Mental Math

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Answer Key & Explanations

Mental Math · Grade 3 · Worksheet 1

1. 703 - 397 = ? Answer: 306 Solution: Round 397 up to 400 (add 3). Subtract 703 - 400 = 303. Since we subtracted 3 extra (400 - 397 = 3), add 3 back: 303 + 3 = 306.
   Full step-by-step solution

   Step 1: Round 397 up to 400 (add 3). Step 2: Subtract 703 - 400 = 303. Step 3: Since we subtracted 3 extra (400 - 397 = 3), add 3 back: 303 + 3 = 306. The answer is 306.

2. 798 + 125 = ? Answer: 923 Solution: Notice that 798 is very close to 800. Add 800 + 125 = 925. Since we added 2 extra (800 - 798 = 2), subtract 2 from the result.
   Full step-by-step solution

   Step 1: Notice that 798 is very close to 800. Step 2: Add 800 + 125 = 925. Step 3: Since we added 2 extra (800 - 798 = 2), subtract 2 from the result. Step 4: 925 - 2 = 923. The answer is 923.

3. 398 + 175 = ? Answer: 573 Solution: Notice that 398 is very close to 400. Add 400 + 175 = 575. Since we added 2 extra (400 - 398 = 2), subtract 2 from the result.
   Full step-by-step solution

   Step 1: Notice that 398 is very close to 400. Step 2: Add 400 + 175 = 575. Step 3: Since we added 2 extra (400 - 398 = 2), subtract 2 from the result. Step 4: 575 - 2 = 573. The answer is 573.

4. Lily is planting flowers in her garden. She has 72 flower seeds and wants to plant them in 8 equal rows. How many seeds should Lily plant in each row? Answer: 9 Solution: Lily has 72 seeds total. She wants to divide them equally into 8 rows. To find how many seeds go in each row, divide 72 by 8.
   Full step-by-step solution

   Step 1: Lily has 72 seeds total. Step 2: She wants to divide them equally into 8 rows. Step 3: To find how many seeds go in each row, divide 72 by 8. Step 4: 72 ÷ 8 = 9 Lily should plant 9 seeds in each row.

5. 198 + 245 = ? Answer: 443 Solution: Notice that 198 is very close to 200. Add 200 + 245 = 445. Since we added 2 extra (200 instead of 198), subtract 2 to compensate: 445 - 2 = 443.
   Full step-by-step solution

   Step 1: Notice that 198 is very close to 200. Step 2: Add 200 + 245 = 445. Step 3: Since we added 2 extra (200 instead of 198), subtract 2 to compensate: 445 - 2 = 443. The answer is 443.

6. A baker needs to arrange 648 cookies on trays. Each tray can hold 9 cookies. How many trays does the baker need? Answer: 72 Solution: The baker has 648 cookies total Each tray holds 9 cookies To find how many trays are needed, divide 648 by 9 648 ÷ 9 = 72 The baker needs 72 trays to hold all the cookies The answer is 72.
   Full step-by-step solution

   Step 1: The baker has 648 cookies total Step 2: Each tray holds 9 cookies Step 3: To find how many trays are needed, divide 648 by 9 Step 4: 648 ÷ 9 = 72 Step 5: The baker needs 72 trays to hold all the cookies The answer is 72.

7. 497 + 268 = ? Answer: 765 Solution: Notice that 497 is very close to 500. Add 500 + 268 = 768. Since we added 3 extra (500 - 497 = 3), subtract 3 from the result.
   Full step-by-step solution

   Step 1: Notice that 497 is very close to 500. Step 2: Add 500 + 268 = 768. Step 3: Since we added 3 extra (500 - 497 = 3), subtract 3 from the result. Step 4: 768 - 3 = 765. The answer is 765.

8. A farmer has 144 eggs to pack into cartons that hold 12 eggs each. How many cartons can the farmer fill completely? Answer: 12 Solution: The farmer has 144 eggs total. Each carton holds 12 eggs. We need to find how many cartons can be completely filled.
   Full step-by-step solution

   Step 1: Understand the problem. The farmer has 144 eggs total. Each carton holds 12 eggs. We need to find how many cartons can be completely filled. Step 2: Set up the division. To find the number of cartons, divide the total number of eggs by the number of eggs per carton: 144 ÷ 12 Step 3: Perform the division. We can think: how many times does 12 go into 144? 12 × 12 = 144 Step 4: Interpret the result. Since 144 ÷ 12 = 12, the farmer can fill 12 cartons completely with no eggs left over. Step 5: Final answer. The farmer can fill 12 cartons completely.

9. Liam is collecting trading cards. He has 125 cards in his main collection and his friend gives him 38 more cards. How many trading cards does Liam have now? Answer: 163 Solution: Liam starts with 125 trading cards. His friend gives him 38 more cards. To find the total number of cards he has now, we add the two amounts together.
   Full step-by-step solution

   Liam starts with 125 trading cards. His friend gives him 38 more cards. To find the total number of cards he has now, we add the two amounts together. Step 1: Write the addition problem. 125 + 38 Step 2: Add the ones place. 5 ones + 8 ones = 13 ones. 13 ones means 1 ten and 3 ones. Write down the 3 in the ones place and carry over the 1 ten to the tens place. Step 3: Add the tens place. 2 tens + 3 tens = 5 tens, plus the 1 ten we carried over makes 6 tens. Write down 6 in the tens place. Step 4: Add the hundreds place. There is 1 hundred and no other hundreds, so write down 1 in the hundreds place. Step 5: Combine the digits. Hundreds: 1, Tens: 6, Ones: 3 That gives 163. So, 125 + 38 = 163. Liam now has 163 trading cards.

10. 497 + 256 = ? Answer: 753 Solution: Notice that 497 is very close to 500. Add 500 + 256 = 756. Since we added 3 extra (500 - 497 = 3), subtract 3 from the result.
    Full step-by-step solution

    Step 1: Notice that 497 is very close to 500. Step 2: Add 500 + 256 = 756. Step 3: Since we added 3 extra (500 - 497 = 3), subtract 3 from the result. Step 4: 756 - 3 = 753. The answer is 753.