'The sum of 10 times n and 7' as an algebraic expression is □n + □. Fill in each blank

10, 7. 10 times n is 10n; then add 7: 10n + 7.

Without the × signs: 7 × x × 3 × x × x = □x^□ Fill in each blank

21, 3. Numbers together: 7 × 3 = 21; x multiplied 3 times is x^3. So it is 21x^3.

Share y into 7 equal parts, then take 3 from each. How much is each part now? A. 7/y − 3 B. (y − 3)/7 C. 7y − 3 D. y/7 − 3 Choose the right answer

D. y/7 − 3. Share first: y/7; then take away: y/7 − 3.

Algebraic expressions & sequences · Ages 12–13

Words into algebra

Turn each phrase into an operation; 'twice the sum' needs brackets.

How to do it

Method

Turn each phrase into an operation; 'twice the sum' needs brackets

Twice the sum of x and 3 = 2(x + 3)

Another way

Check with a number

Take x = 10: (10 + 3) × 2 = 26, 2(10 + 3) = 26

In full

Let a letter stand for the unknown number, then turn the words into operations one by one: '3 more' is + 3, '3 less' is − 3, 'twice' is × 2, 'shared into 4 equal parts' is ÷ 4. Watch the order: 'x minus 5' is x − 5, but '5 minus x' is 5 − x; 'twice x, plus 3' is 2x + 3, but 'twice the sum of x and 3' is 2(x + 3). The × sign can be dropped: 2 × x is written 2x, and x ÷ 4 is written x4. Or check with a number: take x = 10. Twice the sum of x and 3 is (10 + 3) × 2 = 26, and 2(x + 3) gives 26 as well, so it is right.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
'The sum of 10 times n and 7' as an algebraic expression is n + .
Fill in each blank
Show the answer and working
Answer: 10, 7
10 times n is 10n; then add 7: 10n + 7.
Example 2
Without the × signs: 7 × x × 3 × x × x = x^□
Fill in each blank
Show the answer and working
Answer: 21, 3
Numbers together: 7 × 3 = 21; x multiplied 3 times is x³. So it is 21x³.
Example 3
Share y into 7 equal parts, then take 3 from each. How much is each part now?
- A. 7y − 3
- B. y − 37
- C. 7y − 3
- D. y7 − 3
Choose the right answer
Show the answer and working
Answer: D. y7 − 3
Share first: y7; then take away: y7 − 3.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Take y away from 2. What is that as an algebraic expression?
- A. 2 − y
- B. 2y
- C. 2 + y
- D. y − 2
Choose the right answer
Answer:
2.'The sum of 5 times n and 13' as an algebraic expression is n + .
Fill in each blank
Answer:
3.9 times the sum of x and 2 can be written 9x + 2.
True or false?
Answer:
4.Share y into 7 equal parts, then take 2 from each. How much is each part now?
- A. y7 − 2
- B. 7y − 2
- C. y − 27
- D. 7y − 2
Choose the right answer
Answer:
5.Take 10 from y, then multiply by 6. With y = 9, the value is .
Answer:

All the answers

1. A. 2 − y
2. 5, 13
3. False
4. A. y7 − 2
5. −6

Free worksheet: Words into algebraWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

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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