Creating and Manipulating Algebraic Expressions - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Algebraic Expressions.

Siblings

KS 2 & 3 Short Challenge Level:

Weekly Problem 17 - 2013
Anna has 3 brothers and 5 sisters. What is the product of the number of brothers and number of sisters that her brother Tom has?

Kangaroo Subtraction

KS 2 & 3 Short Challenge Level:

Weekly Problem 2 - 2010
Can you solve this 'KANGAROO' alphanumeric subtraction?

Gender Balance

KS 3 Short Challenge Level:

Weekly Problem 36 - 2012
Can you work out how many more boys are in group 1 than girls are in group 2?

Knitting Scarves

KS 3 Short Challenge Level:

Weekly Problem 43 - 2008
A knitted scarf uses three balls of wool. How many balls of wool do I have at the end of the day?

The Square of My Age

KS 3 Short Challenge Level:

Weekly Problem 34 - 2011
Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

Inspector Remorse

KS 3 Short Challenge Level:

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

Refuelling

KS 3 Short Challenge Level:

Weekly Problem 12 - 2009
A car can go r miles on s gallons of petrol. How many gallons of petrol would it need for a journey of t miles?

Forming Groups

KS 3 Short Challenge Level:

Weekly Problem 34 - 2006
Seventy pupils are divided into two groups. Can you work out the differnece between the number of boys in group 1 and the number of girls in group 2?

Four or Five

KS 3 Short Challenge Level:

Weekly Problem 19 - 2012
The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Petrol Prices

KS 3 Short Challenge Level:

Weekly Problem 28 - 2009
How much does $u$ litres of unleaded cost in terms of the cost per litre of 4 star petrol?

Multiple Magic

KS 3 Short Challenge Level:

Weekly Problem 31 - 2009
Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

No Matter

KS 3 Short Challenge Level:

Weekly Problem 2 - 2013
After performing some operations, what number is your answer always a multiple of?

Rectangle Cutting

KS 3 Short Challenge Level:

Weekly Problem 50 - 2009
Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?

KS 3 Short Challenge Level:

Weekly Problem 35 - 2013
The hour hand on the Mad Hatter's watch moves normally, but the minute hand moves too fast! When will it next show the correct time?

Painting the Forth Bridge

KS 3 Short Challenge Level:

Weekly Problem 14 - 2006
Given the rates at which men can paint, how long will it take them to paint the Forth Bridge?

Punky Fish

KS 3 & 4 Short Challenge Level:

Weekly Problem 12 - 2008
A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Building Up

KS 3 & 4 Short Challenge Level:

Weekly Problem 16 - 2015
In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

Reciprocal Values

KS 3 & 4 Short Challenge Level:

Weekly Problem 28 - 2010
Manipulate one algebraic fraction to solve another.

Integer and Integer

KS 3 & 4 Short Challenge Level:

Weekly Problem 39 - 2012
For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Divide and Conquer

KS 3 & 4 Short Challenge Level:

Weekly Problem 23 - 2015
Can you simplify this algebraic expression with many divisions?

Largest Expression

KS 3 & 4 Short Challenge Level:

Weekly Problem 36 - 2006
Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Beans Eating Beans

KS 3 & 4 Short Challenge Level:

Weekly Problem 13 - 2007
The Bean family are very particular about beans. At every meal all Beans eat some beans... At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?

Square and Cube

KS 3 & 4 Short Challenge Level:

Weekly Problem 24 - 2014
The square of a positive number is twice as big as the cube of that number. What is the number?

Crime Figures

KS 3 & 4 Short Challenge Level:

Weekly Problem 34 - 2007
Inspector Remorse had a difficult year in 2004. Find the percentage change in the number of cases solved in 2004 compared with 2003.

Relative Time

KS 3 & 4 Short Challenge Level:

Weekly Problem 25 - 2014
Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

Nine in a Line

KS 3 & 4 Short Challenge Level:

Weekly Problem 9 - 2008
The sum of 9 consecutive positive whole numbers is 2007. What is the difference between the largest and smallest of these numbers?

Pyramidal N-gon

KS 3 & 4 Short Challenge Level:

Weekly Problem 43 - 2014
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

Repeat Product

KS 3 & 4 Short Challenge Level:

Weekly Problem 3 - 2014
Can you work out the value of P+Q+R in the multiplication shown?