The Number System
GradesGrade 7The Number SystemOperations with Rational Numbers

Operations with Rational Numbers

🔢 The Number System
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Operations with Rational Numbers

Add, subtract, multiply, and divide positive and negative rational numbers with confidence.

Rational numbers include all integers, fractions, and terminating or repeating decimals. Operations follow the same rules as with positive numbers, but you must track the sign carefully.

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Same signs → positive product/quotient. Different signs → negative product/quotient.

(−3)×(−4)=+12(−3)×4=−12(-3) \times (-4) = +12 \qquad (-3) \times 4 = -12
❄️Adding integers with a number line
The temperature is −8°F. It drops another 5°F.

−8 + (−5) = −13°F

Both numbers are negative, so we add their absolute values and keep the negative sign.
−34÷12=−34×21=−64=−32\frac{-3}{4} \div \frac{1}{2} = \frac{-3}{4} \times \frac{2}{1} = \frac{-6}{4} = -\frac{3}{2}

Sign rules summary:

1Adding same signs: add absolute values, keep the sign
2Adding different signs: subtract absolute values, keep the sign of the larger
3Subtracting: rewrite as adding the opposite (a − b = a + (−b))
4Multiplying/Dividing: same signs → positive; different signs → negative
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Remember This!

Subtraction is just adding the opposite. Instead of 3 − (−7), think 3 + 7 = 10. "Minus a negative" always becomes addition.

✏️ Try It!

What is −2/3 + 1/4?

Practice with CalcVerse
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