## Adding and Subtracting Through 1,000,000

Adding and subtracting large numbers, including those up to 1,000,000, is a fundamental math skill. Mastering these operations helps you handle complex calculations and understand large quantities in various contexts.

#### Adding Large Numbers

When adding large numbers, it’s crucial to align the digits according to their place values (ones, tens, hundreds, etc.). Start from the rightmost digits and move to the left, carrying over any value greater than 9 to the next place value.

**Example: Adding 345,678 and 123,456**

**Align the numbers by place value**:

`345,678`

+ 123,456**Add the digits from right to left**:Ones place: 8+6=148 + 6 = 148+6=14 (write 4, carry 1)

Tens place: 7+5+1=137 + 5 + 1 = 137+5+1=13 (write 3, carry 1)

Hundreds place: 6+4+1=116 + 4 + 1 = 116+4+1=11 (write 1, carry 1)

Thousands place: 5+3+1=95 + 3 + 1 = 95+3+1=9 (write 9)

Ten thousands place: 4+2=64 + 2 = 64+2=6 (write 6)

Hundred thousands place: 3+1=43 + 1 = 43+1=4 (write 4)

Result: 345,678+123,456=469,134345,678 + 123,456 = 469,134345,678+123,456=469,134

#### Subtracting Large Numbers

When subtracting large numbers, align the digits according to their place values and borrow from the next place value if needed.

**Example: Subtracting 123,456 from 654,321**

**Align the numbers by place value**:

`654,321`

- 123,456**Subtract the digits from right to left**:Ones place: 1−61 - 61−6 (borrow 1 from the tens place, making it 11): 11−6=511 - 6 = 511−6=5

Tens place: 1−51 - 51−5 (borrow 1 from the hundreds place, making it 11): 11−5=611 - 5 = 611−5=6

Hundreds place: 2−42 - 42−4 (borrow 1 from the thousands place, making it 12): 12−4=812 - 4 = 812−4=8

Thousands place: 3−3=03 - 3 = 03−3=0

Ten thousands place: 5−2=35 - 2 = 35−2=3

Hundred thousands place: 6−1=56 - 1 = 56−1=5

Result: 654,321−123,456=530,865654,321 - 123,456 = 530,865654,321−123,456=530,865

###### Fun Example: Adding and Subtracting Apples 🍎

Imagine you have two apple orchards. The first orchard has 452,310 apples, and the second orchard has 378,690 apples. How many apples do you have in total?

**Add the apples**:

diffCopy code`452,310`

+ 378,690**Add the digits from right to left**:Ones place: 0+0=00 + 0 = 00+0=0

Tens place: 1+9=101 + 9 = 101+9=10 (write 0, carry 1)

Hundreds place: 3+6+1=103 + 6 + 1 = 103+6+1=10 (write 0, carry 1)

Thousands place: 2+8+1=112 + 8 + 1 = 112+8+1=11 (write 1, carry 1)

Ten thousands place: 5+7+1=135 + 7 + 1 = 135+7+1=13 (write 3, carry 1)

Hundred thousands place: 4+3+1=84 + 3 + 1 = 84+3+1=8

Total apples: 452,310+378,690=831,000452,310 + 378,690 = 831,000452,310+378,690=831,000

Now, imagine you gave away 150,275 apples to a local market. How many apples are left?

**Subtract the apples given away**:

`831,000`

- 150,275**Subtract the digits from right to left**:Ones place: 0−50 - 50−5 (borrow 1 from tens place, making it 10): 10−5=510 - 5 = 510−5=5

Tens place: 0−70 - 70−7 (borrow 1 from hundreds place, making it 10): 10−7=310 - 7 = 310−7=3

Hundreds place: 0−20 - 20−2 (borrow 1 from thousands place, making it 10): 10−2=810 - 2 = 810−2=8

Thousands place: 1−0=11 - 0 = 11−0=1

Ten thousands place: 3−53 - 53−5 (borrow 1 from hundred thousands place, making it 13): 13−5=813 - 5 = 813−5=8

Hundred thousands place: 7−1=67 - 1 = 67−1=6

Apples left: 831,000−150,275=680,725831,000 - 150,275 = 680,725831,000−150,275=680,725

Understanding how to add and subtract large numbers helps you manage and make sense of substantial quantities, whether in practical scenarios or advanced math problems.