The Big Three: Fractions, Decimals, and Percentages

Here is a quick puzzle. Three friends each ate part of an identical pizza. Aiko ate 3/4 of her pizza. Ben ate 0.7 of his. Cara ate 72% of hers. Who ate the most? Don't calculate yet — just make a guess and hold it in your head. By the end of this lesson you will know exactly how to check who was right.

A fraction, a decimal, and a percentage are three different ways to write the same thing: a part of a whole. A fraction like 3/4 has two parts. The bottom number — called the denominator — tells you how many equal parts the whole is split into. The top number — called the numerator — tells you how many of those parts you have. So 3/4 means 'three out of four equal parts'. A decimal is a way of writing a fraction using the base-10 number system. The digits after the decimal point represent tenths, hundredths, thousandths, and so on. For example, 0.75 means 7 tenths and 5 hundredths, which is the same as 75/100. A percentage (the % symbol is short for 'per cent', meaning 'out of 100') always compares something to 100. So 75% means '75 out of 100'. Because 3/4, 0.75, and 75% all describe exactly the same portion, they are equivalent — equal in value. Here is the key conversion chain you need: 1. Fraction → Decimal: Divide the numerator by the denominator. Example: 3 ÷ 4 = 0.75 2. Decimal → Percentage: Multiply by 100 (move the decimal point two places to the right). Example: 0.75 × 100 = 75% 3. Percentage → Decimal: Divide by 100 (move the decimal point two places to the left). Example: 75 ÷ 100 = 0.75 4. Decimal → Fraction: Write the decimal as a fraction over the correct power of 10, then simplify. Example: 0.75 = 75/100 = 3/4 (dividing top and bottom by 25). The safest way to compare or order a mixed set is to convert everything into decimals — then comparing is straightforward.