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There are **228** NRICH Mathematical resources connected to **Multiplication and division**, you may find related items under Calculations and numerical methods.

Problem
Primary curriculum
Secondary curriculum
### Integrated Product Sudoku

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Longer, Making Shorter

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing Garlic

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's in the Box?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Magic Potting Sheds

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Potting Sheds

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Product Sudoku

The clues for this Sudoku are the product of the numbers in adjacent squares.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Little Man

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Are You Well Balanced?

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### An Easy Way to Multiply by 10?

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Orange Drink

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fair Feast

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lots of Lollies

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Share Bears

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Peaches Today, Peaches Tomorrow...

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trebling

Can you replace the letters with numbers? Is there only one solution in each case?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Is Quicker?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Largest Product

Which set of numbers that add to 100 have the largest product?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Remainders

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cubes Within Cubes

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multiplication Squares

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Goodness Sake

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Tomato and the Bean

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Super Shapes

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Age 7 to 11

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Amy's Dominoes

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pumpkin Pie Problem

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Forgot the Numbers

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Make 100

Find at least one way to put in some operation signs to make these digits come to 100.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Highest and Lowest

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Rules - OK

Can you produce convincing arguments that a selection of statements about numbers are true?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Funny Factorisation

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Expenses

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Puzzling Sweet Shop

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Catrina's Cards

How would you find out how many football cards Catrina has collected?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Amazing Splitting Plant

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Plant

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Age 7 to 11

Challenge Level