Fractions and Decimals in 3 Minutes

Transcript

Fractions and decimals are two costumes for the same number. Three-fourths and zero point seven five are the exact same amount wearing different outfits — and once you can switch between the costumes, comparing and calculating gets much easier.

First, converting a fraction to a decimal. A fraction bar is really a division sign. Three-fourths means three divided by four, which is zero point seven five. One-half is one divided by two, which is zero point five. Some fractions repeat forever — one-third becomes zero point three three three, repeating — and that's fine; it's still the same number.

Second, converting a decimal to a fraction. Read the decimal out loud and it tells you its own fraction. Zero point six is six tenths, so write six over ten. Then simplify: six and ten are both divisible by two, so six tenths reduces to three-fifths. Simplifying means dividing the top and bottom by the same number until nothing divides both — eight-twelfths reduces to two-thirds because four goes into both eight and twelve.

Third, comparing fractions and decimals. The trick is to put both numbers in the same costume. Which is larger, five-eighths or zero point six? Convert five-eighths: five divided by eight is zero point six two five. Now compare zero point six two five with zero point six zero zero — five-eighths wins. Never compare a fraction and a decimal by eyeballing them; convert first.

Fourth, adding and subtracting fractions. If the denominators match, add the tops and keep the bottom: two-sevenths plus three-sevenths is five-sevenths. If they don't match, find a common denominator first. Take one-third plus one-sixth. Sixths work for both: one-third is the same as two-sixths, so two-sixths plus one-sixth is three-sixths, which simplifies to one-half.

Now the mistake that traps almost everyone: adding denominators. One-third plus one-sixth is not two-ninths. The denominator names the size of the pieces — you can only add pieces that are the same size, which is the whole reason common denominators exist.

Quick recap. A fraction is a division problem, so divide to get its decimal; read a decimal aloud to find its fraction, then simplify. Convert to the same form before comparing, and always find a common denominator before adding — never add the bottoms. Ready? The practice quiz is waiting.