Maharashtra Board Class 5 Maths Chapter 9 Decimal Fractions Set 41 Solutions

Std 5 Maths Chapter 9 Decimal Fractions

Question 1. Convert the following into decimal fractions and add them.
(1) 'One and a half metre' and 'two and a half metres'
Answer:\[ \begin{array}{r} 1 \\ 1.5 \text{ m} \\ +2.5 \text{ m} \\ \hline 4.0 \text{ m} \\ \end{array} \]
In simple words: To add quantities like 'one and a half' and 'two and a half', convert them into their decimal forms (1.5 and 2.5 respectively) and then perform standard decimal addition.

🎯 Exam Tip: Ensure proper alignment of decimal points when adding decimal fractions to avoid calculation errors.

(2) 'Five and three quarter rupees' and 'seven and a quarter rupees'
Answer:\[ \begin{array}{r} 1 \quad 1 \\ 5.75 \text{ Rupees} \\ +7.25 \text{ Rupees} \\ \hline 8.00 \text{ Rupees} \\ \end{array} \]
In simple words: Convert phrases like 'three quarter' (0.75) and 'a quarter' (0.25) into decimal form, then add them along with the whole number parts, ensuring currency units are consistent.

🎯 Exam Tip: Accurately convert fractional parts (like 'quarter' or 'three quarter') to their decimal equivalents before adding.

(3) 'Six and a half metres' and 'three and three quarter metres'.
Answer:\[ \begin{array}{r} 1 \\ 6.50 \text{ m} \\ +3.75 \text{ m} \\ \hline 10.25 \text{ m} \\ \end{array} \]
In simple words: Transform verbal descriptions of lengths into decimal numbers (e.g., 'half' is 0.5, 'three quarter' is 0.75) and add them together to find the total length.

🎯 Exam Tip: Pay attention to units (metres in this case) and ensure they are consistently applied throughout the problem.

Question 2.
(1) 23.4 + 87.9
Answer:\[ \begin{array}{r} 1 \quad 1 \\ 23.4 \\ +87.9 \\ \hline 111.3 \\ \end{array} \]
In simple words: To add these decimal numbers, align them by their decimal points and sum each column from right to left, carrying over tens as needed.

🎯 Exam Tip: Vertical alignment of decimal points is crucial for accurate addition of decimal numbers.

(2) 35.74 + 816.6
Answer:\[ \begin{array}{r} 1 \quad 1 \\ 35.74 \\ +816.60 \\ \hline 852.34 \\ \end{array} \]
In simple words: Add these decimal numbers by vertically aligning the decimal points and then performing addition, remembering to add a zero placeholder to 816.6 (as 816.60) for easier calculation.

🎯 Exam Tip: When adding decimals with different numbers of decimal places, add trailing zeros to make the lengths equal, ensuring correct place value alignment.

(3) 6.95 + 74.88
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \\ 6.95 \\ +74.88 \\ \hline 81.83 \\ \end{array} \]
In simple words: Align these two decimal numbers by their decimal points and sum them column by column, carrying over when the sum in a column exceeds nine.

🎯 Exam Tip: Double-check carry-overs, especially when dealing with multiple decimal places, to prevent small arithmetic errors.

(4) 41.03 + 9.98
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \\ 41.03 \\ +9.98 \\ \hline 51.01 \\ \end{array} \]
In simple words: To add these numbers, place them one above the other with decimal points aligned, then add digits in each column, moving from right to left and managing any carries.

🎯 Exam Tip: Practicing column addition with decimals improves speed and accuracy in exams.

Question 3.
(1) 51.4 cm + 68.5 cm
Answer:\[ \begin{array}{r} 51.4 \text{ cm} \\ +68.5 \text{ cm} \\ \hline 119.9 \text{ cm} \\ \end{array} \]
In simple words: Add the two given lengths in centimeters by aligning their decimal points and summing the corresponding digits.

🎯 Exam Tip: Always include the correct unit (cm, m, Rs. etc.) in your final answer.

(2) 94.7 m + 1738.45 m
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \\ 94.70 \text{ m} \\ +1738.45 \text{ m} \\ \hline 1833.15 \text{ m} \\ \end{array} \]
In simple words: To add these lengths, align the decimal points, add a trailing zero to 94.7 (making it 94.70), and then perform standard column addition.

🎯 Exam Tip: Remember to add a zero to the shorter decimal number to match the number of decimal places of the longer number for easier calculation.

(3) 5158.75 + Rs. 841.25
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \quad 1 \quad 1 \\ 5158.75 \\ +\text{Rs. } 841.25 \\ \hline \text{Rs. } 6000.00 \\ \end{array} \]
In simple words: Sum these two rupee amounts by aligning their decimal points and adding column by column, ensuring the rupee symbol is correctly placed in the answer.

🎯 Exam Tip: Treat currency additions like any other decimal addition, focusing on decimal point alignment and accurate arithmetic.

Subtraction Of Decimal Fractions

Study the subtraction of decimal fractions given below. 15.41 - 8.58 6.83

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र दशमलव संख्याओं के घटाव की प्रक्रिया को दर्शाता है, जिसमें संख्या 15.41 में से 8.58 घटाया जा रहा है। यह चित्र उधार लेने (borrowing) की विधि को स्पष्ट करता है, जहां ऊपरी संख्या के विभिन्न स्थानों से मान उधार लेकर घटाव को सरल बनाया जाता है। अंतिम परिणाम 6.83 है।

8 hundredths cannot be subtracted from 1 hundredth, so 1 tenth (or 10 hundredths) from 4 tenths are borrowed. The borrowed 10 hundredths and the original one hundredth make 11 hundredths. 11 hundredths minus 8 hundredths are 3 hundredths. They are written in the hundredths place under the line. The rest of the subtraction is carried out using the same method.

Decimal Fractions Problem Set 41 Additional Important Questions And Answers

Convert the following into decimal fractions and add them.

(1) 'Fourteen and a half rupees' and 'Fifteen and a half rupees'.
Answer:\[ \begin{array}{r} 1 \quad 1 \\ 14.5 \text{ Rupees} \\ +15.5 \text{ Rupees} \\ \hline 30.0 \text{ Rupees} \\ \end{array} \]
In simple words: Convert 'a half' to 0.5 and add these rupee amounts by aligning the decimal points and summing the values.

🎯 Exam Tip: Ensure all parts of the phrase (whole numbers and fractions) are correctly converted to decimals before calculation.

(2) 'Three quarters' and 'a half'
Answer:\[ \begin{array}{r} 1 \\ 0.75 \\ +0.50 \\ \hline 1.25 \\ \end{array} \]
In simple words: Convert 'three quarters' to 0.75 and 'a half' to 0.5, then add these decimal values.

🎯 Exam Tip: Memorizing common fraction-to-decimal conversions (like 1/4, 1/2, 3/4) can save time in exams.

Add The Following:

(1) 37.84 + 12.16
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \\ 37.84 \\ +12.16 \\ \hline 50.00 \\ \end{array} \]
In simple words: Align the decimal points of the two numbers and perform column addition from right to left, including any carry-overs.

🎯 Exam Tip: Pay close attention to the carry-overs, as these are common sources of error in multi-digit addition.

(2) 328.69 + 84.84
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \quad 1 \\ 328.69 \\ +84.84 \\ \hline 413.53 \\ \end{array} \]
In simple words: Add these decimal numbers by placing them with decimal points aligned and summing each place value column, managing carries as necessary.

🎯 Exam Tip: Regularly practice addition of multi-digit decimals to build speed and accuracy.

Solve The Following:

(1) 304.86 m + 70.94 m
Answer:\[ \begin{array}{r} 1 \quad 1 \\ 304.86 \text{ m} \\ +70.94 \text{ m} \\ \hline 375.80 \text{ m} \\ \end{array} \]
In simple words: Add these two measurements in metres by aligning their decimal points and summing the digits in each column.

🎯 Exam Tip: Always write the units (like 'm' for metres) next to your final answer.

(2) 79.56 cm + 19.65 cm
Answer:\[ \begin{array}{r} 1 \quad 1 \quad 1 \\ 79.56 \text{ cm} \\ +19.65 \text{ cm} \\ \hline 99.21 \text{ cm} \\ \end{array} \]
In simple words: To find the total length, align the decimal points of the two measurements in centimeters and add them vertically.

🎯 Exam Tip: Careful alignment of decimal points is the key to accurate decimal addition.

(3) Rs. 64.79 + Rs. 49.5
Answer:\[ \begin{array}{r} 1 \quad 1 \\ \text{Rs. } 64.79 \\ +\text{Rs. } 49.50 \\ \hline 114.29 \\ \end{array} \]
In simple words: Add these two rupee amounts by aligning their decimal points and summing, remembering to convert 49.5 to 49.50 for consistent decimal places.

🎯 Exam Tip: In currency calculations, ensure all values have the same number of decimal places (e.g., two for paise) before adding.