# Resources tagged with: Multiplication & division

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### There are 135 results

Broad Topics > Calculations and Numerical Methods > Multiplication & division

### Like Powers

##### Age 11 to 14 Challenge Level:

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

### Slippy Numbers

##### Age 11 to 14 Challenge Level:

The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.

##### Age 11 to 14 Challenge Level:

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

### As Easy as 1,2,3

##### Age 11 to 14 Challenge Level:

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

##### Age 11 to 14 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

##### Age 11 to 14 Challenge Level:

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

### Super Shapes

##### Age 7 to 11 Short Challenge Level:

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

### Difficulties with Division

##### Age 5 to 11

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

### Divide it Out

##### Age 7 to 11 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

### Repeaters

##### Age 11 to 14 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

### Ducking and Dividing

##### Age 7 to 11 Challenge Level:

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

### Oh! Hidden Inside?

##### Age 11 to 14 Challenge Level:

Find the number which has 8 divisors, such that the product of the divisors is 331776.

##### Age 7 to 14 Challenge Level:

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

### What Two ...?

##### Age 7 to 11 Short Challenge Level:

56 406 is the product of two consecutive numbers. What are these two numbers?

### A Mixed-up Clock

##### Age 7 to 11 Challenge Level:

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?

### 3388

##### Age 11 to 14 Challenge Level:

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

### Two Many

##### Age 11 to 14 Challenge Level:

What is the least square number which commences with six two's?

### Sept03 Sept03 Sept03

##### Age 7 to 11 Challenge Level:

This number has 903 digits. What is the sum of all 903 digits?

### Largest Number

##### Age 11 to 14 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

### Being Resilient - Primary Number

##### Age 5 to 11 Challenge Level:

Number problems at primary level that may require resilience.

### Bundles of Cubes

##### Age 7 to 11 Challenge Level:

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

### Clever Santa

##### Age 7 to 11 Challenge Level:

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

### A One in Seven Chance

##### Age 11 to 14 Challenge Level:

What is the remainder when 2^{164}is divided by 7?

### Surprising Split

##### Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

### What Is Ziffle?

##### Age 7 to 11 Challenge Level:

Can you work out what a ziffle is on the planet Zargon?

### Learning Times Tables

##### Age 5 to 11 Challenge Level:

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

### 1, 2, 3, 4, 5

##### Age 7 to 11 Challenge Level:

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

### Square Subtraction

##### Age 7 to 11 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

### Escape from the Castle

##### Age 7 to 11 Challenge Level:

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

### It Was 2010!

##### Age 5 to 11 Challenge Level:

If the answer's 2010, what could the question be?

### Skeleton

##### Age 11 to 14 Challenge Level:

Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.

### Today's Date - 01/06/2009

##### Age 5 to 11 Challenge Level:

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

### Function Machines

##### Age 7 to 11 Challenge Level:

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

### Month Mania

##### Age 5 to 11 Challenge Level:

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

##### Age 7 to 11 Challenge Level:

Use the information to work out how many gifts there are in each pile.

### Dice and Spinner Numbers

##### Age 7 to 11 Challenge Level:

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

### Tom's Number

##### Age 7 to 11 Challenge Level:

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

### Cows and Sheep

##### Age 7 to 11 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

### X Is 5 Squares

##### Age 7 to 11 Challenge Level:

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

### Machines

##### Age 7 to 11 Challenge Level:

What is happening at each box in these machines?

### The Pied Piper of Hamelin

##### Age 7 to 11 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### Looking at Lego

##### Age 7 to 11 Challenge Level:

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

### The Remainders Game

##### Age 7 to 14 Challenge Level:

Play this game and see if you can figure out the computer's chosen number.

### Rabbits in the Pen

##### Age 7 to 11 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

### Napier's Bones

##### Age 7 to 11 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

### Odds and Threes

##### Age 7 to 11 Challenge Level:

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

### Penta Post

##### Age 7 to 11 Challenge Level:

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

### One Million to Seven

##### Age 7 to 11 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

### Clock Face

##### Age 7 to 11 Challenge Level:

Where can you draw a line on a clock face so that the numbers on both sides have the same total?