Find the product of 32.5 × 0.25 × 3.50
Answers
Step-by-step explanation:
"7 times 8 is 56." Write 6, carry 5.
"7 times 2 is 14, plus 5 is 19." Write 9, carry 1.
"7 times 6 is 42, plus 1 is 43." Write 43.
That is,
7 × 628 = 4396.
Why can we repeatedly add 628 in that way? Because we have distributed 7 to the Tens, Ones, Hundreds of 628, and then added those partial products:
multiplication
When the multiplier has more than one digit --
multiplication
-- follow the same procedure for each digit. When we multiply by 3 tens, the product is 1884 tens. It is not necessary to write 18840. (Lesson 2.) Simply begin the 4 of 1884 in the tens column.
When we multiply by 2 hundreds, the product is 1256 hundreds, and so we write 6 in the hundreds column.
We can state the rule as follows:
2. In writing, how do we multiply whole numbers?
multiplication
Write the multiplier under the multiplicand and draw a line. Multiply the multiplicand by each digit of the multiplier. Place the ones digit of each partial product in the same column as the multiplying digit. Then add the partial products.
Anticipating the next Question, if there were decimal points --
multiplication
-- the multiplication would proceed in exactly the same way. In the answer, we would then separate as many decimal digits as there are in the two numbers together; in this case, three.
Example 1. 96
× 37
672 ← 7 × 96 = 630 + 42
2884 ← 3 × 96 = 270 + 18
3552
On multiplying by 7 ones, write 2 in the ones column.
On multiplying by 3 tens, write 8 in the tens column -- because the partial product 288 means 288 tens.
The student should be able to calculate each partial product mentally by distributing from left to right. We have indicated that above.
Example 2. Multiply 45 × 236.
It does not matter which number you choose as the multiplier, that is, to place on the bottom. However it is more efficient to choose 45 because then there will be only two multiplications rather than three.
multiplication