Writing an Expression
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Revision notes for Edexcel GCSE Maths Writing an Expression. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Writing an Expression

What you'll learn

  • What letters like xxx, mmm and ttt mean in algebra.
  • How to translate words such as more, less, half, twice and each.
  • How to write expressions for totals, costs, ages and amounts.
  • When to write an expression and when to write a formula.

1. Letters can stand for numbers

In algebra, we often use a letter when we do not know the number yet. The question is not asking you to find a final number — it is asking you to write the calculation using the letter.

Definition

Variable

A variable is a letter that stands for a number we do not know yet, or a number that can change. For example, if a price is xxx pounds, then xxx represents the price in pounds.

Definition

Expression

An expression is a mathematical phrase made from numbers, variables and operations. An operation is an action such as add, subtract, multiply or divide. An expression does not have an equals sign.

Definition

In terms of

If a question asks for an expression in terms of certain letters, your answer must use those letters.

Example: half of a price

Example

Half of a ticket price

  1. A full-price ticket has price ppp pounds.

  2. A reduced ticket costs half as much.

A full ticket price split into two equal halves shows that half the price is \frac{p}{2}.

  1. Half means divide by 2.

  2. So the reduced ticket price is p2\frac{p}{2}2p​ pounds.

Key Idea

No need to calculate

If the question gives a letter, your answer will usually still contain that letter. You are writing the rule, not finding one numerical answer.

2. Choosing add or subtract

Words are clues.

  • More than, older than and longer than usually mean add.
  • Less than, fewer than, younger than, eats or gives away usually mean subtract.

Example: more than

Example

More counters

  1. Ravi has mmm counters.

  2. Isla has 7 more counters than Ravi.

Ravi’s counters are represented by m, and Isla has the same amount plus 7 extra counters.

  1. “7 more” means add 7.

  2. Isla has m+7m + 7m+7 counters.

Example: taking some away

Example

Sweets eaten

  1. Aisha starts with nnn sweets.

  2. She eats 5 sweets.

Eating 5 sweets means removing 5 from the starting number n.

  1. Eating sweets means they are taken away, so subtract 5.

  2. Aisha now has n−5n - 5n−5 sweets.

Common Mistake

Subtraction order

For “13 years younger than nnn”, write n−13n - 13n−13, not 13−n13 - n13−n. Start with the original age, then take 13 away.

3. Multiplying by “each”, “per” and “times”

Per means “for each one”. If someone earns hhh pounds per hour, then each hour adds another hhh pounds.

In algebra, we usually miss out the multiplication sign. So 20h20h20h means 20 lots of hhh.

Other key words:

  • twice means multiply by 2
  • three times means multiply by 3
  • each often means multiply

Example: pay per hour

Example

Hourly pay

  1. A worker is paid www pounds for each hour.

  2. One week, the worker does 16 hours.

Sixteen hours means 16 lots of the hourly pay w.

  1. This means 16 lots of www.

  2. The total pay is 16w16w16w pounds.

Example: twice as old

Example

Twice an age

  1. Noah is aaa years old.

  2. His cousin is twice as old as Noah.

  3. Twice means multiply by 2.

  4. The cousin’s age is 2a2a2a years.

Tip

Writing multiplication

Write 16w16w16w, not 16×w16 \times w16×w, when giving your final algebra answer. Both mean the same thing, but 16w16w16w is the neat algebra form.

4. Dividing when you know the total

Sometimes you know the total amount of money and the cost of one item. To find how many items were bought, divide the total by the cost of one item.

Example: tickets sold

Example

Finding the number of tickets

  1. A club sells tickets for £5 each.

  2. The club takes RRR pounds altogether.

The total money R is split into equal £5 ticket prices, so the number of tickets is \frac{R}{5}.

  1. To find the number of tickets, divide the total money by 5.

  2. The number of tickets sold is R5\frac{R}{5}5R​.

Common Mistake

Multiplying instead of dividing

If each ticket costs £5 and the total money is known, you divide by 5. Multiplying would make the total money bigger, not find the number of tickets.

5. Adding parts for a total

A total means all the parts together. If there are different types of item, work out each part first, then add the parts.

Definition

Term

A term is one part of an expression, separated by add or subtract signs. In 3x+2y3x + 2y3x+2y, the terms are 3x3x3x and 2y2y2y.

Example: two different drinks

Example

Cost of drinks

  1. A juice costs jjj pounds and a hot chocolate costs hhh pounds.

The total cost is made from 4 juice costs and 3 hot chocolate costs added together.

  1. The cost of 4 juices is 4j4j4j.

  2. The cost of 3 hot chocolates is 3h3h3h.

  3. Add the two costs to get the total: 4j+3h4j + 3h4j+3h pounds.

Example: packs and items

Example

Counting packs and counting items

  1. A shop has sss small packs and bbb big packs.

The number of packs is different from the number of pens inside the packs.

  1. The total number of packs is just s+bs + bs+b.

  2. Each small pack contains 4 pens, so the small packs contain 4s4s4s pens.

  3. Each big pack contains 10 pens, so the big packs contain 10b10b10b pens.

  4. The total number of pens is 4s+10b4s + 10b4s+10b.

Common Mistake

Packs are not the same as items

s+bs + bs+b counts the number of packs. It does not count the number of individual items inside the packs.

6. Writing a formula

A formula is like an expression, but it includes an equals sign because it tells you what a named total is equal to.

Definition

Formula

A formula is an equation that connects variables. For example, if the total cost is called CCC, a formula starts with C=C =C=.

Example: total cost formula

Example

Cost in pence

  1. A muffin costs 80p and a cookie costs 50p.

  2. Someone buys mmm muffins and kkk cookies.

The total cost formula adds the muffin cost and the cookie cost.

  1. The muffin cost is 80m80m80m pence.

  2. The cookie cost is 50k50k50k pence.

  3. Write the formula for the total cost CCC:

    C=80m+50kC = 80m + 50kC=80m+50k

7. Combining simple expressions

Sometimes you add several expressions together, such as three people’s ages.

Definition

Like terms

Like terms have the same variable part. For example, nnn, nnn and nnn are like terms, so together they make 3n3n3n.

Example: total of three ages

Example

Adding ages

  1. Ben is nnn years old.

  2. Cara is 9 years older than Ben, so Cara is n+9n + 9n+9.

  3. Dan is 4 years younger than Ben, so Dan is n−4n - 4n−4.

  4. Add the three ages, then collect like terms:

    n+(n+9)+(n−4)=3n+5n + (n + 9) + (n - 4) = 3n + 5n+(n+9)+(n−4)=3n+5
Key Idea

Translate before simplifying

First write each part correctly from the words. Then, if you can, collect like terms to make the expression shorter.

Exam technique

In the exam

  1. Underline the word that tells you the operation: more, fewer, twice, half, each or total.

  2. Check the units: pounds, pence, minutes, marbles, packs or individual items.

  3. For totals, find the expression for each part first, then add them.

  4. If a total is named with a letter such as CCC, write a formula with an equals sign.

Self review

Check yourself

  • What expression means “8 more than xxx”?

  • If one box contains 6 rolls and there are ppp boxes, what does 6p6p6p represent?

  • Why is “10 years younger than nnn” written as n−10n - 10n−10?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

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Writing an Expression Revision Guide

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