Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Money, measurements and data in everyday life are full of decimals, and by the end of sixth grade students should handle all four operations with them using the standard algorithms. Fifth grade worked with decimals to hundredths using models and strategies; now the numbers get longer and the expectation is fluency.
Each operation has its own place value logic. Adding and subtracting work when digits of the same place line up, which is why decimal points sit in a column. Multiplying can be done as if the numbers were whole, then the product is placed so that it has as many decimal places as the two factors together. Dividing by a decimal is turned into dividing by a whole number: multiplying both numbers by the same power of ten, as in 7.2 ÷ 0.06 becoming 720 ÷ 6, does not change the quotient. Estimation is the safety net: 3.8 × 4.1 must be near 16, so 155.8 is clearly wrong.
Adding 12.5 + 3.25 with the 5s lined up gives 4.75 or 15.50 in the wrong places. Line up the decimal points, and fill empty places with zeros: 12.50 + 3.25.
Multiplication does not need aligned points. Students should multiply as whole numbers and then count decimal places in the factors.
Turning 4.5 ÷ 0.15 into 450 ÷ 0.15 changes the answer. Both numbers must be multiplied by the same power of ten.
Students may believe 0.125 is greater than 0.3 because it has more digits. Comparing tenths first (1 tenth versus 3 tenths) fixes this.
A roll of ribbon is 7.2 meters long. How many pieces 0.06 meters long can be cut from it?
Answer: 120 pieces can be cut.
Have students estimate before every calculation and compare at the end. For multiplication, connect the decimal-places rule to fractions: 0.3 × 0.4 is 3/10 × 4/10 = 12/100 = 0.12. For division, a short discussion of why 7.2 ÷ 0.06 and 720 ÷ 6 must have the same answer builds understanding of the shortcut.
Real contexts such as unit prices, recipe scaling and measurement keep practice meaningful. Mixed sets where students must choose the operation are closer to what appears on assessments.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 28.286
Line up the decimal points: 23.700 + 4.586 = 28.286.
Answer: B) 8.52
Write 15 as 15.00 and subtract: 15.00 - 6.48 = 8.52.
Answer: 7.74
Multiply 36 × 215 = 7,740. The factors have 1 + 2 = 3 decimal places, so the product is 7.740, which is 7.74.
Answer: D) 24
Multiply both numbers by 10: 96 ÷ 4 = 24.
Answer: 43.125 (also accepted: 43.13)
3.45 × 12.5 = 43.125. In money this rounds to $43.13.
Answer: B) 40
Round to 5 × 8 = 40. The exact product is 39.69, close to 40.
A full lesson with slides, activities and an exit ticket on operations with multi-digit decimals, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.NS.B.3 with an answer key, ready in about a minute.
Make a worksheet →Turn operations with multi-digit decimals into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Fluent addition, subtraction, multiplication and division of multi-digit decimals using the standard algorithm for each operation.
In 5th grade students work to hundredths with models and strategies. In 6th grade the numbers are longer and the standard algorithms are expected.