Adding Decimals for 5th Grade: Align, Add, and Check

Adding decimals is a fundamental skill used in money, measurements, and everyday math. In Grade 5, students add decimals to hundredths or thousandths by aligning decimal points and adding place by place, with regrouping when needed. The key is to align decimal points so that tenths are added to tenths, hundredths to hundredths, and so on. This skill helps students add prices, combine lengths, sum weights, and solve real-world problems involving decimal quantities.

When we add decimals, we use the same place-value logic as whole numbers: we add ones to ones, tenths to tenths, and hundredths to hundredths. The decimal point in the sum goes directly below the decimal points in the addends. If the addends have different numbers of decimal places, we can append zeros to the right of the shorter decimal (e.g., 12.6 = 12.60) without changing its value, so that we can add place by place easily.

DETAILED EXPLANATION

Steps to add decimals:

1. Write the numbers vertically with decimal points aligned. Use additional zeros on the right if needed so that all addends have the same number of decimal places.

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2. Add from right to left, place by place (hundredths, tenths, ones, tens, etc.). Regroup (carry) when a sum is 10 or more.

3. Place the decimal point in the sum directly below the decimal points in the addends.

4. Check the answer by estimating or adding in a different order.

Example: 2.35 + 1.48. Align: 2.35 + 1.48. Add: 5+8=13 (write 3, carry 1); 3+4+1=8; 2+1=3. Sum: 3.83.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

Anna bought apples for $2.35 and oranges for $1.48. How much did she spend in total?

Solutions:

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Step 1: We need to add 2.35 and 1.48. Write vertically with decimal points aligned:

2.35

+ 1.48

Step 2: Add from right to left. Hundredths: 5 + 8 = 13. Write 3, carry 1 to tenths.

Step 3: Tenths: 3 + 4 + 1 = 8. Write 8.

Step 4: Ones: 2 + 1 = 3. Write 3.

Step 5: Place the decimal point in the sum directly below the decimal points in the addends. Sum: 3.83.

Step 6: Anna spent $3.83 in total.

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Answer: $3.83

Example 2

Add 12.6 + 3.45

Solutions:

Step 1: Write 12.6 as 12.60 so both numbers have two decimal places. Align:

12.60

+ 3.45

Step 2: Add from right. Hundredths: 0 + 5 = 5. Tenths: 6 + 4 = 10. Write 0, carry 1 to ones.

Step 3: Ones: 2 + 3 + 1 = 6. Tens: 1 + 0 = 1.

Step 4: Place decimal point. Sum: 16.05.

Answer: 16.05

Example 3

Three lengths are 4.7 m, 2.35 m, and 1.08 m. Find the total length.

Solutions:

Step 1: Add 4.7 + 2.35 + 1.08. Write all with two decimal places: 4.70, 2.35, 1.08. Align:

4.70

2.35

+ 1.08

Step 2: Hundredths: 0 + 5 + 8 = 13. Write 3, carry 1.

Step 3: Tenths: 7 + 3 + 0 + 1 = 11. Write 1, carry 1.

Step 4: Ones: 4 + 2 + 1 + 1 = 8.

Step 5: Decimal point in sum. Total: 8.13 meters.

Answer: 8.13 meters

Example 4

Add 0.456 + 0.78 + 0.3

Solutions:

Step 1: Write all with three decimal places: 0.456, 0.780, 0.300. Align:

0.456

0.780

+ 0.300

Step 2: Thousandths: 6 + 0 + 0 = 6. Hundredths: 5 + 8 + 0 = 13. Write 3, carry 1.

Step 3: Tenths: 4 + 7 + 3 + 1 = 15. Write 5, carry 1. Ones: 0 + 0 + 0 + 1 = 1.

Step 4: Sum: 1.536.

Answer: 1.536