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Common Core Math6th GradeThe Number System

6.NS.3: Compute with Multi-Digit Decimals Fluently

Also written as 6.NS.B.3 and CCSS.MATH.CONTENT.6.NS.B.3 · Cluster: Compute fluently with multi-digit numbers and find common factors and multiples.

Make a 6.NS.3 WorksheetAll 29 6th Grade Math Standards

The Official Wording

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026

What 6.NS.3 Means in Plain English

Sixth graders add, subtract, multiply and divide decimals like 14.75 + 3.6, 2.35 × 1.4 and 48.6 ÷ 12 with the standard written methods, no grids or models required. Fifth grade built the understanding with hundredths and models (5.NBT.7). This year the algorithms become automatic.

The hard part is the decimal point: lining it up to add and subtract, counting decimal places to multiply, and moving it in both numbers to divide. These skills power unit prices in 6.RP.3 and, in 7th grade, negative decimals in 7.NS.3 and percent problems in 7.RP.3.

6.NS.3 I Can Statements

  • I can add and subtract decimals by lining up the decimal points.
  • I can multiply decimals and place the decimal point in the product.
  • I can divide a decimal by a decimal with long division.

6.NS.3 Worked Example

One grocery bill uses three of the four operations, and the decimal point behaves differently in each.

Problem

Three friends buy 2.5 pounds of grapes at $3.60 per pound and a $3.75 box of crackers. They split the total equally. How much does each pay?

Splitting a grocery bill three ways
  1. Multiply for the grapes. Ignore the decimal points first: 25 × 360 = 9,000. Then count decimal places, one in 2.5 and two in 3.60, three in all.2.5 × 3.60 = 9.000 = $9.00
  2. Add the crackers. Line up the decimal points, not the right-hand digits.9.00 + 3.75 = 12.75
  3. Divide by 3. The decimal point in the quotient sits directly above the one in the dividend.12.75 ÷ 3 = 4.25
  4. Every answer here is money, so write it to two decimal places.$4.25 each
Answer$4.25 each

Check it: Multiply back: 3 × $4.25 = $12.75. Take off the crackers: $12.75 - $3.75 = $9.00, which is 2.5 × $3.60 for the grapes.

Common Mistakes with 6.NS.3

Lining up the right-hand digits to add

14.75 + 3.6 written as 14.75 + .36 = 15.11

Try this: Line up the decimal points and pad with a zero: 14.75 + 3.60 = 18.35. Place value, not length, decides the columns.

Lining up the decimal points to multiply

2.35 × 1.4 = 32.90 (two decimal places, copied from 2.35)

Try this: Count the decimal places in both factors, two plus one is three, so 235 × 14 = 3,290 becomes 3.290.

Moving the decimal point in only one number

4.86 ÷ 1.2 = 0.405 (the point moved in 1.2 but not in 4.86)

Try this: Move the point the same number of places in both numbers: 4.86 ÷ 1.2 becomes 48.6 ÷ 12 = 4.05.

Where 6.NS.3 Fits

Comes Before5.NBT.7Add, subtract, multiply and divide decimals to hundredths with models and strategies.5.NBT.5Multiply multi-digit whole numbers with the standard algorithm.6.NS.2Divide multi-digit whole numbers with the standard algorithm.
Alongside6.RP.3Solve unit-price problems, where the prices are decimals.6.EE.7Solve one-step equations whose numbers are decimals.
Comes Next7.NS.3Solve problems with all four operations on rational numbers, including negative decimals.7.RP.3Solve percent problems like tax, tip and discount.

Practice 6.NS.3

Math Worksheet GeneratorFree ToolOpens with decimal addition, subtraction, multiplication and division mixed on one page, with an answer key.DecimalsAll four operationsAnswer key
Make a Worksheet

Quick Check

  1. 26.4 + 3.85
  2. 0.75 × 2.4
  3. A 1.5-liter bottle of juice costs $3.45. What is the price per liter?

6.NS.3: Other Names

6.NS.36.NS.B.3CCSS.MATH.CONTENT.6.NS.B.3

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.