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4th grade

Course: 4th grade > Unit 5

Lesson 1: Remainders
Math
4th grade
Division
Remainders
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Division: FAQ

Google Classroom
Frequently asked questions about division.

What is a remainder?

When we divide one number by another, sometimes the division doesn't come out evenly. The remainder is the part that's left over.
For example, when we divide 17 by 4, we get a quotient of 4 with a remainder of 1.
start color #208170, 17, end color #208170, divided by, start color #543b78, 4, end color #543b78
An array of 17 circles arranged in 4 rows of 4 circles each and 1 row of 1circle.
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What is division with place value?

When we divide larger numbers, we can break them down into smaller chunks using place value.
For example, when we divide 288 by 4, we can divide the 200 by 4, the 80 by 4, and the 8 by 4 and then add the quotients together.
=288÷4=(200÷4)+(80÷4)+(8÷4)=50+20+2=72\begin{aligned} &\phantom{=}\maroonE{288}\div{\blueE4}\\\\ &=(\maroonE{200}\div\blueE4)+(\maroonE{80}\div\blueE4) +(\maroonE{8}\div\blueE4)\\\\ &= 50 + 20 + 2\\\\ &=72 \end{aligned}
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How can we use area models to help us divide?

An area model is a way of visually breaking down a multiplication or division problem into smaller parts. We can use an area model to show the distributive property of multiplication and division.
For example, we can break apart 4, comma, 115, divided by, 4 using the area model below.
An area model split into 4 parts, each with a width of 4 units. From top to bottom the parts have a height of 1,000 units and an area of 4,000 square units; a height of 25 units and an area of 100 square units; a height of 3 units and an area of 12 square units; an unlabeled height and an area of 3 square units.
Try it yourself with these exercises:

What is multi-digit division with partial quotients?

When we divide multi-digit numbers, we can use partial quotients to break the problem down into smaller chunks. For example, when we divide 486 by 3, we can break down 486 into 300, plus, 180, plus, 6.
3)486‾−300‾100186−180‾606−6‾+2‾0162\begin{array}{rr|rl} {3}&\overline{\Big)486}\\ &\mathllap{-}\underline{300}&\purpleD{100}\\ &186\\ &\mathllap{-}\underline{180}&\purpleD{60}\\ &6\\ &\mathllap{-}\underline{6}&\underline{{}+\purpleD{2}}\\ &\goldE{0}&\maroonE{162} \end{array}
Try it yourself with these exercises:

Where do we use division in the real world?

We use division all the time! For example, we might use it to split a bill evenly between a group of friends, to calculate a batting average in baseball, or to figure out how many servings of food we can make from a recipe.

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