Lesson 1: Whole Number Operations

Property

To add whole numbers:
Step 1. Write the numbers so each place value lines up vertically.
Step 2. Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than 9, carry to the next place value.
Step 3. Continue adding each place value from right to left, adding each place value and carrying if needed.

Examples

• To add $57 + 26$, align them vertically. Add the ones: $7 + 6 = 13$. Write down 3, carry 1 to the tens place. Add the tens: $1 + 5 + 2 = 8$. The sum is $83$.
• For $481 + 352$, add the ones: $1+2=3$. Add the tens: $8+5=13$. Write 3, carry 1. Add the hundreds: $1+4+3=8$. The sum is $833$.
• To add $5,280 + 945$, align the numbers carefully. The sum is $6,225$. Adding $0+5=5$, $8+4=12$ (carry 1), $1+2+9=12$ (carry 1), and $1+5=6$.

Explanation

To add big numbers, stack them up so the ones, tens, and hundreds places align. Add each column from right to left. If a column's sum is 10 or more, write down the last digit and 'carry' the other digit to the next column.

Property

To subtract multi-digit numbers, align them by place value and subtract column by column from right to left. If a top digit is smaller than the bottom digit, decompose 1 unit from the place to the left, which is equivalent to adding 10 to the current place. This process may need to be repeated multiple times, including across places with a value of zero.

Examples

Property

To multiply two whole numbers to find the product:

1. Write the numbers so each place value lines up vertically.
2. Multiply the digits in each place value. Work from right to left, starting with the ones place in the bottom number. Multiply the ones digit of the bottom number by each digit in the top number. If a product in a place value is more than 9, carry to the next place value. Write the partial products, lining up the digits. Repeat for the tens place, hundreds place, and so on, using zeros as placeholders.
3. Add the partial products.

Examples

• To multiply $58 \times 4$: First, calculate $4 \times 8 = 32$. Write down the 2 and carry the 3. Then, calculate $4 \times 5 = 20$, and add the carried 3 to get 23. The product is $232$.
• To multiply $76 \times 32$: The first partial product is $2 \times 76 = 152$. The second partial product is $30 \times 76 = 2280$. Add them: $152 + 2280 = 2432$.
• To multiply $408 \times 7$: First, $7 \times 8 = 56$ (write 6, carry 5). Then, $7 \times 0 = 0$, plus the carried 5 is 5. Finally, $7 \times 4 = 28$. The product is $2,856$.

Explanation

When multiplying large numbers, we break the problem down. We multiply the top number by each digit of the bottom number one at a time. These smaller results, called partial products, are then added to get the final answer.