Decimals, Fractions, and Percents Mastery

Chapter 1: Key Concepts

Place Value: Each digit in a number has a position, or place, which determines its value (e.g., tenths, hundredths, thousandths).
Decimals: Numbers that have a whole part and a fractional part separated by a decimal point.
Fractions: Represent parts of a whole, written as one number over another (numerator/denominator).
Rounding: Simplifying a number while keeping its value close to the original number (e.g., rounding 3.76 to 3.8).
Percents: Means “per hundred”; a way to express numbers as parts of 100.
Estimating: Finding a number that is close enough to the right answer, usually by rounding.
Operations: Addition, subtraction, multiplication, and division can be performed with decimals, fractions, and percents, following similar rules as for whole numbers but paying attention to decimal points and denominators.

Chapter 2: Topics

Decimal Place Value and Rounding
Changing Fractions to Decimals
Changing Decimals to Fractions
Comparing and Ordering Decimals
Adding Decimals
Subtracting Decimals
Adding and Subtracting Money
Estimating Decimal Sums and Differences
Multiplying Decimals
Multiplying Money
Estimating Decimal Products
Dividing Decimals by Whole Numbers
Dividing Whole Numbers by Decimals
Dividing Decimals by Decimals
Dividing Money
Estimating Decimal Quotients
Understanding Percent
Percents and Fractions
Percents and Decimals
Multiplying Percents and Fractions

Chapter 3: Examples

1. Decimal Place Value and Rounding

Number: 3.476

3 is in the ones place
4 is in the tenths place
7 is in the hundredths place
6 is in the thousandths place

Round 3.476 to the nearest hundredth: 3.48

2. Changing Fractions to Decimals

3/4 = 0.75

How does 3/4 = 0.75?

Divide the numerator by the denominator:
3 ÷ 4 = 0.75
Think of it in money: If you have 3 out of 4 quarters, you have 75 cents, or $0.75.

3 out of 4 parts are shaded.
Fraction: 3/4 → Decimal: 0.75

Visualize it: Imagine a chocolate bar split into 4 equal pieces.
If you eat 3 pieces, you've eaten 3/4 of the bar, or 0.75 of the whole.

3. Changing Decimals to Fractions

0.6 = 6/10 = 3/5 (write as 6 over 10, then simplify)

4. Comparing and Ordering Decimals

Order: 0.56, 0.605, 0.65 (from least to greatest)

5. Adding Decimals

1.25 + 3.7 = 4.95

How do you add 1.25 + 2.7?

Line up the decimal points:
1.25
+ 2.70
Add zeros if needed to make the same number of decimal places.
(2.7 becomes 2.70)
Add from right to left, just like whole numbers, keeping the decimal point in line.

Always line up the decimal points.
Add as usual, then bring the decimal point straight down.
1.25 + 2.70 = 3.95

Write the answer with the decimal point in the same place:
3.95

6. Subtracting Decimals

5.6 – 2.48 = 3.12

7. Adding and Subtracting Money

$4.20 + $1.35 = $5.55

$7.00 – $2.75 = $4.25

8. Estimating Decimal Sums and Differences

4.67 + 2.19 ≈ 5 + 2 = 7

9. Multiplying Decimals

0.7 × 0.3 = 0.21

How do you multiply 0.7 × 0.3?

Ignore the decimals for now and multiply as whole numbers:
7 × 3 = 21
Count the total decimal places:
- 0.7 has 1 decimal place
- 0.3 has 1 decimal place
- Total: 2 decimal places
Place the decimal in the product:
Start at the right and count 2 places to the left:
21 → 0.21

The overlap (darkest rectangle) is 0.21 of the whole box.
0.7 × 0.3 = 0.21

So, 0.7 × 0.3 = 0.21
(21, with two decimal places)

10. Multiplying Money

$5.25 × 3 = $15.75

11. Estimating Decimal Products

3.6 × 2.1 ≈ 4 × 2 = 8

12. Dividing Decimals by Whole Numbers

4.8 ÷ 6 = 0.8

How do you divide 4.8 ÷ 6?

Write 4.8 as a decimal: 4.8
Think: "How many times does 6 fit into 4.8?"
Divide as you would with whole numbers, then place the decimal:
Ignore the decimal for a moment: 48 ÷ 6 = 8.
Since there is one decimal place in 4.8, the answer is 0.8.

Splitting 4.8 into 6 equal parts gives six "0.8" segments.
4.8 ÷ 6 = 0.8

So, each share is 0.8.
4.8 ÷ 6 = 0.8

13. Dividing Whole Numbers by Decimals

8 ÷ 0.4 = 20

14. Dividing Decimals by Decimals

0.81 ÷ 0.09 = 9

How do you divide 0.81 ÷ 0.09?

Understand what this means:
How many times does 0.09 fit into 0.81?
Move the decimal point in both numbers to make the divisor a whole number:
0.81 ÷ 0.09 becomes 81 ÷ 9 (move decimal two places right for both)
Now, divide:
81 ÷ 9 = 9

There are 9 segments of 0.09 in 0.81.
0.81 ÷ 0.09 = 9

So, 0.81 ÷ 0.09 = 9.
There are 9 groups of 0.09 in 0.81.

15. Dividing Money

$12.00 ÷ 4 = $3.00

16. Estimating Decimal Quotients

9.2 ÷ 2.1 ≈ 9 ÷ 2 = 4.5

17. Understanding Percent

80% means 80 out of 100, or 0.80

18. Percents and Fractions

25% = 25/100 = 1/4

How do you simplify 25/100 to 1/4?

Find the greatest common factor (GCF):
Both 25 and 100 can be divided by 25.
Divide the top and bottom by 25:
25 ÷ 25 = 1
100 ÷ 25 = 4
You get: 1/4

25 out of 100 is the same as 1 out of 4 equal parts.
25/100 = 1/4

So, 25/100 simplifies to 1/4.

19. Percents and Decimals

7% = 0.07

20. Multiplying Percents and Fractions

50% of 3/4 = 0.5 × 0.75 = 0.375

Chapter 4: Pre-Test (40 Questions)

Try to answer all questions before checking the Q & A or Examples chapters.

Chapter 5: Questions and Answers

After you submit your pre-test, step-by-step explanations for only the questions you missed will appear here!

Chapter 6: Post-Test (40 Questions)

Take this post-test after studying the chapters above. Check your answers in the Q & A or Examples chapters if needed.