Standard Algorithm with Decimals (All 4 Operations)

8 is in the tens place, 1 is in the ones place, 2 is in the tenths place, 5 is in the hundredths place, and 3 is in the thousandths place.

I line the numbers up by place value and add them one step at a time, starting with the least value, the farthest to the right. When I get to 5 + 8 = 13, I have to regroup the 1 and add it to the hundreds place. The answer is 735.

I line the numbers up by place value with the greater number on top. Then I subtract each place value, one at a time. Since 8 is greater than 4, I have to regroup 1 from the tens place in 254 to make 10 ones. Now I subtract 14 – 8 = 6, and then subtract 4 – 2 = 2. In the hundreds place, I have 2 – 1 = 1. The answer is 126.

I line the numbers up by place value and first multiply all the numbers in 351 by 6, and then by 2, writing the products above each place and regrouping if needed. At the end, I add the partial products together. The answer is 9,126.

I set up the algorithm with the divisor to the left of the dividend. 56 goes into 95 once with remainder 39. Bring down the 2. 56 goes into 392 seven times with no remainder. The quotient is 17.

I should line them up by place value. The decimal points should also be lined up exactly.

I still want to line the numbers up by place value! If there is no value in a place, I can write a zero in that place. So I add 2.500 + 4.123.

Not this time! I should line them up to the right so that the 9 is above the 1. I ignore the decimal point until I am done calculating.

I look at how many decimal places each factor has. Add them together, and that is how many decimal places the product should have. I can also find out by rounding and estimating the answer.

Multiply the divisor by a power of 10 until it is a whole number. Then multiply the dividend by the same power of 10. Now I can start the long division algorithm.