# 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).