Divide Multi-Digit Decimals

Students divide multi-digit decimals by multiplying both the dividend and divisor by an appropriate power of 10 to create a whole-number divisor, then applying the standard long-division algorithm. They interpret the result in context and check using multiplication.

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Grade 6 · Number System: Multi-Digit Computation · question 1 of 3

0 of 20

20 rungs. A star at the top.

7.2 ÷ 0.9 = .

How it is taught

0:00 of 5:48

Clear decimals by multiplying dividend and divisor the same way.

The quotient stays the same.

Read it: Dividing by a decimal

16.1 ÷ 0.7: the divisor is not whole, so multiply both numbers by 10. 16.1 ÷ 0.7 becomes 161 ÷ 7, which is 23, and the quotient has not changed.

If the divisor is not whole, multiply both numbers by 10, or by 100, until it is.
Divide as with whole numbers: 161 ÷ 7 = 23.
Where the dividend still has a point, keep the quotient's point straight above it.

Multiplying both numbers by 10 keeps the same number of 0.7s in 16.1: 161 ÷ 7 asks the same question.

A whole divisor lets you divide place by place, the way long division works.

Check by multiplying back: 23 × 0.7 = 16.1.

Make the divisor whole by multiplying both numbers by the same 10 or 100, then divide.

Multiplying only the divisor: 16.1 ÷ 7 = 2.3.

Multiply both by 10: 161 ÷ 7 = 23.

23.8 ÷ 7 = ___ — 3.4. Divide as with whole numbers and keep the point above the point: 3.4.

7.2 ÷ 0.3

A juice bottle holds seven point two liters. Each cup holds zero point three liters. How many cups can we fill?

We need to find seven point two divided by zero point three.

We can't divide neatly by a decimal. So multiply BOTH numbers by ten — the answer stays the same. Now it's seventy-two divided by three.

Now we can use long division. Three goes outside the house, seventy-two goes inside.

How many threes fit inside seven? Two. Write two on top.

Multiply: two times three is six. Write six under the seven.

Subtract: seven minus six is one.

Bring down the two next to the one — that makes twelve.

How many threes fit in twelve? Four. Write four on top.

Four times three is twelve. Twelve minus twelve is zero — no remainder!

Grade 6 · Make the divisor a whole number, then divide

So seven point two divided by zero point three equals twenty-four. Twenty-four cups. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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