LF-P5-S2-L23 Three-fraction mixture + four-fraction mixture

Lam Fung Academy· LF Academy

Primary 5 · Semester 2 · 23rd Lesson · Student Handout

Fraction mixed operations + four mixed operations

Unit three · Three fraction mix + four first after order · 65 minutes · 1-to-3 Online Lesson

Corresponding textbooks:"New Thinking in Primary School Mathematics (Second Edition)" Volume 5B Unit 3 + Modern Education 5L B Unit 12
Core traps:🪤 T6 Wrong order of mixed operations · T9 Fractional operations - the numerator forgets to synchronize after the common division · The result is not reduced
SSPA association:🔴 High frequencyPaper 1 accounts for about 15-20%, Paper 2 accounts for about 10%
Prerequisite knowledge:Course 7-8 (Addition and subtraction of different denominators) · Course 9 (Multiplication of fractions) · Course 22 (Division of fractions)
Goal of this course:❶ Continuous addition and subtraction of three fractions ❷ Mixed multiplication and division of three fractions ❸ Four rules of order ❹ Comprehensive formula trap

Student Name: Class: Date: Time Spent:

I.Warm-Up Questions（total 4 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(3, 4, 6) = ? (least common multiple of three numbers)	Basic
2	Calculation:12 + 13= ? (Review addition of common fractions with different denominators)	Basic
3	Calculation:23 × 12= ? (Review multiplication of fractions)	Basic
4	Calculation:34 ÷ 12= ? (Review fraction division: the fraction after ÷ needs to be reversed!)	Advanced

II.Core Knowledge ＋ Worked Examples

Knowledge point 1: Adding and subtracting mixed three fractions🔴 SSPA

① Add and subtract three or more fractions with different denominators →First find the LCM of all denominators
② Each fraction divides to the same denominator (the numerator is expanded simultaneously)
③ The denominator remains unchanged, and the numerator is calculated in the order of addition and subtraction
④ The result is reduced to the simplest fraction (improper fraction → mixed fraction)
⑤ Note: LCM needs to find all denominators, not just two!

Example 1

calculate:12 + 13 + 16 = ？

Example 2

calculate:34 − 12 + 18 = ？

Knowledge Point 1 Synchronization practice (must write out: ①Find the LCM that has/havedenominator ②find a common denominator ③numerator addsubtract in order ④simplify)

#	Question	Difficulty
5	14 + 12 + 18 = ？	🌱
6	23 + 16 + 12 = ？	🌱
7	56 − 13 + 12 = ？	🌿
8	12 + 13 − 14 = ？	🌿

⚠️ Warning: When adding and subtracting three fractions, the LCM must include all denominators. For example, the denominator is 2, 3, 4 → LCM(2,3,4)=12. If it is not LCM(2,3)=6, stop! 4 does not divide 6.

Knowledge point 2: Mixed multiplication and division of third fractions🔴 SSPA required test

Core rule: all division signs become multiplication signs (reverse divisors), then all numerators are multiplied ÷ all denominators are multiplied
① When encountering ÷ →, reverse the fraction after ÷, ÷ becomes ×
② All multiplications are calculated from left to right
③ You cancross reduction(The common factor of any numerator can be reduced by any denominator)
④ Finally, the numerator is multiplied by the denominator ÷ the denominator is multiplied → reduction

🪤 Trap detonation example 3 (the most important demonstration in this class)

calculate:12 × 23 ÷ 14 = ？

❌ Common mistakes (70% students)

12 × 23 ÷ 14 = 26 ÷ 14 = 26 × 14 ❌

Calculate the previous multiplication first, then forget to reverse when dividing, and mistakenly change ×½ into ×2 and then ×¼

✅ Correct solution

12 × 23 × 41 = 86 = 43 = 113

÷¼ → ×4/1, all ÷ become ×, and then reduce from left to right

🧠 Tip: "Change all division signs into multiplication signs, and reverse the subsequent fractions; cross reduction is the most labor-saving, and the numerator and denominator should be equal."

Example 4

calculate:34 ÷ 12 × 23 = ？

Knowledge Point 2 Synchronization practice (write out: ①÷→×reverse ②crosssimplify ③numerator×÷denominator× ④simplify)

#	Question	Difficulty
9	13 × 12 ÷ 16 = ？	🌱
10	25 ÷ 23 × 12 = ？	🌿
11	34 × 23 ÷ 12 = ？	🌿
12	56 ÷ 23 × 12 = ？	🌿

⚠️ High-frequency errors: When mixing multiplication and division, if you do multiplication first and then division, you may make an error. The best strategy: first turn all ÷ into × (reverse the divisors) and process them uniformly.

Knowledge Point 3: Four Mixed Operation Sequences🔴 SSPA Required Exam

Operation precedence (from high to low):
① Parentheses ( )— the calculations inside the parentheses are evaluated first
② Formula: parentheses first, then multiplication and division, and finally addition and subtraction(from left to right at the same level)
③ + and −— Addition and subtraction last (from left to right)
④ Formula: brackets first, then multiplication and division, and finally addition and subtraction(Same level from left to right)

①

Parentheses first

The formula within ( ) must be calculated first

②

Multiplication and division take precedence

× ÷ is calculated before + −

③

Addition and subtraction last

+ − after parentheses and multiplication and division

④

Same level left to right

Operations at the same level are performed from left to right

🪤 Trap detonation example 5

calculate:12 + 13 × 14 = ？

❌ Common Mistake — Doing it Directly from Left to Right

(12+13)×14 = 56×14 = 524

Treat + as if it were on the same level as

✅ Correct solution: first × then +

12 + 112 = 712

Calculate first ⅓×¼=1/12, then add ½=6/12 → 7/12

Example 6

Calculation: (12 + 13) ÷ 16= ? (Note: Calculate first in parentheses, then ÷)

Knowledge Point 3 Synchronization practice (must mark the calculate order: ①brackets → ②×÷ → ③+−)

#	Question	Difficulty
13	12 + 13 ÷ 16 = ？	🌿
14	23 × (12 + 14) = ？	🌿
15	34 − 12 × 13 = ？	🌿

🧠 Tip: "Put parentheses first, then multiplication and division, and finally addition and subtraction; the same level is from left to right, and the order cannot be messed up."

Knowledge Point 4: Comprehensive Application - Four Mixed Text Questions 🔴 SSPA Required

Key to solving the problem:① Understand the question→ Determine which operations are used ②Column comprehensive calculation(note the brackets and order)
③ Calculate step by step in the four order ④ Write a complete answer(Step points will be deducted if you do not write an answer!)

Example 7

Xiao Ming has12cakes, and his mother buys twice as many13cakes. What fraction of the cake does Xiao Ming have now?

Example 8

A rope is34meters long. After using12meters, the remaining23of the rope is used for handicrafts. How much rice did you use to make it?

Knowledge Point Four Synchronization Practice

#	Question	Difficulty
16	Xiaomei has25liters of orange juice. After drinking110liters, she divides the remainder into 3 glasses. How many liters are there in each cup?	🌳
17	One piece of13was used as a gift, and the remaining12was used for decoration. What fraction of the total rope does the decorative part account for?	🌳
18	The younger brother's pocket money belongs to the older brother \|\|\|SEP\|\|\|, and the younger brother's pocket money belongs to the younger brother\|\|\|SEP\|\|\|. What fraction of my sister’s pocket money is that of my brother’s?12, the sister’s is the brother’s23. What fraction of my sister’s pocket money is that of my brother’s?	🌳

III. Lesson Layered Synchronization Practice

Basic layer (total 4 questions, everyone must do)

#	Question	Difficulty
19	13 + 16 + 12 = ？	🌱
20	58 − 14 + 12 = ？	🌱
21	14 × 23 ÷ 12 = ？	🌱
22	12 + 14 ÷ 12 = ？	🌿

Advanced layer (total 3 questions, 🚶🚀 choose do)

#	Question	Difficulty
23	35 + 12 − 110 + 15=? (Four fractions addition and subtraction mixed)	🌿
24	78 ÷ 34 × 12 = ？	🌿
25	(12 − 13) ÷ 16 + 14 = ？	🌳

🌳 challenge layer (total 2 questions, 🚀 choose do, SSPAKiller Questions)

#	Question	Difficulty	Working Space
26	12 + 23 × 34 ÷ 12=? (Four mixing rules: first ×÷, then +−)	🌳
27	23 ÷ 12 × (12 + 14) = ? (Parentheses first, then multiplication and division from left to right)	🌳

IV.🏔️ Ultimate challenge area

#	Question	Difficulty	Working Space
🏔️1	Calculation: (\|\|\|SEP\|\|\| = ? (two brackets, then ×÷ - pay attention to the order!)12 + 13) × (23 − 14) ÷ 16=? (Two parentheses, then ×÷ - pay attention to the order!)	🏔️
🏔️2	Bottle of Juice34Liters. I drank liters of16at breakfast and the remaining23at lunch. How many liters are left after drinking lunch? (Calculation using comprehensive formulas)	🏔️

Advanced mixed question (🚶🚀 choose do)

#	Question	Difficulty	Working Space
M1	12 + 13 ÷ 16 − 14=? (÷ → − → +, pay attention to the order!)	🌳
M2	23 + 12 × (13 + 16) = ? (Brackets first, then ×, and finally +)	🌳

V. Class afterhomework

Basic must-doquestions (total 6 questions, mustwrite outcalculate order mark)

#	Question	Difficulty
H1	12 + 14 + 18 = ？	🌱
H2	35 + 110 + 12 = ？	🌱
H3	23 × 14 ÷ 12 = ？	🌱
H4	34 − 18 + 12 = ？	🌿
H5	12 + 13 × 14 = ？	🌿
H6	35 + 12 × 23 = ？	🌿

For advanced, choose doquestion (total 2 questions, 🚀 choose do)

#	Question	Difficulty	Working Space
H7	23 ÷ 12 + 14 × 23 = ？	🌳
H8	A ribbon is 112meter long. After using \|\|\|SEP\|\|\|, the remaining13is used to wrap gifts. How much rice did it take to wrap the gift?12Used to wrap gifts. How much rice did it take to wrap the gift?	🏔️

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	Three fractions LCM only finds two \|\|\|SEP\|\|\|: denominator 2,3,4 only finds LCM(2,3)=6: Denominator 2,3,4 only looks for LCM(2,3)=6	LCM must include all denominators! LCM(2,3,4)=12
2	When mixing multiplication and division, forget to change ÷ into ×：12×13÷16and only count the first two	All ÷ become × (the divisor is reversed) and are processed uniformly
3	Four order errors—adding and subtracting first, then multiplying and dividing	First ×÷ and then +−, if there are parentheses, it is calculated first
4	Uncommon points in brackets：(12+13) Write directly25	The scores in parentheses must be divided first and then calculated!
5	During cross reduction, only the same denominator group is reduced	The common factors of any numerator can be reduced by any denominator
6	The result is not reduced/improper fraction is not transferred	The final step must be to check the reduction and transfer of mixed fractions
7	The order of expressions in application questions is reflected incorrectly(missing brackets)	Check when formulating: What does the question ask you to do first? Do I need to use parentheses?

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