LF Academy — P5-S1-L08 Student Handout v6

Lam Fung Academy · LF Academy

Primary 5 · 8th Lesson · Student Handout

Adding fractions with different denominators

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 Trap:🪤 T9 Fraction Operations - After the common division, the numerator forgets to expand simultaneously · The result is not reduced
SSPA Association:🔴 High frequencyThe score test is compulsory every year, accounting for about 15-20% of Paper 1
Prerequisite knowledge:Class 7 (Comparison of different denominators and common fractions · LCM calculation · Equivalent fractions and extended fractions)
Objectives of this class:❶ Understand that different parts cannot be added directly ❷ Be proficient in the three-step method ❸ Addition of mixed numbers ❹ Application problems

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	Divide12and13(write the two equivalent fractions after the common denominator)	Advanced
4	Calculate38 + 28= ? (Adding with the same denominator, P4 basics)	Basic
5	Compare23and35which one is bigger? Write down the judgment process.	Advanced

II.Core Knowledge ＋ Worked Examples

Knowledge point 1: Why can’t fractions with different denominators be added directly? 🔴SSPA

① The denominator represents "the number of parts the whole is cut into." Different denominators = different sizes of each portion
② For example:12is cut into2 parts，13is cut into3 parts——The two parts are different sizes!
③ To add, it must first becomethe same parts→ This is thecommon fraction
④ The essence of the common fraction: use "equivalent fractions" (extended fractions) to change the denominator into LCM

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

calculate:56 − 14 = ？

❌ Common mistakes (80% students)

42 = 2

Direct numerator minus numerator, denominator minus denominator

✅ Correct solution

712

LCM(6,4)=12 → 1012 − 312 = 712

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

⚠️ The most frequent error: adding and subtracting different denominators directly without common denominators. Remember: the denominators are different → be sure to connect the denominators first!

⚠️ 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"!

Knowledge Point - Worked Examples (write out ①LCM ②find a common denominator ③calculate ④simplify)

#	Question	Difficulty	Working Space
Example 1	14 + 12 = ？	🌱
Example 2	13 + 16 = ？	🌱

Knowledge point 2: General addition of fractions with different denominators (LCM is greater than the denominator itself) 🔴 SSPA required test

Standard common three-step method:
① LCM |||SEP|||: Short division to find the least common multiple ②Common branch|||SEP|||: simplest fraction/false → band: Simultaneous expansion of molecules ③calculate: Addition of numerators with the denominator unchanged ④reduce: Simplest fraction/false→band

①

Looking for LCM

Find the lowest common multiple using short division

②

common points

The numerator and denominator change simultaneously to LCM

③

calculate

Adding numerators with the denominator unchanged

④

reduce

Simplest false fraction→mixed fraction

example

Example 3:23 + 35 = ？

example

Example 4:38 + 56 = ？

Knowledge Point 2 Synchronization practice

#	Question	Difficulty
6	12 + 13 = ？	🌿
7	23 + 14 = ？	🌿
8	35 + 12 = ？	🌿
9	34 + 16 = ？	🌿
10	58 + 16 = ？	🌿

Knowledge Point 3: Addition of Different Denominators with Mixed Fractions 🔴 SSPA Advanced

Recommended method (conversion to improper fraction method - the least error-prone):
① Mixed fraction → Improper fraction (integer × denominator + numerator) ② Common fraction (find LCM) ③ Calculation ④ Answer → Mixed fraction + reduction

example

Example 5:112 + 223 = ？

example

Example 6:213 + 112 = ？

Knowledge Point 3 Synchronization practice

#	Question	Difficulty	Working Space
11	114 + 223 = ？	🌳
12	125 + 2310 = ？	🌳

III. Lesson Layered Synchronization Practice

Basic layer (total 5 questions, everyone must do)

#	Question	Difficulty
13	14 + 18 = ？	🌱
14	13 + 19 = ？	🌱
15	12 + 14 = ？	🌱
16	15 + 310 = ？	🌱
17	25 + 13 = ？	🌿

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

#	Question	Difficulty
18	35 + 12 = ？	🌿
19	58 + 16 = ？	🌿
20	34 + 16 = ？	🌿
21	114 + 223 = ？	🌳
22	213 + 112 = ？	🌳

🌳 challenge layer (total 3 questions, 🚀 choose do, SSPAKiller Questions)

#	Question	Difficulty
23	213 + 112 + 34=? (Mixture of three fractions, including mixed numbers)	🌳
24	12 + 23 + 16 = ？	🌳
25	A rope is divided into three sections: the first section is13meters, the second section is14meters longer than the first section, and the third section is56meters. How many meters is the total length of the rope? (You need to find the length of the second paragraph first)	🏔️

Knowledge point 4: Application questions on addition of fractions (subject to sub-test word questions) 🔴 SSPA compulsory exam

Four steps to solve the problem:① Circle keywords("Total" "Total" = addition) ②Column ③ Calculation of common score ④ Write a complete answer sentence(Step points will be deducted if you do not write an answer sentence!)

example

Example 7: Xiao Ming has12Pizzas, and Xiaohua has13Pizzas. How many pizzas do they have in total?

applicationquestionpractice (all must do, column → find a common denominator → calculate → answer sentence)

#	Question	Difficulty
26	Xiao Mei drank14liters of orange juice, and Xiao Ming drank12liters. How many liters did they drink in total?	🌿
27	A box of chocolate, my sister ate25boxes, my brother ate13boxes. How many boxes did the two of them eat in total?	🌿
28	The original water bottle contains34liters, then pour13liters into it. How many liters are there now? (Answer with mixed fractions)	🌳

advancedapplicationquestion (🚶🚀 choose do, SSPAPaper 2commonquestion type)

#	Question	Difficulty
29	The cake shop sold25pieces in the morning and13pieces in the afternoon. How many were sold in total throughout the day?	🌿
30	The first section of rope is 114meters, the second section is 213meters. How many meters are the total length of the two sections? (Answer with fractions)	🌳
31	\|\|\|SEP\|\|\| in the garden grows roses,14grows chrysanthemums. What percentage of the garden is occupied by flowers?25Plant chrysanthemums. What percentage of the garden is occupied by flowers?	🌳
32	\|\|\|SEP\|\|\| in the granary is for white rice,16is for brown rice, and25is for red rice. What fraction of the granary is occupied by rice? What percentage is the remainder?13Put red rice. What fraction of the granary is occupied by rice? What percentage is the remainder?	🌳

IV.🏔️ Ultimate challenge area

#	Question	Difficulty
🏔️1	12 + 13 + 14 + 16=? (Adding four fractions with different denominators - find LCM(2,3,4,6))	🏔️
🏔️2	A bottle of juice contains 112liter. I drank13liters for breakfast and14liters for lunch. How many liters are left? (This class is learning addition, but this question uses subtraction!)	🏔️
🏔️3	Normal points account for \|\|\|SEP\|\|\|, tests account for \|\|\|SEP\|\|\|, exams account for \|\|\|SEP\|\|\|. What percentage of the total score do the three items account for? What's left? (Total score = 1)25, the test accounts for13, the exam accounts for14. What percentage of the total score do the three items account for? What's left? (Total score = 1)	🏔️

V. Class afterhomework

Basic must-do questions (total 6 questions, must write find a common denominator step)

#	Question	Difficulty
H1	14 + 18 = ？	🌱
H2	13 + 19 = ？	🌱
H3	12 + 16 = ？	🌱
H4	23 + 14 = ？	🌿
H5	34 + 16 = ？	🌿
H6	Xiao Ming has13pieces of chocolate, and Xiaohua gives him12pieces. How many lines does Xiao Ming have now?	🌿

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

#	Question	Difficulty
H7	A bottle of juice34liters, then pour13liters of water. How many liters are there now? (Answer with fractions)	🌳
H8	Compare56 + 14and12 + 23which one is bigger? How much difference?	🌳
H9	123 + 212 + 34 = ？	🏔️

VI. 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	Add the different denominators directly：12+13=25	Different denominators → Be sure to connect the denominators first!
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 final step must be to check the common factors
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(use the larger common multiple)	Short division is confirmed to be the true "minimum"
6	Mixed fractions are added before they are converted to false	It is recommended to use the "improper fraction conversion method" which is the least error-prone
7	Missing sentences/units in application questions	Must write "Answer:..." + unit, otherwise step points will be deducted

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

📚 Related topics: L07 Comparison of fractions with different denominators · L09 Multiplication of fractions · L22 Division of fractions