1/2, 0.5, and 50%all mean exactly the same amount — half of something. A fraction shows a part out of a whole. A decimal shows the same value using place value past the decimal point. A percentage shows the same value out of 100. They’re translations of one idea, not three separate ideas to memorize.
Converting between them, one direction at a time
Fraction to decimal: divide the top number by the bottom number. 3/4 means 3 ÷ 4 = 0.75. Decimal to percentage: multiply by 100 (or just slide the decimal point two places right). 0.75 becomes 75%. Percentage to fraction: write it over 100 and simplify. 75% is 75/100, which simplifies to 3/4. Every conversion is really just one of these three moves.
Let me show you one
A shirt is 3/5 of the way to being paid off. What percentage is that? Divide: 3 ÷ 5 = 0.6. Multiply by 100: 60%. Same value, written three ways, and each version is useful in a different situation — fractions for exact parts, decimals for calculations, percentages for comparing.
Why a common denominator matters
You can’t add 1/3 + 1/4 directly because thirds and fourths are different-sized pieces — like trying to add 1 apple + 1 orange and calling it 2 of something. Rewriting both with a common denominator (twelfths: 4/12 + 3/12 = 7/12) makes the pieces the same size first, so adding them actually means something.
The mistake I see most
Adding or subtracting fractions by combining numerators and denominators straight across without a common denominator first. The fix is always the same question before any addition or subtraction: are these pieces the same size yet? If not, find a common denominator before doing anything else.
Want to work through it together?
If fractions still feel like the moment math “got hard,” that’s an extremely common turning point — and one that usually unlocks fast once the part-of-a-whole picture is solid underneath the procedures.
