LF-P5-S1-L09 Fraction multiplication (× fraction) + mixed number processing

Lam Fung Academy· LF Academy

Primary 5 · 9th Lesson · Student Handout

Fraction multiplication (× fraction) + mixed number processing

Unit 3 · fraction operation (multiplication) · 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 11
🔴 High frequencyThe score test must be taken every year, accounting for about 12-18% of Paper 1
Prerequisite knowledge:Class 7-8 (Adding common denominators and different denominators), P4 integers Mixed numbersThe sub-test is compulsory every year and accounts for about 12-18% of Paper 1.
Prerequisite knowledge:Lesson 7-8 (Addition of common denominators and different denominators), P4 integers × fractions, HCF and reduction
Our goals:❶ Cross reduction method ❷ Mixed number × fraction (conversion to improper fraction method) ❸ Multiplication of three fractions ❹ Fraction multiplication word 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 3 ×14= ? (Integer × Fraction, P4 Basics)	Basic
2	Calculate13× 2 = ? (fraction × integer)	Basic
3	Convert 112to an improper fraction. Then find the improper fraction forms of 123and 2 \|\|\|SEP\|\|\|.14Improper fraction form.	Basic
4	Reduce615to the simplest fraction. (HCF(6,15) = ?)	Basic
5	Find HCF(6, 8), HCF(4, 10), HCF(9, 12). Why is HCF needed for cross reduction?	Advanced

II.Core Knowledge ＋ Worked Examples

Knowledge Point 1: Fraction × Fraction — Cross Reduction Method 🔴 SSPA

Fraction multiplication rules:
① Numerator × numerator, denominator × denominator:ab × cd = a×cb×d
② Cross reduction (reduce first and then multiply) |||SEP|||: Before multiplication, first combine anynumeratorwith anydenominatorUse HCF to reduce③ Advantages: reduce first and then multiply → numbers become smaller → fewer errors → no need for final reduction
④ Note: reduction can only be between
numerator and denominator |||SEP|||, not numerator and numerator, denominator and denominator!between numerator and denominator, cannot numerator with numerator, denominator with denominator!

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

calculate:23 × 34 = ？

❌ Common mistakes (60% students)

612(not reduced)

Directly multiply and then forget to reduce → Not the simplest answer

✅ Correct solution (cross reduction)

Cross reduction: numerator 2 and denominator 4 are reduced (HCF=2)→13×32=36=12

🧠 Tip: "When doing cross-reduction, do it first. The numerator and denominator are about one round. Multiply the rest first and then check. The answer must be the simplest one."

⚠️ The most frequent error: after multiplying 2/3×3/4=6/12, take it as the answer directly → Forget about reduction! Cross reduction can avoid this error.

⚠️ The second most frequent error: When approximating a division, the numerator is about the numerator and the denominator is about the denominator → This is wrong! It can only be "crossed" (the numerator is about the denominator).

Knowledge Point - Worked Examples (mustfirst crosssimplify, againmultiply)

#	Question	Difficulty	Working Space
Example 1	12 × 25=? (Hint: Reduction of numerator 2 and denominator 2 →15）	🌱
Example 2	34 × 29=? (Hint: Numerator 3 is approximately the same as the denominator 9, Numerator 2 is approximately the same as the denominator 4)	🌿

Knowledge Point 2: Mixed Numbers

Standard procedure for multiplication of mixed fractions:
① Conversion to improper fractions |||SEP|||: Mixed fractions → Improper fractions (integer × denominator + numerator)Cross reduction |||SEP|||: Reduction between numerator and denominator
② Numerator × numerator, denominator × denominatorThe answer is converted back
③ : Improper fraction → Mixed fraction (if necessary) + reduction
④ ⚠️ Absolutely prohibited: Direct multiplication of mixed fractions! Integer × Integer + Fraction × Fraction ≠ Correct answer!
⚠️ Absolutely prohibited: Multiply mixed fractions directly! Integer × Integer + Fraction × Fraction ≠ Correct answer!

①

Convert Improper Fractions

Mixed fraction → Improper fraction

②

cross reduction

The numerator and denominator are reduced using HCF

③

Multiply

Numerator × Numerator Denominator × Denominator

④

Reverse + reduce

False → mixed fraction simplest fraction

🪤 Trap comparison question

Calculate: 112 × 13 = ？

❌ Error: Multiply mixed fractions directly

1×1 + 12×13 = 116

Totally wrong! Mixed numbers must be converted to improper fractions first

✅ Correct: Convert improper fractions first

112=32 → 32×13=36=12

example

Example 3:112 × 13 = ？

example

Example 4:213 × 34 = ？

Knowledge point 3: Multiplying three fractions 🔴 SSPA Advanced

Rule of continuous multiplication:
① Multiply all the numerators and all the denominators
② Comprehensive cross reduction |||SEP|||: Any numerator can be reduced with any denominator (not limited to pairing)③ Suggestion: Comprehensive reduction first → then multiply → the number becomes super small!
④ Example:
(approximate first, then multiply)ab×cd×ef = a×c×eb×d×f(Make an appointment before taking a ride)

example

Example 5:12 × 23 × 34= ? (Hint: Numerator 1, 2, 3 intersects with denominator 2, 3, 4 approximately)

example

Example 6:23 × 35 × 56 = ？

🧠 Formula (continuous multiplication version): "Multiple three brothers in a row, make an appointment together, and then multiply together after the appointment, the answer is so simple."

Knowledge Point 2 + 3 Synchronous practice

#	Question	Difficulty
6	114 × 12 = ？	🌿
7	123 × 15 = ？	🌿
8	12 × 14 × 45 = ？	🌳
9	13 × 34 × 45 = ？	🌳

III. Lesson layered synchronization practice (total 15 questions)

Basic layer (total 5 questions, everyone must do)

#	Question	Difficulty
10	12 × 13 = ？	🌱
11	14 × 12 = ？	🌱
12	23 × 12 = ？	🌱
13	34 × 13 = ？	🌱
14	15 × 56 = ？	🌱

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

#	Question	Difficulty
15	35 × 56 = ？	🌿
16	23 × 38 = ？	🌿
17	114 × 13 = ？	🌿
18	212 × 15 = ？	🌿
19	12 × 13 × 14 = ？	🌳

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

#	Question	Difficulty
20	123 × 35 = ？	🌳
21	213 × 112 = ？	🌳
22	34 × 89 × 12 = ？	🌳
23	114 × 23 × 35 = ？	🌳
24	313 × 35 × 12 = ？	🏔️

Knowledge point 4: Fraction multiplication word problems (subject to sub-test word questions) 🔴 SSPA compulsory exam

Four steps to solve the problem:
① Circle keywords("... of..." = multiplication! "× divided by
② Write a complete answer(Step points will be deducted if you do not write an answer!)
③ Key words:"C divided by B" = A ×
④ Write a complete answer(Points for steps will be deducted if you don’t write an answer!)
Key words:"A divided by B divided by C" = A ×CB

example

Example 7: There are23pieces in a cake, and Xiao Ming eats12pieces among them. What fraction of the whole cake did Xiao Ming eat? (Hint: "where"12= multiplication)

example

Example 8: A rope is 112meter long, use |||SEP|||. How many meters were used? (Tip: Convert mixed fractions to improper fractions first and then multiply them)35. How many meters were used? (Tip: Convert mixed fractions to improper fractions first and then multiply them)

applicationquestionpractice (all must do, column → simplify → calculate → answer sentence)

#	Question	Difficulty
25	A box of biscuits weighs23kilograms, and Xiaomei ate \|\|\|SEP\|\|\|. How many kilograms did Xiaomei eat?14. How many kilograms did Xiaomei eat?	🌿
26	A bottle of juice contains34liters. Xiao Ming poured out \|\|\|SEP\|\|\|. How many liters were poured?23come out. How many liters were poured?	🌿
27	A rectangle is long12meters and its width is long \|\|\|SEP\|\|\|. How many meters wide is it?12. How many meters wide is it?	🌿
28	The elder brother has 112kilogram of candy, and he gives13to his younger brother. How many kilograms were sent?	🌳
29	Mom used34kilograms of flour to make cakes, of which25was used to make cookies. How many kilograms of flour are used to make cookies?	🌳
30	A ribbon is 214meters long, and my sister used \|\|\|SEP\|\|\|. How much rice did your sister use? (Answer with mixed fractions)23. How much rice did your sister use? (Answer with mixed fractions)	🌳

IV.🏔️ Ultimate challenge area (total 3 questions)

#	Question	Difficulty
🏔️1	12 × 23 × 34 × 45=? (Multiplying four fractions - the ultimate in cross reduction!)	🏔️
🏔️2	The rectangular area23is planted with roses, and the rose part with14is a red rose. What fraction of the total area do red roses occupy?	🏔️
🏔️3	The granary contains 513tons of rice.14was used in the first week, and13was used in the second week (note: is it "the rest" or "all"?). The title says "I used13in the second week", which refers to the total amount of13used. How many tons were used in two weeks? How many tons are left?	🏔️

V. Class afterhomework

Basic must do questions (total 5 questions, must write cross simplify step)

#	Question	Difficulty
H1	12 × 12 = ？	🌱
H2	23 × 14 = ？	🌱
H3	13 × 35 = ？	🌱
H4	34 × 23 = ？	🌿
H5	112 × 14 = ？	🌿

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

#	Question	Difficulty
H6	123 × 35 = ？	🌳
H7	212 × 113 = ？	🌳
H8	A rectangular garden34is planted with flowers, and the flowers13are roses. What percentage of the garden are roses?	🌳

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	Cross reduction is done：23×34=612when the answer	First make a cross reduction (the numerator 2 and the denominator 4 are approximately →13×32=36=12）
2	Multiply mixed numbers directly without converting them into improper fractions	The first step in multiplication with mixed numbers = Convert Improper Fractions! No exceptions!
3	The numerator is about the numerator, the denominator is about the denominator	The reduction can only be between the numerator and the denominator (crossover), the numerator cannot be reduced!
4	The result is unreduced：615When the final answer	Finally the HCF reduction must be checked. Cross-reduction first can avoid this problem.
5	Improper fractions are not converted to mixed fractions	When the answer is > 1, the test is required to be converted into a mixed number
6	When multiplying continuously, only one pair of numerator and denominator will be arranged and then stop \|\|\|SEP\|\|\|: Only one pair of numerator and denominator will be arranged, and no other appointment will be made: Only a pair of numerator and denominator are agreed, and no other appointments are made.	When multiplying, all numerators and all denominators can be cross-contracted! Total simplification.
7	Missing answers to application questions/missing units	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 Fractions with different denominators · L10 Fraction word problems · L22 Fraction division · Related topics: L05 Multiplication knowledge · L06 Two-digit numbers multiplied by one digit · L07 Multiplication word problems