# 4.6 Multiplying and Dividing Multi-digit Numbers

## Unit Goals

• Students multiply and divide multi-digit whole numbers using partial products and partial quotients strategies, and apply this understanding to solve multi-step problems using the four operations.

### Section A Goals

• Generate a number or shape pattern that follows a given rule.
• Identify apparent features of a number pattern that were not explicit in the rule itself.

### Section B Goals

• Multiply a whole number of up to four digits by a one-digit whole number, and 2 two-digit numbers using strategies based on place value and the properties of operations.

### Section C Goals

• Divide numbers of up to four digits by one-digit divisors to find whole-number quotients and remainders, using strategies based on place value, properties of operations, and the relationship between multiplication and division.

### Section D Goals

• Use the four operations to solve problems that involve multi-digit whole numbers and assess the reasonableness of answers.

### Glossary Entries

• common denominator
The same denominator in two or more fractions. For instance, $$\frac{1}{4}$$ and $$\frac{5}{4}$$ have a common denominator.

• composite number
A whole number with more than 1 factor pair.

• denominator
The bottom part of a fraction that tells how many equal parts the whole was partitioned into.

• dividend
The number being divided. For example, when 37 is divided by 5, we call 37 the dividend.

• equivalent fractions
Fractions that have the same size and describe the same point on the number line. For example, $$\frac{1}{2}$$ and $$\frac{2}{4}$$ are equivalent fractions.

• factor pair of a whole number
A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.

• mixed number
A number expressed as a whole number and a fraction less than 1.

• multiple of a number
The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.

• numerator

The top part of a fraction that tells how many of the equal parts are being described.

• prime number
A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.

• remainder
The number left over when we take away as many equal groups as we can from a number.

• rounding

A formal way to say which number a given number is closer to. For example, for 182, the number 180 is the closest multiple of ten and 200 is the closest multiple of a hundred. We can round 182 to 180 (if rounding to the nearest ten) or 200 (if rounding to the nearest hundred).