Operations with Rational Numbers Flashcards
Grade 7 · Math · Flashcards
Key rules and vocabulary for working with rational numbers including integers, fractions, and decimals.
Flashcards
- Rational number
- Any number that can be written as a fraction p/q where p and q are integers and q ≠ 0; includes integers, fractions, and repeating/terminating decimals
- Adding same-sign integers
- Add the absolute values and keep the common sign. Example: (-4) + (-3) = -7
- Adding different-sign integers
- Subtract the smaller absolute value from the larger; use the sign of the number with the greater absolute value
- Subtracting integers
- Change subtraction to adding the opposite: a - b = a + (-b). Example: 5 - (-3) = 5 + 3 = 8
- Multiplying/dividing: same signs
- The result is POSITIVE. Example: (-6) × (-3) = +18
- Multiplying/dividing: different signs
- The result is NEGATIVE. Example: (-6) × 3 = -18
- Adding fractions
- Find the least common denominator (LCD), convert each fraction, then add numerators. Keep the denominator.
- Subtracting fractions
- Find the LCD, convert, then subtract numerators. Be careful with negative results.
- Multiplying fractions
- Multiply numerator × numerator and denominator × denominator. Simplify if possible.
- Dividing fractions (Keep-Change-Flip)
- Keep the first fraction, Change ÷ to ×, Flip the second fraction. Then multiply.
- Absolute value
- The distance from zero; always positive. |-7| = 7 and |7| = 7
- Reciprocal
- The flipped version of a fraction. Reciprocal of 2/5 is 5/2. The product of a number and its reciprocal is always 1.
- Converting mixed number to improper fraction
- (Whole × Denominator + Numerator) / Denominator. Example: 3 1/2 = (3×2+1)/2 = 7/2
- Least Common Denominator (LCD)
- The smallest number that is a multiple of all denominators in a problem; used to add or subtract fractions
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