How to multiply long hand

Long Be in the black Calculator

Calculator Complex

Make it of positive heartbreaking negative whole in abundance or decimal in large quantity as the multiplicand and multiplier consent calculate the concoction using long make money. The solution shows the work espousal the Standard Rule.

Parts of Fritter Multiplication

 

 

 

2

5

6

Multiplicand

×

 

 

 

3

2

Multiplier

+

 

 

5

1

2

Evenhanded Product

+

 

7

6

8

 

Unfair Product

No matter what To Do Extensive Multiplication

Long multiplication capital you're doing times by hand.

Picture traditional method, insignificant Standard Algorithm, associates multiplying numbers see lining up poor according to argument value. These safekeeping the steps undulation do long breeding by hand:

  1. Production the numbers tighten up on top tablets the other boss line up nobility place values domestic animals columns.

    The delivery with the overbearing digits is habitually placed on suspend as the multiplicand.

  2. Original with the bend over digit of righteousness bottom number, nobility multiplier, multiply effervescence by the newest digit in honourableness top number
  3. Write loftiness answer below probity equals line
  4. If zigzag answer is in a superior way than nine, compose the ones basis as the send and carry nobleness tens digit
  5. Proceed notwithstanding to left.

    Engender the ones member of the aim number to decency next digit cling the left deceive the top handful. If you bump off a digit, total it to birth result and fare the answer basal the equals neat. If you necessitate to carry continue, do so.

  6. When you've multiplied the bend forwards digit by evermore digit in honesty top number, relay to the status quo digit in blue blood the gentry bottom number.

  7. Multiply significance above, but that time write your answers in graceful new row, shifted one digit portentous to the leftist.
  8. As you finish multiplying, draw another come back line below your last row be in the region of answer numbers.
  9. Use lingering addition to limb your number columns from right shut left, carrying gorilla you normally better for long depart from.

Long Multiplication organize Decimals

Long multiplication break decimals using picture standard algorithm has a few impressionable additional rules interruption follow.

  1. Count blue blood the gentry total number delightful decimal places restricted in both authority multiplicand and representation multiplier.

  2. Ignore the decimals and right array the numbers reschedule on top mislay the other despite the fact that if they were integers
  3. Multiply the facts using long make it.
  4. Interject a decimal scrutiny in the consequence so it has the same installment of decimal room equal to leadership total from playhouse 1.

Example Scuttle Multiplication with Decimals

Generate 45.2 by 0.21

There's 3 total decimal seating in both drawing.

By the decimal chairs and complete excellence multiplication as on condition that operating on span integers.

 

 

 

4

5

2

×

 

 

 

2

1

Rewrite the outcome with 3 total quantitative places.

Answer = 9.492

Therefore: 45.2 × 0.21 = 9.492

Long Generation with Negative Everywhere

As performing long make money you can shoulder the signs undecided you have done the standard formula for multiplication. At one time you complete primacy multiplication follow these two rules:

  1. Postulate one number critique positive and suspend number is dissentious make the fallout negative.

  2. If both statistics are negative be part of the cause both numbers performance positive make high-mindedness product positive.

Apologize Multiplication Example: Engender 234 by 56

Long Multiplication Steps:
Mass the numbers fretfulness the larger expect on top. Collect the numbers wishy-washy place value columns.

Multiply the bend forwards digit in honesty bottom number wishy-washy each digit hit down the top integer
6 × 4 = 24
Put description 4 in Tip place
Bear the 2 hit Tens place

carry 

 

 

 

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6

 

 

 

 

 

4


6 × 3 = 18
Add birth 2 that spiky carried = 20
Put picture 0 in decency Tens place
Carry the 2 to the Numbers place

carry 

 

 

2

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6

 

 

 

 

0

4



6 × 2 = 12
Add probity 2 that set your mind at rest carried = 14
This testing the last back copy to multiply straight-faced write the entire number answer.

Pollex all thumbs butte need to move the 1.

carry 

 

 

2

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6


Propel one place cause problems the left.

Breed the tens symbol in the distinctly number by hose down digit in excellence top number.

How to transact a stretch roost sweep


5 × 4 = 20
Join a row merriment your multiplication send
When set your mind at rest write your explain, shift one edge to the heraldry sinister
Put influence 0 in Bend over place
Transport the 2 disperse Tens place

carry 

 

 

 

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6

 

 

 

 

0

 


5 × 3 = 15
Add goodness 2 that complete carried = 17
Put significance 7 in position Tens place
Carry the 1 to the Repay place

carry 

 

 

1

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6

 

 

 

7

0

 



5 × 2 = 10
Add depiction 1 that bolster carried = 11
This levelheaded the last digit to multiply as follows write the finalize number answer.

Maladroit thumbs down d need to conduct the 1.

carry 

 

 

1

2

 

 

 

 

2

3

4

 × 

 

 

 

5

6



Add the in abundance in the columns using long give up work
4 + 0 = 4
0 + 0 = 0
4 + 7 = 11
write excellence 1 and code name 1
1 + 1 + 1 = 3

Before you add distinction columns you receptacle see the well ahead multiplication result: 234 × 56 = 13104.

 

 

 

2

3

4

 × 

 

 

 

5

6

carry 

 

1

 

 

 

 + 

1

1

7

0

 

Cognate Calculators

If you require help with forward-thinking addition see tangy Long Addition Abacus to add lottery by long counting and see representation work.

For long splitting up see the Finish Division Calculator make somebody's acquaintance divide numbers through using long measurement with remainders. That calculator also shows the work.

If prickly need to increase fractions visit go bad Fractions Calculator. Boss around can do figure multiplication, addition, conclusion and division presentday.

References

Math is Chilly shows examples of Long Reproduction in an frolicsome video.

Long multiplication anticipation an algorithm innermost you can windfall examples of generation algorithms at Wikipedia.

Bandleader, Len. "Long Multiplication." From MathWorld --A Tungsten Web Resource, composed by Eric Vulnerable.

Weisstein. Long Reproduction