 # Change Missing Number Problems into Algebra (2)

In this worksheet, students express missing number problems algebraically. Key stage:  KS 2

Curriculum topic:   Maths and Numerical Reasoning

Curriculum subtopic:   Equations and Algebra

Difficulty level:   ### QUESTION 1 of 10

When we use algebra, we use letters to stand for numbers that we are trying to find.

Algebra is like a language with its own rules.

a stands for a number.

a + 2 is 2 more than the number.

a - 7 is 7 less than the number.

5a is 5 times the number. (N.B. We don't use the × sign in algebra because it looks like the letter x.)

a/4 or ¼a is a quarter of the number or the number divided by 4. (N.B. We don't use the ÷ sign in algebra.)

Example

I think of a number.

I double it and take away 5.

Then I add this to half the original number.

I get 20.

Write this using algebra.

Use n for the number I think of.

n is the number I think of.

Double it to get 2n.

Take away 5 to get 2n - 5.

Then add this to ½n to give 2n - 5 + ½n .

This equals 20.

So we write:

2n - 5 + ½n = 20

I think of a number.

I double it and add 5.

Then I add this to three times the original number.

I get 20.

Write this using algebra.

Use n for the number I think of.

5n + 3 = 20

5n - 5 = 20

2n + 5 + 3n = 20

20n - 5 = 3n

I think of a number.

I multiply it by 5 and add 2.

Then I take away 6.

I get 11.

Write this using algebra.

Use n for the number I think of.

6n - 5 = 11

2n + 5 - 6 = 11

5n + 2 - 6n = 11

5n + 2 - 6 = 11

I think of a number.

I treble it and subtract 2.

Then I add this to three times the original number.

I get 62.

Write this using algebra.

Use n for the number I think of.

3n - 2 + 3n = 62

3n + 5n = 62

3n + 62 = 3

3n + 62 = 3n

I think of a number.

I divide it by 5 and add 2.

Then I add this to twice the original number.

I get 24.

Write this using algebra.

Use n for the number I think of.

n/5 + 2 + 2n = 24

7n + 2n = 5

5n + 2 = 24

5n ÷ 24 = 2

I think of a number.

I divide it by 2 and add 2.

Then I add three times the original number.

I get 72.

Write this using algebra.

Use n for the number I think of.

½n + 2 + 3n = 72

n/2 - 2 = 72

3n + 2 = 72

2n + 72 = 3n

I think of a number.

I multiply it by 5 and subtract 5.

Then I take away three times the original number.

I get 19.

Write this using algebra.

Use n for the number I think of.

n/3 + 5 = 19

n/5 + 3 = 19

5n - 5 - 3n = 19

5n - 5 + 3n = 19

I think of a number.

I divide it by 3 and subtract 2.

Then I take away 3.

I get 2.

Write this using algebra.

Use n for the number I think of.

2n ÷ 3 - 3 = 2

n/3 + 2 = 2

3n + 2 = 3

n/3 - 2 - 3 = 2

I think of a number.

I divide it by 4 and add 4.

Then I add this to 4 times the original number.

I get 72.

Write this using algebra.

Use n for the number I think of.

n/4 - 72 + 4n = 4

4n + ¼ + 4n = 72

4n + 4 + 4 = 72

¼n + 4 + 4n = 72

I think of a number.

I divide it by 4 and add 12.

Then I add this to 12 times the original number.

I get 61.

Write this using algebra.

Use n for the number I think of.

¼n + 24n = 61

n/4 + 12 + 12n = 61

12n + 4 - 12n = 61

4n + 4 = 61

I think of a number.

I multiply it by 12 and add 12.

Then I take away a quarter of the original number.

I get 106.

Write this using algebra.

Use n for the number I think of.

12n - 12¼n = 106

12n + 12 - ¼n = 106

12n - 12 + ¼n = n

12n + 12 - ¼n = 106n

• Question 1

I think of a number.

I double it and add 5.

Then I add this to three times the original number.

I get 20.

Write this using algebra.

Use n for the number I think of.

2n + 5 + 3n = 20
EDDIE SAYS
• Question 2

I think of a number.

I multiply it by 5 and add 2.

Then I take away 6.

I get 11.

Write this using algebra.

Use n for the number I think of.

5n + 2 - 6 = 11
EDDIE SAYS
Five times n and add 2, then take away 6 to get 11.
• Question 3

I think of a number.

I treble it and subtract 2.

Then I add this to three times the original number.

I get 62.

Write this using algebra.

Use n for the number I think of.

3n - 2 + 3n = 62
EDDIE SAYS
Multiply n by 3 and subtract 2, then add 3n to get 62.
• Question 4

I think of a number.

I divide it by 5 and add 2.

Then I add this to twice the original number.

I get 24.

Write this using algebra.

Use n for the number I think of.

n/5 + 2 + 2n = 24
EDDIE SAYS
Divide n by 5 and add 2, then add 2n to get 24.
• Question 5

I think of a number.

I divide it by 2 and add 2.

Then I add three times the original number.

I get 72.

Write this using algebra.

Use n for the number I think of.

½n + 2 + 3n = 72
EDDIE SAYS
• Question 6

I think of a number.

I multiply it by 5 and subtract 5.

Then I take away three times the original number.

I get 19.

Write this using algebra.

Use n for the number I think of.

5n - 5 - 3n = 19
EDDIE SAYS
Five times n and subtract 5, then subtract 3n to get 19.
• Question 7

I think of a number.

I divide it by 3 and subtract 2.

Then I take away 3.

I get 2.

Write this using algebra.

Use n for the number I think of.

n/3 - 2 - 3 = 2
EDDIE SAYS
Divide n by 3 and subtract 2, then subtract 3 to get 2.
• Question 8

I think of a number.

I divide it by 4 and add 4.

Then I add this to 4 times the original number.

I get 72.

Write this using algebra.

Use n for the number I think of.

¼n + 4 + 4n = 72
EDDIE SAYS
Find a quarter of n and add 4, then add 4n to get 72.
• Question 9

I think of a number.

I divide it by 4 and add 12.

Then I add this to 12 times the original number.

I get 61.

Write this using algebra.

Use n for the number I think of.

n/4 + 12 + 12n = 61
EDDIE SAYS
Divide n by 4 and add 12, then add 12n to get 61.
• Question 10

I think of a number.

I multiply it by 12 and add 12.

Then I take away a quarter of the original number.

I get 106.

Write this using algebra.

Use n for the number I think of.

12n + 12 - ¼n = 106
EDDIE SAYS
12 times n and add 12, then take away ¼n to get 106.
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