations are absolutely correct. We write digits one below the other according to their place values while adding whole numbers. We do the same thing here. Remember that while writing down an addition problem and the total, the decimal points should always be written one below the other.

Study the following additions. (Note that: 10 tenths = 1 unit. 10 hundredths = 1 tenth)

Example (1) Add : 7.09 + 54.93

First, add the digits in the 100ths place. 9 + 3 = 12.

The 1 from the sum 12 in the hundredths place is carried over to the tenths place and 2 is written in the hundredths place. Adding 1 + 9 gives 10 tenths or 1 unit. This 1 is carried over to the units place. O is left in the tenths place. Then, the addition is completed in the usual way.

Example (2) Add : 45.83 + 167.4

45.83 We arrange the numbers so that the places and
+
167.4 decimal points come one below the other.

\( \frac{4}{10} = \frac{4 \times 10}{10 \times 10} = \frac{40}{100} \) Therefore, to make the denominators of the fractions equal, 167.4 is written as 167.40 and then the fractions are added.

As usual, the digits with the smallest place values are added first and then those with bigger place values are added serially.

Example (3) 10.46 Rs.
+
35.92 Rs.
―
46.38 Rs.

Example (4) 48.80 m
+ 2.57 m
―
51.37 m.

Example (5) 7.5 cm
+
14.2 cm
+
9.6 cm
―
31.3 cm

Decimal Fractions Problem Set 40 Additional Important Questions and Answers

Question 1. Thirty and a quarter
Answer: \( 30\frac{1}{4} \) = 30.25
In simple words: Thirty and a quarter is the sum of 30 and 1/4, which translates to 30 plus 0.25, resulting in 30.25.

🎯 Exam Tip: Pay attention to the conversion of common fractions like 1/4 to their decimal equivalents.

Question 2. Thirty and a half
Answer: \( 30\frac{1}{2} \) = 30.50 = 30.5
In simple words: Thirty and a half means 30 combined with 0.5 (for 1/2), giving a decimal value of 30.5.

🎯 Exam Tip: Remember that adding or removing trailing zeros after the decimal point does not change the number's value, e.g., 30.50 is the same as 30.5.

Question 3. Thirty and three quarters
Answer: \( 30\frac{3}{4} \) = 30.75
In simple words: Thirty and three quarters is 30 plus 3/4, which is 30 plus 0.75, resulting in 30.75.

🎯 Exam Tip: Be consistent in converting the fractional part to a decimal before adding it to the whole number.