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Tiếng Việt

The 3 times table and dividing by 3

Lesson 1.2 · 15 min read · Updated

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Mai puts cakes into boxes. Each box holds 33 cakes. Mai fills 55 boxes. How many cakes does Mai have altogether?

You could add 3+3+3+3+33+3+3+3+3. But adding so many times is long and easy to get wrong. The 3 times table helps you work much faster.

Let's explore

Count the cakes as Mai fills one more box each time.

  • 11 box has 33 cakes.
  • 22 boxes have 3+3=63+3=6 cakes.
  • 33 boxes have 6+3=96+3=9 cakes.
  • 44 boxes have 9+3=129+3=12 cakes.
  • 55 boxes have 12+3=1512+3=15 cakes.

Each new box adds 33 more cakes. So 55 boxes hold 1515 cakes. We write 3×5=153\times 5=15.

Now go the other way. Mai has 1515 cakes and puts 33 in each box. You count 55 boxes. We write 15÷3=515\div 3=5.

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On the number line: 5 jumps of 3 reach 15

Learn the table below. Each row gives you one multiplication and one division.

3 times table Division facts for 3
3×1=33\times 1=3 3÷3=13\div 3=1
3×2=63\times 2=6 6÷3=26\div 3=2
3×3=93\times 3=9 9÷3=39\div 3=3
3×4=123\times 4=12 12÷3=412\div 3=4
3×5=153\times 5=15 15÷3=515\div 3=5
3×6=183\times 6=18 18÷3=618\div 3=6
3×7=213\times 7=21 21÷3=721\div 3=7
3×8=243\times 8=24 24÷3=824\div 3=8
3×9=273\times 9=27 27÷3=927\div 3=9
3×10=303\times 10=30 30÷3=1030\div 3=10

You see: going down one row, the product goes up by 33. To divide by 33, you only need to remember the matching multiplication.

Examples

We start with a multiplication you may not know yet. Take the answer from the row just above and add 33.

Now go the other way to divide.

Use multiplication to solve a problem from everyday life.

When we know the total and the size of each group, we divide.

Key terms

Summary

  • In the 3 times table, going down one row adds 33 to the product, from 3×1=33\times 1=3 to 3×10=303\times 10=30.
  • 3×5=153\times 5=15 means 55 groups with 33 in each.
  • To divide by 33, find the matching multiplication: 3×8=243\times 8=24, so 24÷3=824\div 3=8.
  • Many equal groups: multiply. Sharing equally or making groups: divide. Remember the unit in the answer.

Practice

Each exercise comes with what you need and how to start. Try it yourself first, then open the solution.

Exercise 1

Work out in your head: a) 3×53\times 5; b) 3×83\times 8.

What you need and how to start

What you need: count on in threes, or take the answer from the row above and add 33.

Steps:

  1. Part a: count on in threes five times.
  2. Part b: you know 3×7=213\times 7=21, so add 33.
Show solution

a) 3×5=3+3+3+3+3=153\times 5=3+3+3+3+3=15.

b) 3×8=3×7+3=21+3=243\times 8=3\times 7+3=21+3=24.

Answer. a) 1515; b) 2424.

Exercise 2

Fill in the missing numbers in the pattern: 3,6,9,□,15,□,213, 6, 9, \square, 15, \square, 21.

What you need and how to start

What you need: each number in the pattern is 33 more than the one before it.

Steps:

  1. The number after 99 is 9+39+3.
  2. The number after 1515 is 15+315+3.
Show solution

9+3=129+3=12 and 15+3=1815+3=18. The full pattern is 3,6,9,12,15,18,213, 6, 9, 12, 15, 18, 21.

Check. 18+3=2118+3=21. Correct.

Answer. 1212 and 1818.

Exercise 3

Work out: a) 18÷318\div 3; b) 27÷327\div 3.

What you need and how to start

What you need: to divide by 33, find the multiplication by 33 that gives the dividend.

Steps:

  1. Part a: 3×□=183\times\square=18.
  2. Part b: 3×□=273\times\square=27.
Show solution

a) 3×6=183\times 6=18, so 18÷3=618\div 3=6.

b) 3×9=273\times 9=27, so 27÷3=927\div 3=9.

Answer. a) 66; b) 99.

Exercise 4

Write >>, << or == in the box: 3×7  □  203\times 7 \;\square\; 20.

What you need and how to start

What you need: work out the multiplication first, then compare the two numbers.

Steps:

  1. Work out 3×73\times 7.
  2. Compare the result with 2020.
Show solution

3×7=213\times 7=21. Since 21>2021>20, we have 3×7>203\times 7>20.

Answer. The sign >>.

Exercise 5

A teacher shares 1515 pens equally between 33 children. How many pens does each child get?

What you need and how to start

What you need: sharing equally means dividing.

Steps:

  1. What do we know? 1515 pens shared equally between 33 children. What is asked? How many pens each child gets.
  2. How do we solve it? Work out 15÷315\div 3, then check with multiplication.
Show solution

The number of pens each child gets is: 15÷3=5 (pens).15\div 3=5\ \text{(pens)}.

Check. 3×5=153\times 5=15. Correct.

Answer. 55 pens.

Exercise 6

Each row in the school garden has 33 plant pots. The garden has 1010 rows like this. How many plant pots are there altogether?

What you need and how to start

What you need: many equal groups means multiplication.

Steps:

  1. What do we know? 33 pots in each row and 1010 rows. What is asked? The number of pots altogether.
  2. How do we solve it? Work out 3×103\times 10 and write the unit.
Show solution

The number of plant pots altogether is: 3×10=30 (pots).3\times 10=30\ \text{(pots)}.

Answer. 3030 plant pots.

Exercise 7

Remember the last lesson: finding a missing number in an addition. Find the missing number: □+12=3×7\square+12=3\times 7.

What you need and how to start

What you need: the missing addend is the total minus the addend you know.

Steps:

  1. Work out 3×73\times 7 to find the total.
  2. Take away 1212 from the total.
Show solution

3×7=213\times 7=21, so □+12=21\square+12=21. The missing addend is 21−12=921-12=9.

Check. 9+12=219+12=21. Correct.

Answer. 99.

Exercise 8 Challenge

Mrs Hoa has 2727 apples and puts them into bags with 33 apples in each bag. She gives away 44 bags. How many apples does Mrs Hoa have left?

What you need and how to start

What you need: this problem has several steps: a division, a subtraction, then a multiplication.

Steps:

  1. Find how many bags there were at first: 27÷327\div 3.
  2. Find how many bags are left after giving away 44.
  3. Change the bags left into apples.
Show solution

At first there were 27÷3=927\div 3=9 (bags). After giving away 44 bags, 9−4=59-4=5 (bags) are left. The apples left are 3×5=153\times 5=15 (apples).

Check. She gave away 3×4=123\times 4=12 apples, and 27−12=1527-12=15. Correct.

Answer. 1515 apples.

Mini test

Mini test

Marked like the Vietnamese graduation exam: Part I 0.25 points per question; Part II up to 1 point per question (1, 2, 3, 4 correct statements give 0.1, 0.25, 0.5, 1 point); Part III 0.5 points per question.

Part I. Multiple choice

Question 1. 3×63\times 6 equals
Question 2. 27÷327\div 3 equals
Question 3. Which of these is correct?
Question 4. 1818 cakes are put into boxes with 33 cakes in each box. How many boxes are there?

Part II. True or false

Question 1. We know that 3×8=243\times 8=24. Look at these calculations.
a) 24÷3=824\div 3=8.
b) 3×9=24+63\times 9=24+6.
c) 3×7=24−33\times 7=24-3.
d) 24÷3=2124\div 3=21.

Part III. Short answer

Question 1. Ha puts flowers in vases, 33 in each vase. She fills 99 vases. How many flowers does Ha have altogether?

Question 2. A teacher shares 3030 sweets equally between 33 children. How many sweets does each child get?

Show answers and explanations
  1. Part I, question 1: B. 3×6=3×5+3=15+3=183\times 6=3\times 5+3=15+3=18. Option A is the mistake of adding 3+63+6 instead of multiplying.
  2. Part I, question 2: A. Since 3×9=273\times 9=27, we get 27÷3=927\div 3=9. Option B is the mistake of taking 27−327-3, and option D is 27+327+3.
  3. Part I, question 3: D. 3×9=3×8+3=24+3=273\times 9=3\times 8+3=24+3=27. The others should be 1212, 2121 and 1515.
  4. Part I, question 4: B. We make groups of 33: 18÷3=618\div 3=6 (boxes). Option A is 18−318-3, option C is 18+318+3 and option D is 18×318\times 3.
  5. Part II, question 1: a) True; b) False; c) True; d) False. a) True: from 3×8=243\times 8=24 we get 24÷3=824\div 3=8. b) False: 3×9=27=24+33\times 9=27=24+3. c) True: 3×7=21=24−33\times 7=21=24-3. d) False: 24÷3=824\div 3=8, and 2121 is the answer to 24−324-3.
  6. Part III, question 1: 27. 3×9=273\times 9=27 (flowers).
  7. Part III, question 2: 10. 30÷3=1030\div 3=10, because 3×10=303\times 10=30 (sweets).