LF-P5-S2-L22 Fraction ÷ Integer + Fraction ÷ Fraction

Lam Fung Academy· LF Academy

Primary 5 · Semester 2 · 22nd Lesson · Student Handout

Fraction division (1)

Unit three · fraction÷integer ＋ fraction÷fraction · 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 11
Core traps:🪤 T3 Fraction division - forgetting to invert the divisor after the division sign (÷ becomes × reciprocal) · T9 The result is not reduced
SSPA association:🔴 High frequencyThe sub-test must be taken every year, accounting for about 12-18% of Paper 1
Prerequisite knowledge:Course 7 (common denominators with different denominators) · Course 9 (multiplication of fractions, including mixed numbers × fractions)
Goals of this course:❶ Fraction ÷ whole number (=× reciprocal) ❷ Fraction ÷ fraction (reverse after division sign) ❸ Division of mixed numbers ❹ Division word problems

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	Write the reciprocal of \|\|\|SEP\|\|\|.23The countdown.	Basic
2	Write what are the reciprocals of \|\|\|SEP\|\|\|?15、34、52What are the reciprocals of ?	Basic
3	Convert 213into an improper fraction.	Basic
4	Calculation:34 × 12= ? and reduce the results. (Review multiplication of fractions)	Basic

II.Core Knowledge ＋ Worked Examples

Knowledge Point 1: Fraction ÷ Integer🔴 SSPA

① Core rule: fraction ÷ integer = fraction × (reciprocal of integer)
② For example:23 ÷ 2 = 23 × 12 = 26 = 13
③ Reciprocal of integer a =1a(remember: a = |||SEP|||, the reciprocal isa1④ After division, it must be reduced! The numerator and denominator are divided by the greatest common factor (HCF) at the same time)1a）
④ It must be reduced after division! Divide both the numerator and denominator by the highest common factor (HCF)

Example 1

calculate:34 ÷ 2 = ？

Example 2

calculate:56 ÷ 4 = ？

Knowledge Point 1 Synchronization practice (write out: ① turn × reciprocal ② numeratormultiplynumerator·denominatormultiplydenominator ③simplify)

#	Question	Difficulty
5	23 ÷ 2 = ？	🌱
6	58 ÷ 5 = ？	🌱
7	47 ÷ 3 = ？	🌿
8	910 ÷ 6 = ？	🌿

⚠️ The most frequent error: ÷2 is treated as ×2 instead of × 12! Remember: ÷Integer = ×The reciprocal of that integer.

Knowledge Point 2: fraction÷fraction = × reciprocal🔴 SSPA Must-Test

Core formula:ab ÷ cd = ab × dc = a×db×c
① The divisor after the division signmust be inverted (the numerator and denominator are swapped)② The division sign becomes a multiplication sign ③ Then calculate by fraction multiplication ④ Must reduce
Don’t make a mistake: only the fraction after the division sign is inverted!
⑤ Make no mistake: only the fraction after the division sign is inverted!

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

calculate:23 ÷ 14 = ？

❌ Common mistakes (60% students)

23 × 14 = 212 = 16

Forgot to reverse the divisor of 14! Treat it directly as a multiplication sign.

✅ Correct solution

23 × 41 = 83 = 223

÷14 → ×41 (the fraction after the division sign must be reversed!)

🧠 Tip: "Invert the division sign and turn it into a multiplication sign. The numerator is multiplied by the numerator and the denominator is multiplied by the denominator. The answer must be simplified!"

Example 4

calculate:35 ÷ 23 = ？

Knowledge Point 2 Synchronization practice (mustwrite out: ①÷→× ②divide number inversion ③simplify)

#	Question	Difficulty
9	12 ÷ 13 = ？	🌱
10	34 ÷ 12 = ？	🌱
11	56 ÷ 23 = ？	🌿
12	45 ÷ 310 = ？	🌿

⚠️ High-frequency trap: Just remember "reverse" but also reverse the previous scores! For example, 23÷45 is incorrectly written as 32×54 — wrong! Only what follows ÷ is inverted.

Knowledge Point 3: Division with Mixed Fractions🔴 SSPA Advanced

Standard three-step method:
① mixed fraction → improper fraction(integer × denominator + numerator)
② Reverse the divisor after the division sign, the division sign becomes the multiplication sign
③ Multiply the numerator by the numerator and the denominator by the denominator→ Reduction → Convert the improper fraction to a mixed fraction

①

Convert Improper Fractions

Convert all mixed numbers into improper fractions

②

divisor reversal

÷The following fraction is reversed

③

Multiplication calculation

Numerator × Numerator Denominator × Denominator

④

Reduction·Return

Reduction + Improper Fraction → Mixed Fraction

Example 5

Calculate: 112 ÷ 23 = ？

Example 6

Calculate: 213 ÷ 112 = ？

Knowledge Point 3 Synchronization practice

#	Question	Difficulty
13	114 ÷ 12 = ？	🌿
14	212 ÷ 113 = ？	🌳
15	123 ÷ 34 = ？	🌳

❌ Trap: Mixed fractions are reversed before they are false.

112 ÷ 23 = 12 × 32 ❌

Just separate the numerator and denominator of 1½ – big mistake!

✅ Correct: Convert improper fractions first

32 × 32 = 94 = 214

1½ = 3/2 → 3/2 ÷ 2/3 = 3/2 × 3/2 = 9/4

Knowledge Point 4: Fraction Division Application Questions 🔴 SSPA Required Exam

Four-step method to solve the problem:① Circle keywords("Share equally" "Each..." "How many servings can..." = division)
② Column formula(Total amount ÷ per serving = number of servings; Total amount ÷ number of servings = per serving)
③ Calculate according to the division steps ④ Write a complete answer(Step points will be deducted if you do not write an answer!)

Example 7

34A cake is divided equally among 5 people. What fraction of the cake does each person get?

Example 8

A ribbon is56meters long, cut into sections every14meters. How many pieces can it be cut into?

Knowledge Point 4: Synchronized practice (column → calculate → answer sentence)

#	Question	Difficulty
16	12A pancake is divided equally among 3 people. What fraction of the pancake does each person get?	🌿
17	A bottle of juice contains45liters. Pour one cup for every25liter. How many cups can be filled?	🌿
18	A rope is 212meters long and cut into sections every12meter. How many pieces can it be cut into?	🌳

III. Lesson Layered Synchronization Practice

Basic layer (total 4 questions, everyone must do)

#	Question	Difficulty
19	35 ÷ 3 = ？	🌱
20	47 ÷ 2 = ？	🌱
21	38 ÷ 14 = ？	🌱
22	56 ÷ 512 = ？	🌿

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

#	Question	Difficulty
23	79 ÷ 23 = ？	🌿
24	115 ÷ 35 = ？	🌿
25	910 ÷ 35 = ？	🌿

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

#	Question	Difficulty	Working Space
26	34 ÷ 23 ÷ 12=? (Continuous division of three fractions - calculate the first two first, then ÷ the third result)	🌳
27	214 ÷ 112 = ？	🌳

IV.🏔️ Ultimate challenge area

#	Question	Difficulty	Working Space
🏔️1	A rope is 312meters long. Use half of it first, and then cut the remaining14meters into a section. How many pieces can it be cut into? (You need to find the remaining length first, and then ÷ the length of each paragraph)	🏔️
🏔️2	A box of candy weighs34kilograms, and each18kilogram contains a small package. After filling 3 bags, how many bags of candy can be left?	🏔️

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

#	Question	Difficulty	Working Space
A1	23Kilograms of sugar, one pack per19kg. How many bags can be packed?	🌿
A2	The original water bottle contains34liters. After drinking13liters, pour the remaining water into 2 cups. How many liters of water are in each cup?	🏔️

V. Class afterhomework

Basic must doquestion (total 6 questions, mustwrite out complete step: ÷→×→reverse→simplify)

#	Question	Difficulty
H1	25 ÷ 2 = ？	🌱
H2	38 ÷ 3 = ？	🌱
H3	12 ÷ 14 = ？	🌱
H4	34 ÷ 13 = ？	🌿
H5	710 ÷ 25 = ？	🌿
H6	112 ÷ 12 = ？	🌿

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

#	Question	Difficulty	Working Space
H7	213 ÷ 114 = ？	🌳
H8	There are35liters in a bottle of orange juice. Pour a small glass for every320liter. After filling 2 cups, how many more cups can be filled?	🏔️

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	÷integer is treated as×integer：34 ÷ 2 = 64	÷2 = ×12, not ×2! The reciprocal of an integer is 1/integer
2	÷Fraction forgetting to reverse the divisor：23 ÷ 14 = 212	÷14 = ×41, only the one after the division sign is inverted!
3	Reverse the previous fraction as well：23÷45=32×54	Only fractions after ÷ are inverted! The front is unchanged, the back is reversed.
4	The answer is not reduced：612as the final answer	Must be reduced to the simplest fraction (numerator and denominator ÷ HCF)
5	Improper fractions are not converted to mixed fractions	Numerator > Denominator → Convert into mixed numbers (subject to the requirements of the division test)
6	Mixed fractions are divided directly by ÷without conversion: 1½÷2	You must first convert to an improper fraction (1½ = 3/2), and then follow the division steps
7	Application question "number of copies vs. each copy" confusion	Total amount ÷ amount per serving = number of servings; total amount ÷ number of servings = amount per serving. Distinguish clearly!

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

📚 Related topics: L09 Multiplication of fractions · L23 Mixing of three fractions · Related topics: L02 Two-digit division · L03 Three-digit division · L05 Four word problems