# Multi-Digit and Fraction Computation

## Objective

Divide decimals by decimals using the standard algorithm.

## Common Core Standards

### Core Standards

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• 6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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• 5.NBT.B.7

## Criteria for Success

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1. Understand that multiplying a dividend and divisor by the same power of ten creates equivalent division problems with the same solution.
2. Create equivalent division problems with whole number divisors that can be solved using the standard algorithm.
3. Apply the standard algorithm for division to solve problems.

## Tips for Teachers

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• Dividing with decimals is a fluency expectation in sixth grade. Ensure students have opportunities to build towards fluency throughout the unit and the year. See our Guide to Procedural Skills and Fluency for additional information and strategies.
• The following tools or materials are useful for this lesson: large graph or grid paper for computations, calculators to check answers.

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## Anchor Problems

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### Problem 1

Consider the division problem ${19.2 ÷ 1.6}$

Written as a fraction, the problem becomes ${\frac{19.2}{1.6}}$.

1. Multiply the fraction by ${\frac{10}{10}}$​ to ​​create an equivalent division problem with whole numbers. Then use the standard algorithm for division to find the quotient.

2. How can you apply this approach to solve other decimal division problems?

#### Guiding Questions

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### Problem 2

Divide: ${526.76 ÷ 1.3}$

First, write an equivalent division problem with a whole number divisor. Then solve and check your answer using multiplication.

#### Guiding Questions

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### Problem 3

Which division problems below will have the same solution as ${580.6÷8.44}$?

Explain your reasoning for each equivalent problem.

a.     ${580.6 ÷ 844}$

b.     ${5,806 ÷ 844}$

c.     ${58,060 ÷ 844}$

d.     ${580,600 ÷ 844}$

e.     ${5,806 ÷ 84.4}$

f.     ${58.06 ÷ 0.844}$

#### Guiding Questions

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## Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Include procedural problems involving all types of decimal division problems.
• Include examples where the decimal answer is rounded to a given place value.
• Include error analysis problems.

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Sophia’s dad paid $43.25 for 12.5 gallons of gas. 1. What is the cost of one gallon of gas? 2. Approximately how many gallons of gas can you get for$1? Round to the nearest hundredth.

#### References

Illustrative Mathematics Buying Gas

Buying Gas, accessed on Sept. 28, 2017, 3:55 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

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