LF-P5-S1-L07 Comparison of fractions with different denominators + addition + subtraction

Lam Fung Academy· LF Academy

Primary 5 · 7th Lesson · Student Handout

Fractions with Different Denominators: Comparison, Addition and Subtraction

Unit 3 · Fraction operation · 65 minutes · 1-to-3 Online Lesson

Corresponding textbooks:"New Thinking in Primary School Mathematics (Second Edition)" Volume 5A, Unit 3 + Modern Education 5A, Unit 10
Core Traps:🪤 T9 Fraction Operations - LCM Error Finding · The numerator forgets to expand simultaneously after the common division · The result is not reduced
SSPA Association:🔴 High frequencyThe score test is required every year, accounting for about 15-20% of Paper 1
Prerequisite knowledge:P4 Addition and subtraction of fractions with the same denominator · LCM calculation · Equivalent fractions and extended fractions
Course goal:❶ Comparison of fractions with different denominators (common fraction → ratio) ❷ Addition of different denominators (three-step method for common denominators) ❸ Subtraction of different denominators ❹ Mixed application of addition and subtraction of fractions
Next class connection:Class 8 (In-depth practice of adding fractions with different denominators) - This class lays a solid foundation for comparison and basic addition and subtraction

Student Name: Class: Date: Time Spent:

I.Warm-Up Questions（total 5 question，5 minutes）

🍕 分數大作戰

通分、約分、四則混合！避開分母陷阱。連續答對分數翻倍！

⚡ 開始挑戰 →

#	Question	Difficulty
1	Calculate LCM(4, 6) = ?	Basic
2	Calculate LCM(3, 5) = ?	Basic
3	Compare23and35which one is bigger? Write down the judgment process.	Advanced
4	Calculate37 + 27= ? (Adding with the same denominator, P4 basics)	Basic
5	Calculate59 − 29= ? (Subtraction with the same denominator, P4 basic)	Basic

II.Core Knowledge ＋ Worked Examples

Knowledge point 1: Comparison of fractions with different denominators - the ratio of the common denominator🔴 SSPA

① Different denominators = different sizes of each part, the numerators cannot be directly compared
② Three-step comparison method:Find LCM → common denominator (expand the denominator to the same denominator) → compare the sizes of the molecules
③ After the common denominator, the fraction with a larger molecule is larger; the fraction with a smaller molecule is smaller
④ Comparison of three or more fractions: all common denominators to the same denominator (LCM of all) denominators), and then arrange the molecules
⑤ Trap T9:LCM error finding → The basics of general division are wrong → The whole question is wrong!

Example 1

Comparing34and56, which one is larger? Write down the general process.

Example 2 (Ordering three fractions)

Arrange23、34、56from largest to smallest.

⚠️ The most frequent error: compare the numerators directly without common denominators! Different denominators → different sizes of each portion → the numerators cannot be directly compared!

Knowledge Point 2: Addition of Fractions with Different Denominators - Three-Step Method for Common Fractions 🔴 SSPA Required Exam

① Why can't you add it directly?The denominator represents the serving size. Different denominators = different sizes of parts, you cannot add the numerator directly
② Three steps:Find LCM (least common multiple of the denominator) → Expand the fraction (the numerator is expanded simultaneously) → The denominator remains unchanged and the numerators are added
③ The answer must beReduction(the simplest fraction); improper fraction must beConvert mixed fractions
④ Trap T9:When converting fractions, only change the denominator and forget to expand the numerator simultaneously!

①

Find LCM

Find the lowest common multiple using short division

②

General/expanded

The numerator and denominator change simultaneously to LCM

③

calculate

Adding numerators with the denominator unchanged

④

reduce

Simplest false fraction→mixed fraction

🪤 Example of trap detonation (the most important demonstration in this class)

calculate:12 + 13 = ？

❌ Common mistakes (80% students)

Direct numerator plus numerator, denominator plus denominator

✅ Correct solution

LCM(2,3)=6 → 36 + 26 = 56

Example 3

Calculation:23 + 34= ? (Write down the four steps of ①LCM ②general split ③calculation ④reduction)

🧠 Tip: "First understand the LCM, then multiply the numerator and keep the denominator unchanged. The answer must be simplified."

⚠️ The second most frequent error: only changing the denominator when dividing the whole number, forgetting to expand the numerator simultaneously. "The molecules follow and ride"!

⚠️ The third most frequent error: the answer is not reduced. For example, 612 must be written as 12! One point will be deducted if the test is not simplified.

Knowledge point 3: Subtraction of fractions with different denominators - exactly the same steps as addition 🔴 SSPA required test

① Subtraction and addition useexactly the same general division steps- the only difference: the last step is "numerator subtraction" instead of "numerator addition"
② Notes on subtraction:Make sure that the numerator of the minuend ≧ the numerator of the minuend (after common division). If it is not enough → Borrowing is required (with fractions)
③ The answer also requiresReductionto the simplest fraction

🪤 Trap example (subtraction)

calculate:56 − 14 = ？

❌ Common mistakes

42 = 2

Direct numerator minus numerator, denominator minus denominator

✅ Correct solution

712

LCM(6,4)=12 → 1012 − 312 = 712

Example 4

calculate:78 − 23 = ？

Knowledge point 4: Mixed addition and subtraction of fractions + application questions 🔴 SSPA must take the exam

① Mixed addition and subtraction:First divide all to the same denominator (LCM of all denominators), then calculate the numerator by +-, and finally reduce
② Four steps to solve the application problem:Circle the key words → Column formula (use + or − for judgment) → Calculate the common denominator → Write a complete answer
③ Keywords: "Total" "Total" = Addition; "remaining" and "difference" = subtraction; "more than..." → Find the number first and then add

Example 5

Calculation:34 + 16 − 13= ? (mixing of addition and subtraction of three fractions)

Example 6 (example of application questions)

A bottle of juice contains34liters. Xiao Ming drank13liters, and his mother poured in12liters. How many liters of juice are there in the bottle now? (Answer with mixed fractions)

III. Lesson Layered Synchronization Practice

Basic layer (total 6 questions, everyone must do)

#	Question	Difficulty
7	Comparing12and25, which one is larger? (Write down the process of passing grades)	🌱
8	calculate:13 + 16 = ？	🌱
9	calculate:14 + 12 = ？	🌱
10	calculate:35 − 110 = ？	🌱
11	calculate:23 − 16 = ？	🌱
12	Comparing38and512, which one is larger? (LCM = 24)	🌿

Advanced layer (total 5 questions, 🚶🚀 choose do)

#	Question	Difficulty
13	calculate:25 + 310 = ？	🌿
14	calculate:34 − 16 = ？	🌿
15	calculate:56 − 13 = ？	🌿
16	Comparing47and59, which one is larger? (Pass score required, LCM = 63)	🌿
17	Calculation:12 + 13 − 16= ? (mix of addition and subtraction)	🌿

🌳 challenge layer (total 5 questions, 🚀 choose do, SSPAKiller Questions)

#	Question	Difficulty
18	Sorting the three scores: Arrange56、34、712from large to small.	🌳
19	Calculation:23 + 14 + 16= ? (Adding three fractions, LCM = 12)	🌳
20	Calculation:78 − 16 − 14= ? (Subtraction of three fractions)	🌳
21	Xiao Ming originally had34cakes, ate13cakes, and bought12cakes. How many cakes are there now?	🌳
22	Among the three fractions \|\|\|SEP\|\|\|, what is the difference between the largest and the smallest?23、512、12, what is the difference between the maximum and minimum?	🌳

IV.applicationquestionpractice (text questionspecial topic, SSPAMust-Test)

Application problem solving strategies 🔴 SSPA

① Circle keywords:"total" "total" → addition; "remaining" "difference" "less than" → subtraction
② Column formula:Use fraction symbols to write the complete formula
③ Common fraction calculation:Find LCM → Expand → Add and subtract molecules → Reduction
④ Write an answer sentence:"Answer:... (Unit)" - Step points will be deducted for not writing an answer sentence!

applicationquestion (total 6 questions, all must do, column → find a common denominator → calculate → answer sentence)

#	Question	Difficulty
23	Xiao Mei drank14liters of orange juice, and Xiao Ming drank12liters. How many liters did they drink in total?	🌿
24	A box of chocolate, my sister ate25boxes, my brother ate13boxes. How many boxes did the two of them eat in total?	🌿
25	A rope is56meters long, cut off14meters. How many meters are left?	🌿
26	The original water bottle contains34liters, then pour13liters into it. How many liters are there now? (Answer with mixed fractions)	🌳
27	The cake shop sold25cakes in the morning and13cakes in the afternoon. How many were sold in total throughout the day?	🌿
28	A bottle of juice contains78liters. Xiao Ming drank14liters and Xiaohua drank13liters. How many liters are left? (subtract twice)	🌳

V.🏔️ Ultimate challenge area (total 3 questions, 🚀 choose do, SSPA finale level)

#	Question	Difficulty
🏔️1	Calculation:12 + 13 + 14 + 16= ? (Adding four fractions with different denominators - find LCM(2,3,4,6))	🏔️
🏔️2	Compare the equation A =34 + 16with the equation B = \|\|\|SEP\|\|\|. Which result is greater? How much difference?23 + 14. Which result is greater? How much difference?	🏔️
🏔️3	A rope is 2 meters long.13was used on the first day, and the remaining12was used on the second day. How many meters are left? (Hint: Remaining after the first day = 2 −23 = 43meters; used the remaining on the second day12 = 43 × 12）	🏔️

VI.Class afterhomework

Basic must-do questions (total 5 questions, must write find a common denominator step)

#	Question	Difficulty
H1	Comparing23and34, which one is larger? Write down the general process.	🌱
H2	calculate:12 + 16 = ？	🌱
H3	calculate:13 + 19 = ？	🌱
H4	calculate:34 − 12 = ？	🌱
H5	calculate:56 − 13 = ？	🌱

Advanced choose doquestion (total 3 questions, 🚀 choose do)

#	Question	Difficulty
H6	calculate:23 + 14 = ？	🌿
H7	One cake, Xiao Ming ate14pieces, and Xiaohua ate13pieces. How many cakes did the two of them eat together?	🌿
H8	There are56liters in a bucket of water, and14liters are used. How many liters are left?	🌿

VII. The Lessoncorecommon errorsummary

✅ Self-examination in this hall (tick after completion)

☐ I know the pitfalls of solving each knowledge point ☐ I can complete 🌱basic questions independently ☐ I can challenge 🌿advanced questions ☐ I remember the formula

🎯 Review of Learning Objectives - After completing this lesson you should be able to:

☐ Identify all trap types in our hall ☐ Solve 🌱basic questions independently (100% correct) ☐ Challenge🌿Advanced questions (80%+ correct) ☐ Explain the lesson formula to classmates

#	common error	Correct Approach
1	Direct addition and subtraction with different denominators：12+13=25	Different denominators → Be sure to connect the denominators first! Find LCM → Expand → Calculate again
2	After splitting, the molecules forget to expand simultaneously.	"Multiply the numerator" - multiply the denominator by the same number and multiply the numerator by the same number
3	The answer is not reduced：612when the answer	The last step must be to check the common factors and convert them into the simplest fraction
4	Improper fractions are not converted to mixed fractions	Numerator > Denominator → Convert into mixed numbers (subject to the requirements of the division test)
5	LCM error finding(replace LCM with larger common multiple)	Short division confirmed to be the true "least" common multiple
6	When comparing, only look at the numerator and not the denominator	Different denominators → Different sizes of parts → Comparison must be made only after dividing the parts
7	Missing sentences/units in application questions	You must write "Answer:..." + unit (liter, meter, unit), otherwise step points will be deducted

Lam Fung Academy · LF Academy · We don't teach math. We teach trap avoidance.