What is a fraction?
FoundationA fraction tells you how many equal parts of a whole you have taken.
- Denominator (bottom) = total equal parts
- Numerator (top) = parts taken
- Parts must be equal
1Summary 重點摘要
A fraction tells you how many equal parts of a whole you have taken.
2Vocabulary cards Vocabulary
The top number: how many parts are taken.
The bottom number: how many equal parts the whole is divided into.
Every part must be the same size.
A fraction with numerator 1, like 14.
The horizontal line in a fraction, e.g. the middle of 38.
The complete object being divided; a whole pizza counts as 1.
A fraction with numerator smaller than denominator, like 38; always less than 1.
Read the denominator first: 38 is read "three eighths".
3Step by step Steps
- Step 1: Divide into equal partsCut a pizza into 8 parts, and the parts must be equal — every piece exactly the same size — before fractions can describe them; uneven pieces will not do. Fair, equal sharing is the starting point of all fractions.
- Step 2: Count for the denominatorThe whole is divided into 8 equal parts, so the denominator (below the line) is 8. The denominator tells how many equal parts the whole was split into; the bigger it is, the finer the parts. Count all the parts first, then write it.
- Step 3: Count for the numeratorYou ate 3 of the parts, so the numerator (above the line) is 3. The numerator tells how many parts were taken, counted from the equal shares; the denominator manages the whole, the numerator the taking, and the two places must not swap.
- Step 4: Write the fractionWrite 3 above and 8 below: 38, read as three eighths. In Chinese you say the denominator first and the numerator second. The fraction line can be seen as the act of dividing, marking out 3 parts from the 8 equal ones.
- Step 5: Compare sizesWith the same denominator, the bigger numerator wins: of 38 and 58, both take parts from the same 8 equal shares, and taking 5 parts is more than taking 3, so 58 > 38. From one whole, more parts taken means more.
- Step 6: Bigger denominator, smaller partsWhich is bigger, 12 or 18? A cake divided into 2 gives far bigger pieces than one divided into 8, so 12 > 18. The bigger the denominator, the smaller each part — this goes against first impressions, so draw pictures to check.
4Diagrams Diagrams
5Worked example Example
Example: a cake is cut into 6 equal parts and younger sister eats 2 of them. What fraction of the cake did she eat, and how much is left?
- The whole is one cake cut into 6 equal parts, so the denominator = 6.
- She ate 2 parts, so the numerator = 2.
- Write the fraction 26, meaning 2 of the 6 equal parts.
- Simplify: dividing the top and bottom of 26 by 2 gives 13, the same amount.
- What is left: 6 − 2 = 4 parts, which is 46 = 23.
- Answer: Sister ate 26 = 13 of the cake, and 46 = 23 is left. We fixed the denominator 6 and the numerator 2 to write 26, then simplified it to 13; the remaining 4 parts are written 46 = 23. Eaten plus left gives 13 + 23 = 1, exactly the whole cake, so the answer is correct.
6Common mistakes Mistakes
7Quick check Quick check
Q1What is the denominator of 59? What does it mean?
Q2A rope is cut into 4 equal parts; you take 1 part. Write the fraction.
Q3Are 38 and 83 the same? Why?
Q4A melon is cut into 10 equal parts and you eat 7. What fraction did you eat, and what fraction is left?
Q5Which is biggest: 12, 14 or 18? Why?
8Recap Recap
- Denominator (bottom) = total equal parts
- Numerator (top) = parts taken
- Parts must be equal
- Read the denominator first: 38 is "three eighths"
- Same denominator: bigger numerator means bigger fraction