GSEB Class 6 Maths Solutions Chapter 8 દશાંશ સંખ્યાઓ Exercise 8.6

Question 1. બાદબાકી કરોઃ
(a) 20.75 રૂપિયામાંથી 18.25 રૂપિયા
(b) 250 મીટરમાંથી 202.54 મીટર
(c) 8.40 રૂપિયામાંથી 5.36 રૂપિયા
(d) 5.206 કિમીમાંથી 2.051 કિમી
(e) 2.107 કિલોમાંથી 0.314 કિલો
Answer:
(a) Here, we need to subtract \( 18.25 \) Rs from \( 20.75 \) Rs.
\[ \begin{array}{r} 20.75 \text{ Rs} \\ - 18.25 \text{ Rs} \\ \hline 2.50 \text{ Rs} \end{array} \] Thus, \( 20.75 \text{ Rs} - 18.25 \text{ Rs} = 2.50 \text{ Rs} \).
(b) Here, we need to subtract \( 202.54 \) meters from \( 250 \) meters.
\[ \begin{array}{r} 250.00 \text{ meters} \\ - 202.54 \text{ meters} \\ \hline 47.46 \text{ meters} \end{array} \] Therefore, \( 250 \text{ meters} - 202.54 \text{ meters} = 47.46 \text{ meters} \).
(c) Here, we need to subtract \( 5.36 \) Rs from \( 8.40 \) Rs.
\[ \begin{array}{r} 8.40 \text{ Rs} \\ - 5.36 \text{ Rs} \\ \hline 3.04 \text{ Rs} \end{array} \] Hence, \( 8.40 \text{ Rs} - 5.36 \text{ Rs} = 3.04 \text{ Rs} \).
(d) Here, we need to subtract \( 2.051 \) km from \( 5.206 \) km.
\[ \begin{array}{r} 5.206 \text{ km} \\ - 2.051 \text{ km} \\ \hline 3.155 \text{ km} \end{array} \] So, \( 5.206 \text{ km} - 2.051 \text{ km} = 3.155 \text{ km} \).
(e) Here, we need to subtract \( 0.314 \) kg from \( 2.107 \) kg.
\[ \begin{array}{r} 2.107 \text{ kg} \\ - 0.314 \text{ kg} \\ \hline 1.793 \text{ kg} \end{array} \] Thus, \( 2.107 \text{ kg} - 0.314 \text{ kg} = 1.793 \text{ kg} \).
In simple words: For each part, you need to take away the second number from the first number. Make sure to align the decimal points correctly before subtracting.

Exam Tip: Always align decimal points vertically before performing subtraction. If one number has fewer decimal places, add trailing zeros to match the other number's precision.

Question 2. કિંમત શોધો :
(a) \( 9.756 - 6.28 \)
(b) \( 21.05 - 15.27 \)
(c) \( 18.5 - 6.79 \)
(d) \( 11.6 - 9.847 \)
Answer:
(a) Here, we will consider \( 6.28 \) as \( 6.280 \).
\[ \begin{array}{r} 9.756 \\ - 6.280 \\ \hline 3.476 \end{array} \] So, \( 9.756 - 6.28 = 3.476 \).
(b) Here, we need to subtract \( 15.27 \) from \( 21.05 \).
\[ \begin{array}{r} 21.05 \\ - 15.27 \\ \hline 5.78 \end{array} \] So, \( 21.05 - 15.27 = 5.78 \).
(c) Here, we will consider \( 18.5 \) as \( 18.50 \).
\[ \begin{array}{r} 18.50 \\ - 6.79 \\ \hline 11.71 \end{array} \] So, \( 18.5 - 6.79 = 11.71 \).
(d) Here, we will consider \( 11.6 \) as \( 11.600 \).
\[ \begin{array}{r} 11.600 \\ - 9.847 \\ \hline 1.753 \end{array} \] So, \( 11.6 - 9.847 = 1.753 \).
In simple words: To find the value, subtract the second number from the first number, making sure to align the decimal points and add zeroes if necessary for even length.

Exam Tip: In subtraction with decimals, it's a good practice to pad numbers with trailing zeros so they have the same number of decimal places before beginning the calculation.

Question 3. રાજુએ 35.65 રૂપિયાનું પુસ્તક ખરીદું. તેણે દુકાનદારને 50 રૂપિયા આપ્યા, તો દુકાનદાર પાસેથી રાજુએ કેટલા રૂપિયા પાછા મેળવ્યા?
Answer: Raju purchased a book for a certain amount. He gave the shopkeeper \( 50 \) Rs. The price of the book was \( 35.65 \) Rs. The amount the shopkeeper will return to Raju is calculated as follows: Amount returned \( = 50 \text{ Rs} - 35.65 \text{ Rs} \)
\[ \begin{array}{r} 50.00 \text{ Rs} \\ - 35.65 \text{ Rs} \\ \hline 14.35 \text{ Rs} \end{array} \] Thus, Raju will receive \( 14.35 \text{ Rs} \) back from the shopkeeper.
In simple words: Raju bought a book. He gave the shopkeeper some money. To find out how much money he got back, subtract the book's price from the money he gave.

Exam Tip: When dealing with money transactions, always ensure to clearly identify the total amount paid and the cost of the item to correctly calculate the change.

Question 4. રાની પાસે 18.50 રૂપિયા હતા. તેણે 11.75 રૂપિયાનો એક આઇસક્રીમ ખરીદ્યો, તો તેની પાસે હવે કેટલા રૂપિયા રહ્યા?
Answer: Rani initially had \( 18.50 \) Rs. She purchased an ice cream that cost \( 11.75 \) Rs. The amount of money Rani has left is found by subtracting the cost of the ice cream from her initial money: Money remaining \( = 18.50 \text{ Rs} - 11.75 \text{ Rs} \)
\[ \begin{array}{r} 18.50 \text{ Rs} \\ - 11.75 \text{ Rs} \\ \hline 6.75 \text{ Rs} \end{array} \] So, Rani now has \( 6.75 \text{ Rs} \) left.
In simple words: Rani had some money. She spent some of it on ice cream. To find out how much she has now, take away the ice cream's cost from her starting money.

Exam Tip: In problems involving money spent, it's essential to clearly establish the initial amount and the expense to calculate the remaining balance accurately.

Question 5. ટીના પાસે 20 મીટર 5 સેમી લાંબું કાપડ હતું. તેણે પડદા બનાવવા માટે 4 મીટર 50 સેમી લંબાઈનું કાપડ તેમાંથી કાપ્યું, તો તેની પાસે કેટલું કાપડ બાકી રહ્યું?
Answer: Tina possessed a total cloth length of \( 20 \) meters \( 5 \) cm. This can be written as \( 20.05 \) meters. She cut \( 4 \) meters \( 50 \) cm of cloth to make curtains. This is equivalent to \( 4.50 \) meters. We understand that \( 1 \) meter \( = 100 \) cm, so \( 1 \) cm \( = \frac{1}{100} \) meter. The remaining cloth with Tina is calculated as follows: Total cloth length \( = 20 \text{ meters } 5 \text{ cm} = 20.05 \text{ meters} \) Cloth cut for curtains \( = 4 \text{ meters } 50 \text{ cm} = 4.50 \text{ meters} \) Remaining cloth \( = 20.05 \text{ meters} - 4.50 \text{ meters} \)
\[ \begin{array}{r} 20.05 \text{ meters} \\ - 4.50 \text{ meters} \\ \hline 15.55 \text{ meters} \end{array} \] Hence, Tina has \( 15.55 \) meters of cloth left.
In simple words: Tina had a long piece of cloth. She cut a part of it to make curtains. To find out how much cloth is left, subtract the cut piece from the total length she had. Remember to change all lengths to the same unit, like meters.

Exam Tip: When solving problems with mixed units (like meters and centimeters), always convert all measurements to a single, consistent unit before performing any calculations to avoid errors.

Question 6. નમિતા દરરોજ 20 કિમી 50 મીટરની મુસાફરી કરે છે. તેમાંથી તે 10 કિમી 200 મીટર અંતર બસ દ્વારા અને બાકી રહેલ અંતર રિક્ષા દ્વારા મુસાફરી કરે છે, તો તે રિક્ષા દ્વારા કેટલું અંતર કાપે છે?
Answer: Namita's total distance traveled each day is \( 20 \) km \( 50 \) meters. This can be expressed as \( 20.050 \) km. The distance she covers by bus is \( 10 \) km \( 200 \) meters, which is \( 10.200 \) km. The remaining distance is traveled by auto-rickshaw. To find the distance traveled by auto-rickshaw, we subtract the bus distance from the total distance: Distance by auto-rickshaw \( = 20.050 \text{ km} - 10.200 \text{ km} \)
\[ \begin{array}{r} 20.050 \text{ km} \\ - 10.200 \text{ km} \\ \hline 9.850 \text{ km} \end{array} \] Thus, Namita covers \( 9.850 \) km by auto-rickshaw.
In simple words: Namita travels a certain distance every day. She uses a bus for part of the journey. To find out how far she travels by auto-rickshaw, subtract the bus distance from her total travel distance. Always convert all units to kilometers first.

Exam Tip: When working with distances in different units (km and meters), convert all values to the larger unit (km) to simplify calculations and prevent mistakes.

Question 7. આકાશે 10 કિગ્રાની શાકભાજી ખરીદી. તેમાંથી તેણે 3 કિગ્રા 500 ગ્રામ ડુંગળી, 2 કિગ્રા 75 ગ્રામ ટામેટાં અને બાકીના બટાકા ખરીધાં, તો તેણે કેટલા કિગ્રા બટાકા ખરીદ્યા?
Answer: Akash purchased a total of \( 10 \) kg of vegetables. Among these, the weight of onions was \( 3 \) kg \( 500 \) grams, which is \( 3.500 \) kg. The weight of tomatoes was \( 2 \) kg \( 75 \) grams, which is \( 2.075 \) kg. The rest of the vegetables were potatoes. First, we find the total weight of onions and tomatoes: Total weight of onions and tomatoes \( = 3.500 \text{ kg} + 2.075 \text{ kg} \)
\[ \begin{array}{r} 3.500 \text{ kg} \\ + 2.075 \text{ kg} \\ \hline 5.575 \text{ kg} \end{array} \] So, the combined weight of onions and tomatoes is \( 5.575 \) kg. Now, to find the weight of potatoes, we subtract the combined weight of onions and tomatoes from the total weight of vegetables: Weight of potatoes \( = 10 \text{ kg} - 5.575 \text{ kg} \)
\[ \begin{array}{r} 10.000 \text{ kg} \\ - 5.575 \text{ kg} \\ \hline 4.425 \text{ kg} \end{array} \] Therefore, the weight of potatoes Akash bought is \( 4.425 \) kg.
In simple words: Akash bought many vegetables. We know how much onions and tomatoes he bought. To find out how many potatoes he got, first add up the weight of the onions and tomatoes. Then, take that total away from the full weight of all the vegetables. Remember to convert grams to kilograms first.

Exam Tip: When dealing with multiple items and a total weight, first sum up the known item weights, and then subtract this sum from the total to find the weight of the unknown item. Ensure consistent units throughout.