Algebraic expressions & sequences · Ages 12–13
Reading algebra as words
The step worked out last sets how it reads.
How to do it
Method
The step worked out last sets how it reads
3(x + 5): 3 times the sum of x and 5
Another way
Put in a number and follow the steps
x = 2: 2 + 5 = 7, 7 × 3 = 21
In full
To read an expression, find the step worked out last: it sets the shape of the sentence. 3x + 5: times first, then plus, so the last step is plus: '3 times x, plus 5'. 3(x + 5): the bracket first, then times, so '3 times the sum of x and 5'. x − 24: divide last, so 'x minus 2, then divided by 4'. In a situation, the number with the letter says how much each one is, and a number alone is the fixed part: n books at $8 each plus $5 postage is 8n + 5. Or put in a number, work in order and say each step you did: with x = 2, 3(x + 5) is 2 + 5 = 7, then times 3, so '3 times the sum'.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
n books cost 87n + 15 dollars in all: each book is $, and postage is $ on top.
Fill in each blank
Show the answer and working
Answer: 87, 15
The 87 multiplying n is the price of each book; the 15 alone doesn't change with n, so it is the fixed postage.
Example 2
How does x − 28 read in words?
- A. x minus 28
- B. 28 times x
- C. 28 minus x
- D. x divided by 28
Choose the right answer
Show the answer and working
Answer: A. x minus 28
x − 28 starts from x and takes away 28.
Example 3
May has x dollars and buys 5 notebooks at y dollars each. What does x − 5y stand for?
- A. The total cost of 5 notebooks
- B. How much more 5 notebooks cost than x dollars
- C. The price of one notebook
- D. The money May has left after buying them
Choose the right answer
Show the answer and working
Answer: D. The money May has left after buying them
5y is what the 5 notebooks cost; taken from May's x dollars, it leaves the money remaining.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.How does 4x + 9 read in words?
- A. 9 times x, plus 4
- B. 4 times x, plus 9
- C. 4 times the sum of x and 9
- D. 9 times the sum of x and 4
Choose the right answer
Answer:
2.8x3 means 8 times x to the power 3.
True or false?
Answer:
3.How does 7x − 16 read in words?
- A. x minus 1, times 7, then divided by 6
- B. x times 7, minus the quotient of 1 divided by 6
- C. 6 divided by the difference of x times 7 and 1
- D. x times 7, minus 1, then divided by 6
Choose the right answer
Answer:
4.A pen costs x dollars and a notebook y dollars. What does 6x + 9y stand for?
- A. The total for 15 pens
- B. The total for 9 pens and 6 notebooks
- C. How much more 6 pens cost than 9 notebooks
- D. The total for 6 pens and 9 notebooks
Choose the right answer
Answer:
5.Ka-yan has x dollars and buys 7 notebooks at y dollars each. What does x − 7y stand for?
- A. The money Ka-yan has left after buying them
- B. The price of one notebook
- C. The total cost of 7 notebooks
- D. How much more 7 notebooks cost than x dollars
Choose the right answer
Answer:
All the answers
- 1. B. 4 times x, plus 9
- 2. True
- 3. D. x times 7, minus 1, then divided by 6
- 4. D. The total for 6 pens and 9 notebooks
- 5. A. The money Ka-yan has left after buying them
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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