Integers, Fractions, Decimals & PEMDAS
Core arithmetic rules for signs, fractions, decimals, and order of operations that every algebra problem depends on.
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Questions Covered in This Set
12 cards to master
What are integers?
The whole numbers plus their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ... (no fractions or decimals).
Rule for adding two numbers with the SAME sign
Add the sizes and keep the sign. Example: -7 + (-5) = -12.
Rule for adding numbers with DIFFERENT signs
Subtract the smaller size from the larger, and keep the sign of the bigger number. Example: -9 + 4 = -5.
How do you handle subtracting a negative, like 6 - (-3)?
Subtracting is adding the opposite, so 6 - (-3) = 6 + 3 = 9. Two minus signs in a row make a plus.
Sign rules for multiplying and dividing
Same signs give a positive; different signs give a negative. An even number of negative factors → positive; odd → negative.
Why is -3² different from (-3)²?
In -3² the exponent applies only to the 3, giving -(3·3) = -9. In (-3)² the negative is inside the parentheses, giving (-3)(-3) = 9.
How do you divide fractions?
Flip the second fraction and multiply. (2/3) ÷ (4/5) = (2/3)(5/4) = 10/12 = 5/6.
What must you do before adding or subtracting fractions?
Find a common denominator. 2/3 + 1/4 → 8/12 + 3/12 = 11/12. Never add denominators.
What does PEMDAS stand for, with the asterisk?
Parentheses, Exponents, Multiplication/Division (left to right as equals), Addition/Subtraction (left to right as equals). MD and AS do not outrank each other.
Evaluate 12 ÷ 3 × 2
8. Work left to right: 12 ÷ 3 = 4, then 4 × 2 = 8 (not 12 ÷ 6 = 2).
How do you count decimal places when multiplying decimals?
Add the total decimal places in the factors. 0.3 × 0.04 = 0.012 (1 place + 2 places = 3 places).
Evaluate 8 + 2(5 - 3)² ÷ 4
10. Parentheses: 2; exponent: 4; then 2×4 = 8 and 8 ÷ 4 = 2; finally 8 + 2 = 10.
