Unit 5 · Topic 02 · Fractions and Decimals
Kabir cut a pizza into 4 slices and ate 3, calling it 3/4. Anaya cut a bigger pizza into 4 slices and ate all 5 she'd cooked separately, calling it 5/4.
Ms. Rao pointed out that 3/4 and 5/4 aren't the same kind of fraction at all.
One stays neatly under a whole; the other spills over into more than one whole entirely.
"In 3/4," said Ms. Rao, "the top number (numerator) is SMALLER than the bottom number (denominator). This is called a PROPER fraction — it represents less than one whole." She then wrote 5/4. "Here the numerator is BIGGER than the denominator. This is an IMPROPER fraction — it represents more than one whole."
"Can we write 5/4 in a way that shows the whole pizza plus the extra?" asked Anaya. She split it: 5/4 = 4/4 + 1/4 = 1 whole + 1/4 = 1¼. "That's called a MIXED NUMBER — a whole number plus a proper fraction written together."
Ms. Rao then wrote 4/4. "What kind of fraction is this?" Kabir noticed numerator equals denominator. "It equals exactly 1 whole," he said. She also introduced UNIT fractions — fractions with numerator exactly 1, like 1/4 or 1/7 — the basic building block every other fraction is made from multiples of.
"So every fraction fits somewhere," summarised Anaya. "Proper if it's less than a whole, improper if it's more, and any improper fraction can be rewritten as a mixed number to show the whole part separately. Unit fractions are the simplest building blocks of all."
A proper fraction has a numerator smaller than its denominator, representing less than one whole (e.g. 3/4).
An improper fraction has a numerator equal to or bigger than its denominator, representing one whole or more (e.g. 5/4).
A mixed number combines a whole number and a proper fraction, like 1¼, and is another way to write an improper fraction.
A unit fraction has a numerator of exactly 1, like 1/4 or 1/7 — the basic building block of fractions.
Write shaded and unshaded fractions for a circle split into four equal parts.
Convert 7/6 to a mixed number and 2 3/4 to 11/4.
Convert 3 4/7 to 25/7 using multiply-then-add.
Loading questions…