Add, subtract, multiply, and divide decimals using a standard algorithm.
Arkansas Academic Standards:
6.NS.B.3
Use computational fluency to add, subtract, multiply, and divide multi-digit decimals and fractions using a standard algorithm for each operation
Note: A standard algorithm can be viewed as, but should not be limited to, the traditional recording system. A standard algorithm denotes any valid base-ten strategy.
Common Core State Standards:
Math.6.NS.3 or 6.NS.B.3
Georgia Standards of Excellence (GSE):
MGSE6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using
the standard algorithm for each operation.
Mississippi College- and Career-Readiness Standards:
6.NS.3
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
North Carolina - Standard Course of Study:
6.NS.3
Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals.
Tennessee Academic Standards:
6.NS.B.3
Fluently add, subtract, multiply, and divide multi-digit decimals using a standard algorithm for each operation.
Wisconsin Academic Standards:
6.NS.B.3
Flexibly and efficiently add, subtract, multiply, and divide multi-digit decimals using strategies or
algorithms based on place value, visual models, the relationship between operations, and the
properties of operations.
Pennsylvania Core Standards:
CC.2.1.6.E.2
Identify and choose appropriate processes to compute fluently with multi-digit numbers.
Pennsylvania Core Standards:
M06.A-N.2.1.1
Solve problems involving operations (+, –, ×, and ÷) with whole numbers, decimals (through thousandths), straight computation, or word problems.
Florida - Benchmarks for Excellent Student Thinking:
MA.6.NSO.2.1
Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
6th Grade Math - Decimal Operations Lesson
The most important step when adding decimal numbers is to line up the decimal points. Then, the sum of decimal numbers can be found by adding each column from right to left, starting with the smallest decimal place.
Example:
6
9
2
.2
4
+
3
7
7
.5
4
Add the columns from right to left. Remember to regroup when a column's sum is greater than 9.
1
6
9
2
.2
4
+
3
7
7
.5
4
1
0
6
9
.7
8
The most important step when subtracting decimal numbers is to line up the decimal points. Then, the difference of decimal numbers with more than one digit can be found by subtracting each column from right to left, starting with the smallest decimal place.
Example:
4
4
7
.6
1
-
1
7
2
.4
6
Subtract the columns from right to left. Remember to regroup when the top number in a column is less than the bottom number.
3
14
5
11
4
4
7
.6
1
-
1
7
2
.4
6
2
7
5
.1
5
To multiply by a decimal number, remove the decimal point(s) and multiply as if the numbers were whole numbers.
Then, move the decimal point in the product one space to the left for each decimal place in the original problem.
Example:
Step 1: Write the second number under the first number so that the last digits are lined up.
Step 2: Rewrite the problem without any decimal points.
Step 3: Multiply the ones digit in the bottom number by each digit in the top number. Remember to regroup when a product is greater than 9.
Step 4: Add a placeholder zero to the ones column. Multiply the tens digit in the bottom number by each digit in the top number. Remember to regroup when a product is greater than 9.
Step 5: Add to find the product.
Step 6: Move the decimal point one space to the left for each decimal place in the original problem. There are three decimal places in the original problem, so move the decimal point three spaces to the left.
To divide by a decimal, move the decimal point in the divisor to the end of the number. Then, move the decimal point in the dividend the same number of spaces to the right.
Example:
Step 1: Write the dividend under the long division symbol, and write the divisor to the left of the long division symbol.
Step 2: Move the decimal point in the divisor one space to the right so that it is at the end of the number. Move the decimal point in the dividend one space to the right as well.
Step 3: Divide as if 151.8 were a whole number. The first two digits of the dividend is less than the divisor, so divide the first three digits of the dividend by the divisor (151 ÷ 33 = 4 R19).
Step 4: Bring down the next digit in the dividend, and divide (198 ÷ 33 = 6).
Step 5: Write the decimal point in the quotient directly above where it is in the dividend.
6th Grade Math - Decimal Operations Lesson
