Fractions (I): Introduction
FoundationSplit a cake into 4, each is 14.
- A fraction shows parts of an equally divided whole
- Numerator on top (parts taken), denominator below (total parts)
- 12 reads one half, 14 reads one quarter
1Summary 重點摘要
Split a cake into 4, each is 14.
2Vocabulary cards Vocabulary
A number showing parts of an equally divided whole, e.g. 14.
The top number of a fraction; it tells how many parts are taken.
The bottom number of a fraction; it tells how many equal parts the whole has.
The complete object before cutting, e.g. a whole apple.
Parts of the same size; fractions only work with equal sharing.
One part out of 2 equal parts.
One part out of 4 equal parts.
Say the denominator first: 34 reads three quarters.
3Step by step Steps
- Part 1: Fractions start with equal sharingFractions start with equal sharing. Cut a pizza into 4 equal pieces, and each piece is one quarter, written 14. If the pieces are big and small, you cannot call each one 14, because every part of a fraction must be the same size.
- Part 2: Denominator below, numerator aboveIn 14, the bottom 4 is the denominator and tells us the whole is cut into 4 equal parts; the top 1 is the numerator and tells us we take 1 part. The denominator always goes below and the numerator always goes above.
- Part 3: How to read fractionsFractions are read in a fixed way: 12 is read as one half, 14 as one quarter, and 34 as three quarters. Say the denominator first, then the numerator, so 34 is read as three quarters.
- Part 4: Compare only within the same wholeA fraction only makes sense within the same whole. Half of a big pizza and half of a small pizza are both called 12, but the big pizza's half is really more. Before comparing fractions, check whether they belong to the same whole.
- Part 5: Bigger denominator, smaller pieceThe more pieces the whole is cut into, the smaller each piece is. Cut the same cake into 2 parts and each is 12, bigger than the 14 from 4 parts, which is bigger than the 18 from 8 parts. A bigger denominator means a smaller part.
- Part 6: Putting parts together34 means three 14s. Cut a cake into 4 parts and eat 3 of them: you have eaten 34 and 14 is left. Putting all four quarters together makes the whole cake again, that is 44 = 1.
4Diagrams Diagrams
5Worked example Example
Example: a chocolate bar has 8 equal squares. Ming eats 3 of them. What fraction did he eat, and what fraction is left?
- The whole bar is cut into 8 equal squares, so the denominator is 8.
- Ming ate 3 squares, so the numerator is 3: he ate 38 of the bar.
- There are 8 − 3 = 5 squares left, so 58 of the bar remains.
- Check: 38 plus 58 makes 88, which is exactly the whole bar.
- Answer: Answer: Ming ate 38 and 58 is left. The denominator shows how many equal parts the whole has, the numerator shows how many were eaten, and the eaten part plus the remaining part makes the whole, which is 1.
6Common mistakes Mistakes
7Quick check Quick check
Q1A cake is cut into 4 equal pieces. What is each piece?
Q2How do you read 12?
Q3In 38, which number is the denominator?
Q4Which piece is bigger: 12 or 16?
Q5A 10-square chocolate bar: you eat 7 squares. What fraction is eaten?
8Recap Recap
- A fraction shows parts of an equally divided whole
- Numerator on top (parts taken), denominator below (total parts)
- 12 reads one half, 14 reads one quarter
- Bigger denominator, smaller piece: 18 < 14 < 12
- Sharing must be equal before writing fractions