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1. Adding and subtracting decimals

Warm-up

Three quick questions from earlier lessons.

Discover

Ana adds $2.5 + 1.25$ and gets $1.50$ . What went wrong?

She lined up the last digits, not the decimal points
Nothing

Key idea

Line up the decimal points.

To add or subtract decimals, line up the decimal points (write zeros to fill empty places), then add or subtract place by place, regrouping when needed: 1 one = 10 tenths, 1 tenth = 10 hundredths.

Worked example

$7.3 - 2.68$ .

7.30 - 2.68

Fill the hundredths.

4.62

Regroup.

Your turn, guided

Your turn: $3.4 + 0.75$ .

4.15

3.40 + 0.75.

Practice ★

Compute $27.1 + 11.81$ .
Compute $16.8 + 26.44$ .

Compute $31 - 7.3$ .

Watch out!

Practice ★★

Compute $14.1 - 3.5$ .
Compute $35.3 - 3.7$ .

Exit ticket

Three questions to check you have got it.

Compute $27.1 + 11.81$ .
Compute $16.8 + 26.44$ .
Compute $11.3 + 22.85$ .

Summary card

Adding and subtracting decimals

Line up the points; regroup as with whole numbers.

Watch out: never subtract the smaller digit from the larger by habit.

2. Multiplying decimals

Warm-up

Three quick questions from earlier lessons.

Discover

$0.3 \times 0.2$ : three tenths of two tenths. Which is it?

$0.06$
$0.6$

Key idea

Multiply as whole numbers, then count decimal places.

To multiply decimals, multiply as if they were whole numbers. The product has as many decimal places as the factors together (tenths × tenths = hundredths). Estimate to check.

Worked example

$1.5 \times 2.4$ .

15 \times 24 = 360

Whole numbers.

3.60 = 3.6

1 + 1 places.

Your turn, guided

Your turn: $0.4 \times 0.7$ .

0.28

28 hundredths.

Practice ★

Compute $6.9 \times 5$ .
Compute $9.7 \times 3$ .

Compute $0.6 \times 0.6$ .

Watch out!

Practice ★★

Compute $9.9 \times 1.6$ .
Compute $4.8 \times 3.5$ .

Boss problem. Markers cost 1.1 dollars each. You buy 3 markers and pay with a 20-dollar bill.

Exit ticket

Three questions to check you have got it.

Compute $6.9 \times 5$ .
Compute $9.7 \times 3$ .
Compute $9.6 \times 8$ .

Summary card

Multiplying decimals

Multiply, then count the decimal places.

Watch out: estimate to place the point.

3. Dividing decimals

Warm-up

Three quick questions from earlier lessons.

Discover

How many 0.5-liter bottles can be filled from 3 liters?

Key idea

Make the divisor a whole number.

To divide by a decimal, multiply both numbers by 10, 100, … until the divisor is whole:

a \div b = (10a) \div (10b)

. Then divide; use long division and keep going after the point if needed. Dividing by a number less than 1 gives a larger result.

Worked example

$4.8 \div 0.6$ .

48 \div 6

× 10 both.

8

Divide.

Your turn, guided

Your turn: $9.6 \div 4$ .

2.4

96 tenths ÷ 4.

Practice ★

Compute $7.3 \div 2$ .
Compute $5.7 \div 2$ .

Compute $97 \div 0.1$ .

Watch out!

Practice ★★

How many 0.5-liter cups can be filled from 1.9 liters of juice? Compute $1.9 \div 0.5$ .
How many 0.4-liter cups can be filled from 8.2 liters of juice? Compute $8.2 \div 0.4$ .

Exit ticket

Three questions to check you have got it.

Compute $7.3 \div 2$ .
Compute $5.7 \div 2$ .
Compute $2.9 \div 4$ .

Summary card

Dividing decimals

Scale both numbers to make the divisor whole.

Watch out: dividing by 0.something makes it bigger.

Answers: Arithmetic in base ten

1. Adding and subtracting decimals

$\frac{3891}{100}$
$\frac{1081}{25}$

$\frac{237}{10}$

$\frac{53}{5}$
$\frac{158}{5}$

$\frac{3891}{100}$
$\frac{1081}{25}$
$\frac{683}{20}$

2. Multiplying decimals

$\frac{69}{2}$
$\frac{291}{10}$

$\frac{9}{25}$

$\frac{396}{25}$
$\frac{84}{5}$

$\frac{69}{2}$
$\frac{291}{10}$
$\frac{384}{5}$

3. Dividing decimals

$\frac{73}{20}$
$\frac{57}{20}$

$970$

$\frac{19}{5}$
$\frac{41}{2}$

$\frac{73}{20}$
$\frac{57}{20}$
$\frac{29}{40}$