Decimal Operations

Grade 4 · Math · Study Guide

Learn how to add, subtract, and understand decimals using place value.

A decimal is a way of writing numbers that are between whole numbers. The decimal point separates the whole number part from the fractional part. The first place after the decimal point is the tenths place, and the second place is the hundredths place. So 3.47 means 3 ones, 4 tenths, and 7 hundredths.

To add or subtract decimals, the most important rule is to line up the decimal points. When decimal points are aligned, all place values line up correctly. Then add or subtract as you would with whole numbers. For example, 2.6 + 1.38 becomes 2.60 + 1.38 = 3.98. Adding a zero at the end of 2.6 does not change its value but helps line up the columns.

To compare decimals, look at each place value from left to right. The digit in the tenths place is worth more than the digit in the hundredths place. For example, 0.7 is greater than 0.65 because 7 tenths (0.70) is more than 6 tenths and 5 hundredths (0.65).

Decimals connect to fractions: 0.1 = 1/10, 0.01 = 1/100, and 0.25 = 25/100 = 1/4. Understanding this connection helps with estimation and real-life problems like money and measurement.

Key terms

Decimal: A number that uses a decimal point to show values less than one whole.
Decimal point: The dot that separates the whole number part from the fractional part of a decimal.
Tenths: The first place value to the right of the decimal point; 0.1 = one tenth.
Hundredths: The second place value to the right of the decimal point; 0.01 = one hundredth.
Equivalent decimals: Decimals that have the same value; 0.5 and 0.50 are equivalent.
Align decimal points: Lining up decimal points when adding or subtracting so that place values match correctly.

Flashcards

Place value chart for decimals: Ones . Tenths . Hundredths; e.g., 5.63 = 5 ones, 6 tenths, 3 hundredths
Adding decimals rule: Line up the decimal points, add zeros if needed to make lengths equal, then add normally
0.5 = ?: 5/10 = 1/2; five tenths; the decimal halfway between 0 and 1
0.25 = ?: 25/100 = 1/4; twenty-five hundredths; one quarter
Compare 0.4 and 0.40: They are equal — adding a trailing zero after a decimal does not change its value
Compare 0.6 and 0.59: 0.6 > 0.59 because 0.6 = 0.60 and 60 hundredths > 59 hundredths
2.5 + 1.7: 4.2 — add tenths: 5 + 7 = 12, write 2 carry 1; add ones: 2 + 1 + 1 = 4
Decimal and money connection: $3.47 = 3 dollars + 4 dimes + 7 pennies; money is a real-life decimal model

Questions

What is 1.4 + 2.35?
1. 3.39
2. 3.75
3. 3.79
4. 4.75
Show answer
Answer: 3.75
1.4 + 2.35: write as 1.40 + 2.35. Add hundredths: 0 + 5 = 5. Add tenths: 4 + 3 = 7. Add ones: 1 + 2 = 3. Answer: 3.75.
When adding 3.2 and 4.75, you should line up the decimal points before adding.
Show answer
Answer: True
Lining up decimal points ensures that tenths align with tenths and hundredths align with hundredths, making the addition correct.
The digit 6 in the number 5.67 is in the _____ place.
Show answer
Answer: tenths
In 5.67, the first digit after the decimal point is 6, which is in the tenths place. The 7 is in the hundredths place.
Which decimal is greater: 0.8 or 0.75?
1. 0.75 because it has more digits
2. 0.8 because 8 tenths > 7 tenths
3. They are equal
4. Cannot be determined
Show answer
Answer: 0.8 because 8 tenths > 7 tenths
0.8 = 0.80 = 80 hundredths. 0.75 = 75 hundredths. Since 80 > 75, 0.8 is greater. More digits does not mean a larger value.
4.50 − 1.30 = _____
Show answer
Answer: 3.20
4.50 − 1.30: Subtract hundredths: 0 − 0 = 0. Subtract tenths: 5 − 3 = 2. Subtract ones: 4 − 1 = 3. Answer: 3.20.

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