Question

a: number facts
try not to use a calculator. have someone time how long it takes you & record this time in the box below.

adding & subtracting

1. \\(327 + 220 = \dots\dots\dots\dots\dots\\)
2. \\(510 + 266 = \dots\dots\dots\dots\dots\\)
3. \\(217 + 995 = \dots\dots\dots\dots\dots\\)
4. \\(488 + 839 = \dots\dots\dots\dots\dots\\)
5. \\(962 - 401 = \dots\dots\dots\dots\dots\\)
6. \\(568 - 446 = \dots\dots\dots\dots\dots\\)
7. \\(726 - 568 = \dots\dots\dots\dots\dots\\)
8. \\(725 - 386 = \dots\dots\dots\dots\dots\\)

multiplying & dividing

1. \\(5 \times 3 = 15\\)
2. \\(4 \times 4 = 16\\)
3. \\(9 \times 6 = 54\\)
4. \\(7 \times 2 = 14\\)
5. \\(7 \times 8 = 56\\)
6. \\(9 \times 10 = 90\\)
7. \\(8 \times 9 = \dots\dots\dots\dots\dots\\)

Explanation:

🆕 New Concept Discovered: Multi-Digit Addition and Subtraction
Working with place values to add and subtract larger numbers.

Step 1: Solve the addition problems (Questions 1–4)

To add these numbers, we align the digits by their place values (ones, tens, hundreds) and add from right to left, carrying over to the next column when a sum is 10 or greater.

1. \( 327 + 220 \)

• Ones: \( 7 + 0 = 7 \)
• Tens: \( 2 + 2 = 4 \)
• Hundreds: \( 3 + 2 = 5 \)
• Result: \( 547 \)

1. \( 510 + 266 \)

• Ones: \( 0 + 6 = 6 \)
• Tens: \( 1 + 6 = 7 \)
• Hundreds: \( 5 + 2 = 7 \)
• Result: \( 776 \)

1. \( 217 + 995 \)

• Ones: \( 7 + 5 = 12 \) (write down 2, carry over 1)
• Tens: \( 1 + 9 + 1 \text{ (carry)} = 11 \) (write down 1, carry over 1)
• Hundreds: \( 2 + 9 + 1 \text{ (carry)} = 12 \)
• Result: \( 1212 \)

1. \( 488 + 839 \)

• Ones: \( 8 + 9 = 17 \) (write down 7, carry over 1)
• Tens: \( 8 + 3 + 1 \text{ (carry)} = 12 \) (write down 2, carry over 1)
• Hundreds: \( 4 + 8 + 1 \text{ (carry)} = 13 \)
• Result: \( 1327 \)

Step 2: Solve the subtraction problems (Questions 5–8)

To subtract, we align the digits by place value and subtract from right to left. If a digit on top is smaller than the digit below it, we borrow 1 from the next column to the left.

1. \( 962 - 401 \)

• Ones: \( 2 - 1 = 1 \)
• Tens: \( 6 - 0 = 6 \)
• Hundreds: \( 9 - 4 = 5 \)
• Result: \( 561 \)

1. \( 568 - 446 \)

• Ones: \( 8 - 6 = 2 \)
• Tens: \( 6 - 4 = 2 \)
• Hundreds: \( 5 - 4 = 1 \)
• Result: \( 122 \)

1. \( 726 - 568 \)

• Ones: \( 6 - 8 \) (borrow 1 from tens: \( 16 - 8 = 8 \))
• Tens: \( 1 - 6 \) (borrow 1 from hundreds: \( 11 - 6 = 5 \))
• Hundreds: \( 6 - 5 = 1 \)
• Result: \( 158 \)

1. \( 725 - 386 \)

• Ones: \( 5 - 6 \) (borrow 1 from tens: \( 15 - 6 = 9 \))
• Tens: \( 1 - 8 \) (borrow 1 from hundreds: \( 11 - 8 = 3 \))
• Hundreds: \( 6 - 3 = 3 \)
• Result: \( 339 \)

Step 3: Solve the multiplication problems (Questions 9–14)

We find the product of the single-digit and double-digit multiplication facts.

1. \( 5 \times 3 = 15 \)
2. \( 4 \times 4 = 16 \)
3. \( 9 \times 6 = 54 \)
4. \( 7 \times 2 = 14 \)
5. \( 7 \times 8 = 56 \)
6. \( 9 \times 10 = 90 \)

Answer:

Adding & Subtracting

1. 547
2. 776
3. 1212
4. 1327
5. 561
6. 122
7. 158
8. 339

Multiplying & Dividing

1. 15
2. 16
3. 54
4. 14
5. 56
6. 90