Leaving out the × sign

The idea

The product of a number and a letter-number is written without the × sign, with the number first, so 4 × n is written 4n.

The table of 4

Look at the sequence 4, 8, 12, 16, 20, 24, 28, … These are the multiples of 4. The 3rd term is 4 × 3. The 29th term is 4 × 29.

*n* stands for any position. Which expression gives the term at position *n*?

• 4 × n
• n + 4
• 4 + n

Hide the × sign

Algebra is written in short. Tap each × to leave it out. Then change the number and check the value.

Number first, no ×

4 × n is shortened to 4n: skip the × and write the number first, then the letter. Every product in an expression shortens the same way.

4n does not mean 4 and then n. When *n* = 6, 4n is 4 × 6 = 24. It is not 46.

The product of a number and a letter-number is written without the × sign, with the number first: 4 × n is written 4n.

• Long | Short
• 4 × n | 4n
• n × 7 | 7n
• c × 35 + j × 60 | 35c + 60j
• 5 × m + 3 | 5m + 3

Notes

The product of a number and a letter-number is written without the × sign, with the number first: 4 × n is written 4n.

Check yourself

Write n × 9 the short way.

Find the value of 7k when *k* = 4.

Answer: 28

7k = 7 × 4 = 28.

Find the value of 5m + 3 when *m* = 2.

Answer: 13

5 × 2 + 3 = 10 + 3 = 13.

Which is the short way to write 3 × a + 8 × b?

• n9. The number goes first, then the letter.
• 9 × n. That is the long way. The × sign is left out in the short way.
• 9n — correct. Yes! No × sign, and the number comes first.
• 3a + 8b — correct. Yes! Each product shortens on its own.
• 38ab. Each product shortens on its own: 3a means 3 × a and 8b means 8 × b.
• a3 + b8. The number goes first, then the letter.