The Distributive Law
⏱ 0:33📘 Grade 4 · Laws of arithmetic
A rectangle (4 + 6) long and 3 wide splits into 4 × 3 and 6 × 3, so (4 + 6) × 3 = 4 × 3 + 6 × 3. In general (a + b) × c = a × c + b × c.
The videos are narrated in Mandarin Chinese with on-screen subtitles.
📚 What you will learn
- A rectangle (4 + 6) long and 3 wide has area (4 + 6) × 3.
- Cut it into two parts: 4 × 3 and 6 × 3. The total area doesn’t change.
- (a + b) × c = a × c + b × c: multiply each part, then add.
- It makes mental maths easier: 38 × 9 + 62 × 9 = (38 + 62) × 9 = 900.
🎙️ What the video says (in Chinese)
- (4 + 6) × 3 和 4 × 3 + 6 × 3，一样吗？用长方形来看一看！
- 长方形长 4 + 6，宽 3，面积是 (4 + 6) × 3。
- 分成两块：左边 4 × 3，右边 6 × 3，合起来面积不变。
- 所以 (4 + 6) × 3 = 4 × 3 + 6 × 3 = 30
- 乘法分配律：(a + b) × c = a × c + b × c
✏️ Try it yourself
Work out 25 × 7 + 75 × 7 the easy way.
Show answer
(25 + 75) × 7 = 700
Work out 101 × 12.
Show answer
100 × 12 + 1 × 12 = 1212
🎬 More videos
🎬 Number Bonds of 10Split 10 dots with a stick: 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5 — and back again. Learn the “friends of 10”.Watch →🎬 Telling the Time: O'ClockMeet the hour hand and the minute hand. When the minute hand points to 12, the hour hand tells you the hour: 3 o'clock, 8 o'clock.Watch →🎬 The Make-Ten Trick: 9 + 49 needs 1 more to make 10, so split 4 into 1 and 3: 9 + 1 = 10, then 10 + 3 = 13. Watch it happen in a ten-frame.Watch →🎬 The Break-Ten Trick: 13 − 93 is too small to take away 9, so open the bundle of ten: 10 − 9 = 1, then 1 + 3 = 4. So 13 − 9 = 4.Watch →🎬 Yuan, Jiao and FenSwap money: one 1-yuan note is ten 1-jiao coins, and one 1-jiao coin is ten 1-fen coins. Then pay 3 yuan 5 jiao for a pencil.Watch →🎬 Tens and OnesBundle ten sticks into one ten. 3 bundles and 5 loose sticks make 35: 3 in the tens place and 5 in the ones place.Watch →🎬 What Is Multiplication?3 plates with 4 apples each: 4 + 4 + 4 = 12 becomes “3 fours”, written 3 × 4 = 12. With 10 plates, multiplication wins by a mile.Watch →🎬 The 9 Times Table Finger TrickHold up ten fingers and fold down the 3rd: 2 fingers on the left, 7 on the right, so 9 × 3 = 27. Works all the way from 9 × 1 to 9 × 9.Watch →🎬 Why Is the Remainder Smaller Than the Divisor?Make squares from 13 sticks, 4 sticks each: 3 squares and 1 left over, so 13 ÷ 4 = 3 R 1. If 4 were left, you could make one more square!Watch →🎬 Hours and MinutesThe minute hand moves 1 minute per small mark and 5 minutes per big mark. Hour hand just past 8, minute hand on 3: 8:15.Watch →🎬 Sharing Equally: What Division MeansShare 12 peaches among 3 monkeys, one round at a time. Each gets 4: that is sharing equally, written 12 ÷ 3 = 4.Watch →🎬 Measuring with a RulerLine one end up with 0 and read where the other end points: 6 cm. If you start at 2 and end at 8, subtract: 8 − 2 = 6 cm. And 1 m = 100 cm.Watch →🎬 Times As Many2 red flowers and 6 yellow ones: circle the yellow flowers in twos and you get 3 groups, so there are 3 times as many. Then 6 ÷ 2 = 3.Watch →🎬 Meet FractionsCut a pizza into 2 equal parts: each part is 1/2. Learn the numerator and denominator, then 1/4 and 3/4 — and why the parts must be equal.Watch →🎬 Area of a RectangleCover a 4 cm × 3 cm rectangle with 1 cm² squares: 4 in a row, 3 rows, 12 squares. So area = length × width = 4 × 3 = 12 cm².Watch →🎬 Long and Short Months: The Knuckle TrickMake a fist and count across your knuckles: knuckles are 31-day months, the dips between them are 30-day months. February is special: 28 or 29 days.Watch →🎬 How to Use a ProtractorTwo things must line up: the centre on the vertex and the zero line on one side. Then read from the zero you started on: 60°, not 120°.Watch →🎬 Parallel and Perpendicular LinesTwo lines on a flat surface that never meet are parallel; lines that cross at a right angle are perpendicular, meeting at the foot of the perpendicular.Watch →🎬 The Pancake ProblemA pan holds 2 pancakes and each side takes 3 minutes. Never leave a space empty and 3 pancakes take 3 rounds, 9 minutes, instead of 12.Watch →🎬 Reading Big NumbersSplit the number into groups of four from the right: the wan group and the ones group. 30070500 is read 三千零七万零五百.Watch →🎬 Chickens and Rabbits in a Cage8 heads, 26 legs. Ask every animal to lift two legs: 10 legs are left, all rabbit legs, 2 per rabbit. So 5 rabbits and 3 chickens.Watch →🎬 Angles of a Triangle Add Up to 180°Tear off the three corners of a triangle and put them together: they make a straight angle. So the angles of any triangle add up to 180°.Watch →🎬 What Decimals MeanSplit a square into 10 equal parts: one part is 1/10 = 0.1. Into 100 parts: one is 1/100 = 0.01. 35 small squares are 0.35.Watch →🎬 Circumference of a CircleRoll a circle and measure it with its diameter: the circumference is always about 3.14 times the diameter. Meet π and C = πd.Watch →🎬 The Pythagorean TheoremCount the little squares: on a right triangle with sides 3 and 4, 9 + 16 makes exactly 25 — the square of the long side.Watch →
← All lesson videos
