Basic Math Test- Decimal Operations and Practice Questions

What Are Decimal Operations?

Decimals are just fractions in disguise. That .75 on your receipt? It's 75/100. That $4.99 price tag? It's 4 and 99 hundredths. Once you see decimals this way, operations become way less intimidating.

This guide covers the four basic operations: addition, subtraction, multiplication, and division. No fluff. Just the rules and practice questions to lock them in.

Adding and Subtracting Decimals

Here's the one rule that matters: line up the decimal points. Everything else follows from that.

The Alignment Method

Write your numbers vertically. Make sure the decimals sit in the same column. Then pad with zeros if one number has fewer decimal places. Add or subtract as usual.

Example: 12.34 + 5.6

  12.34
+  5.60   ← padded with zero
--------
  17.94

Example: 20 - 7.458

  20.000   ← padded with zeros
-  7.458
--------
  12.542

That's it. Line them up. Add or subtract. Don't let trailing zeros trip you up.

Common Mistakes

Multiplying Decimals

Multiplication is different. You don't line up decimal points. Instead, you count decimal places.

Step-by-Step Process

Step 1: Multiply the numbers as if they were whole numbers. Ignore the decimals completely.

Step 2: Count the total decimal places in BOTH original numbers.

Step 3: Starting from the right of your product, move the decimal that many places.

Example: 3.4 × 2.7

Step 1: 34 × 27 = 918
Step 2: 3.4 has 1 decimal place, 2.7 has 1 decimal place = 2 total
Step 3: 918 → 9.18
Answer: 9.18

Example: 0.25 × 0.4

Step 1: 25 × 4 = 100
Step 2: 0.25 has 2 decimal places, 0.4 has 1 = 3 total
Step 3: 100 → 0.100 → 0.1
Answer: 0.1

When you need to add leading zeros to reach the decimal place, include them. 0.1 and 0.100 are the same value, but proper placement matters.

Dividing Decimals

Dividing decimals has two scenarios: dividing by a whole number, or dividing by a decimal.

Dividing a Decimal by a Whole Number

Easier than you think. Bring down the decimal point directly above into your answer, then divide normally.

Example: 156.8 ÷ 4

    39.2
4 ) 156.8
    12 ↓
    36
    28
    28
     0
Answer: 39.2

Dividing by a Decimal: The Trick

Convert the divisor into a whole number. Multiply both numbers by the same power of 10. Then divide normally.

Example: 14.4 ÷ 1.2

Multiply both by 10: 144 ÷ 12
Divide: 144 ÷ 12 = 12
Answer: 12

Example: 7.5 ÷ 0.25

Multiply both by 100: 750 ÷ 25
Divide: 750 ÷ 25 = 30
Answer: 30

The key insight: multiplying both numbers by the same amount doesn't change the answer. It just makes the math easier.

Decimal Operations Reference Table

Operation Key Rule Common Error
Addition Align decimal points, pad with zeros Misaligned columns
Subtraction Align decimal points, pad with zeros Forgetting to borrow
Multiplication Count total decimal places, then place in answer Counting decimal places wrong
Division Convert divisor to whole number first Forgetting to multiply dividend

Practice Questions: Decimal Operations

Work through these. No calculator until you've tried by hand.

Addition & Subtraction

  1. 8.5 + 3.27 = ?
  2. 15.6 - 7.83 = ?
  3. 100 - 0.99 = ?
  4. 4.008 + 12.4 + 7 = ?
  5. 56.3 - 21.75 = ?

Multiplication

  1. 4.2 × 3 = ?
  2. 0.5 × 0.8 = ?
  3. 1.25 × 0.4 = ?
  4. 6 × 0.03 = ?
  5. 2.5 × 2.5 = ?

Division

  1. 15.5 ÷ 5 = ?
  2. 8 ÷ 0.4 = ?
  3. 3.6 ÷ 0.6 = ?
  4. 12.5 ÷ 2.5 = ?
  5. 0.72 ÷ 0.08 = ?

Answer Key

Compare your answers. If you got any wrong, figure out where your process broke down.

Addition & Subtraction Answers

  1. 11.77
  2. 7.77
  3. 99.01
  4. 23.408
  5. 34.55

Multiplication Answers

  1. 12.6
  2. 0.4
  3. 0.5
  4. 0.18
  5. 6.25

Division Answers

  1. 3.1
  2. 20
  3. 6
  4. 5
  5. 9

Getting Started: Your Decimal Action Plan

If decimals still feel shaky, here's what to do:

Speed comes after accuracy. You can always get faster. But if you build sloppy habits now, you'll fight them forever.

Quick Rules Summary

Print this. Tape it somewhere. Refer back until it's automatic.