'The sum of 7 times n and 16' as an algebraic expression is □n + □. Fill in each blank

7, 16. 7 times n is 7n; then add 16: 7n + 16.

When x = 9, 5x + 9 = □

54. Put the × back: 5 × 9 + 9 = 45 + 9 = 54.

141. Put 16 for n: 8 × 16 + 13 = 128 + 13 = 141.

Algebraic expressions · Ages 12–13

From “Words into algebra” to “Growing patterns and the n-th term”, step by step, each skill with its methods, worked examples and answers.

Words into algebraTurn each phrase into an operation; 'twice the sum' needs brackets
MethodTwice the sum of x and 3 = 2(x + 3)
Another way: Check with a numberTake x = 10: (10 + 3) × 2 = 26, 2(10 + 3) = 26
Situations into algebraWork it once with real numbers, then swap in the letter
Method$8 each, 3 books: 8 × 3; n books: 8n dollars
Another way: Start from the relationshipTotal = price × quantity = 8 × n = 8n
Reading algebra as wordsThe step worked out last sets how it reads
Method3(x + 5): 3 times the sum of x and 5
Another way: Put in a number and follow the stepsx = 2: 2 + 5 = 7, 7 × 3 = 21
Substitution and input–output machinesSwap in the number and put back the ×; to go back, do the opposite
Method2x + 3, x = 4: 2 × 4 + 3 = 11
Another way: Backwards for the inputOutput 11: 11 − 3 = 8, 8 ÷ 2 = 4
Patterns in sequencesLook at neighbours: same gap, same multiple, or the sum of the two before
Method3, 7, 11, 15: add 4 each time, next 15 + 4 = 19
Another way: Write out the gaps1, 3, 6, 10: gaps 2, 3, 4, next 10 + 5 = 15
Growing patterns and the n-th termFrom term 1 to term n, only n − 1 additions
Method3 + (n − 1) × 4 = 4n − 1
Another way: Compare with multiples4, 8, 12, 16 each less 1: 3, 7, 11, 15, so 4n − 1

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Words into algebra →
'The sum of 7 times n and 16' as an algebraic expression is n + .
Fill in each blank
Show the answer and working
Answer: 7, 16
7 times n is 7n; then add 16: 7n + 16.
Example 2Substitution and input–output machines →
When x = 9, 5x + 9 =
Show the answer and working
Answer: 54
Put the × back: 5 × 9 + 9 = 45 + 9 = 54.
Example 3Growing patterns and the n-th term →
The n-th term of a sequence is 8n + 13. Term 16 is .
Show the answer and working
Answer: 141
Put 16 for n: 8 × 16 + 13 = 128 + 13 = 141.

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