Multiply fractions, decimals, and mixed numbers. Grade 9 Alberta mathematics with practice problems.
Lesson 3.4 of Rational Numbers in Grade 9 Math — Alberta curriculum lessons.
To multiply rational numbers, we follow specific sign rules that apply to both integers and decimals.
💡 Quick Rule. What if you have more than two integers? You can use the same sign rules even when multiplying three or more numbers!
Just count the number of negative signs ("−") in the question:
🔢 Counting Negatives.
Example:(−2) × (−3) × 4There are two negatives (even number): result is positive.(−2) × (−3) × 4 = +24
💡 Pro Tip. Multiply two integers at a time and keep track of the signs as you go. This makes complex expressions much easier to handle!
Step 1. Ignore the decimal points. Multiply the numbers as if they were whole numbers.Step 2. Multiply normally. Perform the standard multiplication.Step 3. Count the decimal places. Count the total number of decimal places in both numbers combined.Step 4. Place the decimal point. Starting from the right of your answer, move the decimal point to the left by the total number of decimal places you counted.
We follow the same rules as for integers when multiplying fractions — but with a few key fraction steps:. 1. No need for a common denominator.2. Multiply the numerators (top numbers).3. Multiply the denominators (bottom numbers).4. Simplify or reduce the answer to lowest terms if possible.
💡 Pro Tip. You can simplify before multiplying to make calculations easier. This technique is called cross-reduction and can save you lots of time!
📝 Key Points to Remember.
Sign Rules:(+)(+) = +(−)(−) = +(+)(−) = −
Let's multiply:(−3) × 4We're multiplying a negative by a positive.Step 1: 3 × 4 = 12Step 2: Since the signs are different, the answer is negative.✅ Answer: −12
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