Adding and Subtracting Decimals with Two Decimal Digits

This is a complete lesson with instruction and exercises about adding and subtracting decimals with two decimal digits (hundredths). It first compares decimal addition with fraction addition, and uses number lines to help students understand how to add decimals mentally. The lesson contains exercises, word problems, and pattern exercises.

1. Try to solve these
    problems without reading
    the lesson! Each time, write
    the corresponding fractions
    below the decimals.

a.	0.05	+	0.04	=

	5 100	+	4 100	=

b.	0.07	+	0.04	=

	100	+	100	=

c.	0.37	–	0.06	=

	100	–	100	=

d.	0.45	+	0.65	=

	100	+	100	=

e.	3.25		–	1.08		=

	3	100	–	1	100	=

You can add or subtract the hundredths and whole numbers separately. Examples:

0.11	+	0.09	=	0.20
11 hundredths	+	9 hundredths	=	20 hundredths

2.90	–	1.07	=	1.83
2 and 90 hundredths	–	1 and 7 hundredths	=	1 and 83 hundredths

2. Add and subtract mentally. Think how many hundredths there are in each number.

0.03 + 0.09 = ______

2.03 + 2.09 = ______

0.52 + 0.43 = ______

1.55 + 1.25 = ______

1.03 – 0.03 = ______

4.03 – 2.01 = ______

0.10 – 0.08 = ______

20.06 – 1.03 = ______

Often you need to use the fact that 100 hundredths makes one whole. Notice carefully:

0.90	+	0.11	=	1.01
90 hundredths	+	11 hundredths	=	101 hundredths

1.12	–	0.20	=	0.92
112 hundredths	–	20 hundredths	=	92 hundredths

Shortcut: when all of the numbers in the problem all have hundredths, add or subtract as if there was
no decimal point. Then put the decimal point in the answer so it has two decimals (hundredths).

3. Add and subtract. Be careful and remember that 100 hundredths makes one whole.

0.97 + 0.04 = ______

2.96 + 0.06 = ______

0.95 + 0.11 = ______

8.91 + 0.11 = ______

1.03 – 0.04 = ______

7.01 – 0.05 = ______

1.12 – 0.16 = ______

4.01 – 0.50 = ______

Try to add these without reading further. Then read on!

0.2 + 0.05 = _______

0.7 + 0.04 = _______

0.12 + 0.5 = _______

0.2 + 0.05 = _____

What do you think? If you are at 0.2 and go five hundredths (0.05) further, where will you end up?

2 10	+	5 100
↓		↓
20 100	+	5 100	=	25 100

0.2	+	0.05
↓		↓
0.20	+	0.05	=	0.25

Let's write 0.2 and 0.05 as fractions. They have
different denominators (10 and 100).

Before adding, we can convert the first one into hundredth parts. Then they both have a denominator 100 and you can add easily.

When you add them as decimals (0.2 and 0.05), you can tag a zero on the end of 0.2 (two tenths), so it becomes 0.20 (twenty hundredths).
This is the same process as writing 2/10 as 20/100.

Let's check the other two problems you tried earlier. We will write them so that the addends have the same amount of decimals.

0.7	+	0.04			If you are at 0.7 and go four hundredths further, where do you end up?
↓		↓
0.70	+	0.04	=	______

0.12	+	0.5			If you are at 0.5 and go twelve hundredths further, where do you end up?
↓		↓
0.12	+	0.50	=	______

Confused about this “tagging a zero” stuff? Look below:

0	. 2	=	0	. 2	0
ones	tenths		ones	tenths	hund- redths

0.2 has zero ones and two tenths.
0.20 has zero ones, two tenths and zero hundredths.
So both have the same amount of ones, tenths, and hundredths.
They are equal!

4. Add mentally. Before adding, tag a zero to the number with only one decimal so that the addends
will have the same amount of decimals. Write the problems using fractions also.

a.	0.10	+	0.05	=	0.15

=	10 100	+	5 100	=	15 100

b.	0.04	+	0.4	=	______

=	100	+	100	=	100

c.	0.6	+	0.09	=	______

=	100	+	100	=	100

5. Add mentally. Before adding, you can tag a zero to the number with only one decimal.

a. 0.11 + 0.5 = _______	b. 0.24 + 0.2 = _______	c. 0.3 + 0.39 = _______
d. 0.22 + 0.7 = _______	e. 0.2 + 0.41 = _______	f. 0.27 + 0.8 = _______

6. Continue the patterns.

a. 0.91

+ 0.02 = _____

b. 0.80

– 0.05 = _____

c. 2.90

+ 0.03 = _____

d. 1.77

+ 0.11 = _____

7. Add enough hundredths to make the next whole tenth. Remember, 0.5 = 0.50.

a. 0.47 + _____ = 0.5

b. 0.55 + _____ = 0.6

c. 0.06 + _____ = 0.1

d. 0.32 + _____ = 0.4

e. 0.88 + _____ = ______

f. 0.97 + _____ = ______

8. Explain why the following additions are wrong.

a. 0.99 + 0.1 = 1

b. 0.43 + 0.59 = 0.102

9. Subtract from a whole number.

a.	1 – 0.6 = _____ 1 – 0.67 = _____

b.	2 – 0.6 = _____ 2 – 0.57 = _____

c.	4 – 0.23 = _____ 4 – 0.13 = _____

Remember? 100 cm makes one meter.

Therefore, 1 cm is one-hundredth part of 1 meter.

In other words, 1 cm = 0.01 m.

5 cm = 0.05 m

64 cm = 0.64 m

2 m 12 cm = 2.12 m

10. Convert between meters and centimeters, and solve the problems.

a. 0.73 m = __________ cm

b. 2.82 m = __________ cm

c. _________ m = 9 m 80 cm

d. _________ m = 306 cm

e. A boy is 1.15 m tall and a bush is 156 cm
tall. Which is taller? How much taller?

f. A table is 2.40 m long and 0.90 m wide.
Find its perimeter in meters.

g. A door that is 90 cm wide will have a
    decorative board above it. The decorative
    board is now 1.25 m long. How much needs
    to be cut off from the board so that it fits?

h. The height of a room is 2.25 m. How much
space is left above a person's head who is
186 cm tall?

11. Add and subtract mentally. You can tag a zero to the decimal with only tenths.

a. 0.04 + 0.1 = _______ 0.14 + 0.1 = _______	b. 0.28 + 0.1 = _______ 0.25 + 0.5 = _______	c. 2.04 + 0.1 = _______ 3.08 + 0.6 = _______
d. 13.53 + 0.4 = _______ 5.03 + 2.25 = _______	e. 0.3 + 0.05 = _______ 0.03 + 0.5 = _______	f. 0.8 – 0.09 = _______ 0.9 – 0.08 = _______
g. 1.3 – 0.07 = _______ 1.3 – 0.7 = _______	h. 6.2 – 1.2 = _______ 6.2 – 1.25 = _______	i. 2 – 0.1 = _______ 3 – 0.08 = _______

12. Find what was added!

1.00

1.06

1.11

1.19

1.2

1.37

1.44

1.5

1.65

Math Lessons menu

Place Value Grade 1 Using a 100-bead abacus in elementary math Teaching tens and ones Practicing with two-digit numbers Counting in groups of ten Skip-counting practice (0-100) Comparing 2-digit numbers Cents and dimes Grade 2 Three-digit numbers Comparing 3-digit numbers Grade 3 Place value with thousands Comparing 4-digit numbers Rounding & estimating Rounding to the nearest 100 Grade 4 Place value - big numbers	Add & subtract lessons Grade 1 Missing addend concept (0-10) Addition facts when the sum is 6 Addition & subtraction connection Grade 2 Fact families & basic addition/subtraction facts Sums that go over over the next ten Add/subtract whole tens (0-100) Add a 2-digit number and a single-digit number mentally Add 2-digit numbers mentally Regrouping in addition Regrouping twice in addition Regrouping or borrowing in subtraction Grade 3 Mental subtraction strategies Rounding & estimating	Multiplication Grade 3 Multiplication concept as repeated addition Multiplication on number line Commutative Multiply by zero Word problems Order of operations Structured drill for multiplication tables Drilling tables of 2, 3, 5, or 10 Drilling tables of 4, 11, 9 Grade 4 Multiplying by whole tens & hundreds Distributive property Partial products - the easy way Partial products - video lesson Multiplication algorithm Multiplication Algorithm — Two-Digit Multiplier Scales problems - video lesson Estimation when multiplying
Division Grade 3 Division as making groups Division/multiplication connection Division is repeated subtraction Zero in division Division that is not exact (remainder) Divisibility Grade 4 How to teach long division Long division as repeated subtraction Why long division works Zero in dividend Remainder & long division Two-digit divisor Review of division topics Divisibility Divisibility within 0-1000 Divisibility rules Prime factorization 1 Prime factorization 2 Sieve of Eratosthenes	Fraction Lessons Understanding fractions Finding fractional parts with division Mixed numbers Fractions to mixed numbers and vv. Adding like fractions Equivalent fractions Adding unlike fractions 1 Adding unlike fractions 2: Finding the common denominator Adding mixed numbers Subtracting mixed numbers Subtracting mixed numbers 2 Measuring in inches Comparing fractions Simplifying fractions Multiply fractions by whole numbers Multiply fractions by fractions Multiplication and area Simplify before multiplying Dividing fractions by whole numbers Dividing fractions: fitting the divisor Dividing fractions: reciprocal numbers Dividing fractions: using the shortcut	Geometry Lessons Lines, rays, and angles Measuring angles Parallel & perpendicular Acute, obtuse, and right triangles Angle sum of a triangle Equilateral & isosceles triangles Circles Symmetry Altitude of a triangle Polygons Perimeter Area of rectangles Area of right triangles Area of parallelograms Area of triangles Area versus Perimeter Angles in Polygons (PDF) Review: Area of Polygons (PDF) Surface Area (PDF)
Decimals Lessons Decimals videos Decimals (1 decimal digit) Decimal place value (1 decimal digit) Decimals (2 decimal digits) Decimal place value (2 decimal digits) Decimals (3 decimal digits) Add & subtract (1 decimal digit) Add & subtract (2 decimal digits) Add and subtract decimals — practice Comparing decimals Multiply a decimal by a whole number Multiply decimals by decimals Divide decimals—mental math Divide decimals by decimals Multiply and divide decimals by 10, 100, and 1000 Decimals review lesson	Percents Lessons How to teach proportions Percent - the basic concept Percentage of a number—mental math How to calculate a percentage of a number How to calculate percentages Basics of percent of change	General Four habits of highly effective math teaching Why are math word problems SO difficult for children? Hint: it has to do with a "recipe" that many math lessons follow. The do's and don'ts of teaching problem solving in math Advice on how you can teach problem solving in elementary, middle, and high school math. How to set up algebraic equations to match word problems Students often have problems setting up an equation for a word problem in algebra. To do that, they need to see the RELATIONSHIP between the different quantities in the problem. This article explains some of those relationships. Seven reasons behind math anxiety and how to prevent it Mental math "mathemagic" with Arthur Benjamin (video) Keeping math skills sharp in the summer Geometric vanish puzzles Science resources Short reviews of the various science resources and curricula I have used with my own children.