# The Distributive Law in Addition (numbers <20)

In this worksheet, students use the distributive law in addition.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Use Relationships Between Operations

Difficulty level:

### QUESTION 1 of 10

In this worksheet, we use the distributive law for addition.

Example

Work out the values of A, B, C and D.

5×3 + 5×4 =
 A
+
 B
=
 C

5×(3 + 4) =
 D

A = 15
B = 20
C = 35
D = 35

This means that    5 x 3 + 5 x 4   is the same as   5 x (3 + 4)

This is the DISTRIBUTIVE LAW.

NB.  Do not then confuse this with the commutative law, so please ensure that you put as an answer:

5 x (3 + 4) and not 5 x (4 + 3) even though they are equal

Solve the following equation for A, B and C.

6 × 2 + 6 × 3 = 6 × (
 A
+
 B
)   =
 C
 2 3 15 25 30 A B C

Solve the following equation for A, B and C.

8 × 6 + 8 × 4 = 8 × (
 A
+
 B
)   =
 C
 2 4 6 20 80 A B C

Solve the following equation for A, B and C.

7 × 7 + 7 × 3 = 7 × (
 A
+
 B
)   =
 C
 2 3 7 35 70 A B C

Solve the following equation for A, B and C.

2 × 3 + 2 × 7 = 2 × (
 A
+
 B
)   =
 C
 2 3 7 10 20 A B C

Solve the following equation for A, B and C.

7 × 7 + 7 × 4 = 7 × (
 A
+
 B
)   =
 C
 4 7 11 33 77 A B C

Solve the following equation for A, B and C.

3 × 9 + 3 × 3 = 3 × (
 A
+
 B
)   =
 C
 3 9 12 24 36 A B C

Solve the following equation for A, B and C.

8 × 3 + 8 × 5 = 8 × (
 A
+
 B
)   =
 C
 3 5 8 46 64 A B C

Solve the following equation for A, B and C.

6 × 7 + 6 × 5 = 6 × (
 A
+
 B
)   =
 C
 5 7 12 63 72 A B C

Solve the following equation for A, B and C.

5 × 7 +5 × 5 = 5 × (
 A
+
 B
)   =
 C
 5 7 12 30 60 A B C

Solve the following equation for A, B and C.

9 × 7 + 9 × 3 = 9 × (
 A
+
 B
)   =
 C
 3 7 9 10 90 A B C
• Question 1

Solve the following equation for A, B and C.

6 × 2 + 6 × 3 = 6 × (
 A
+
 B
)   =
 C
 2 3 15 25 30 A B C
EDDIE SAYS
If you are struggling look back at the introduction. A in this instance is 2 as this is the second number in the first sum B is 3 as this is the second number in the second sum. C is 6 x 5 (3+2) which is 30. How did you do?
• Question 2

Solve the following equation for A, B and C.

8 × 6 + 8 × 4 = 8 × (
 A
+
 B
)   =
 C
 2 4 6 20 80 A B C
EDDIE SAYS
Let's repeat the same process that we did before. To find A we look for the second number in the first sum. This makes A = 6 To find B, we look for the second number in the second sum. This makes B = 4 To find C we simply need to complete the sum 8 x 10 (6+4) = 80. So, C = 80 Are you starting to get the hang of this?
• Question 3

Solve the following equation for A, B and C.

7 × 7 + 7 × 3 = 7 × (
 A
+
 B
)   =
 C
 2 3 7 35 70 A B C
EDDIE SAYS
Are you feeling happier with this now? A = 7 (this is the second number in the first sum) B = 3 (this is the second number in the second sum) C = 7 x 10 (7+3) = 70
• Question 4

Solve the following equation for A, B and C.

2 × 3 + 2 × 7 = 2 × (
 A
+
 B
)   =
 C
 2 3 7 10 20 A B C
EDDIE SAYS
Ok, you know what to do now. We look for the second number in the first sum to work out A. A = 3 To find out B we look to the second number in the second sum. B = 7 For C, we are now going to complete the sum. 2 x 10 (3+7) = 20 How did you do?
• Question 5

Solve the following equation for A, B and C.

7 × 7 + 7 × 4 = 7 × (
 A
+
 B
)   =
 C
 4 7 11 33 77 A B C
EDDIE SAYS
The more you do the easier this gets, right? Start with finding A. Look to the second number of the first sum. A = 7 For B, we are looking at the second number in the second sum which is 4. B = 4. So, now C must be the answer to 7 x 11 (7 + 4) = 77
• Question 6

Solve the following equation for A, B and C.

3 × 9 + 3 × 3 = 3 × (
 A
+
 B
)   =
 C
 3 9 12 24 36 A B C
EDDIE SAYS
You've got this now... Just put the system into place and you should have no problem here! A = 9 B = 3 C = 3 x 12(9 +3) = 36
• Question 7

Solve the following equation for A, B and C.

8 × 3 + 8 × 5 = 8 × (
 A
+
 B
)   =
 C
 3 5 8 46 64 A B C
EDDIE SAYS
Here we go... A = 3 B = 5 C = 8 x 8 (3+5) = 64 Remember to get to the answer for C you need to first add the number from A to B so in this case, it is 3 + 5 which gives a total of 8. Don't forget this step, it's really important!
• Question 8

Solve the following equation for A, B and C.

6 × 7 + 6 × 5 = 6 × (
 A
+
 B
)   =
 C
 5 7 12 63 72 A B C
EDDIE SAYS
Ok, nearly there! You know what to do now. A = 7 B = 5 C = 6 x 12 = 72 Did you get this right?
• Question 9

Solve the following equation for A, B and C.

5 × 7 +5 × 5 = 5 × (
 A
+
 B
)   =
 C
 5 7 12 30 60 A B C
EDDIE SAYS
Just apply the system... A = 7 B = 5 C = 5 x 12 = 60 Your confidence must be sky high!
• Question 10

Solve the following equation for A, B and C.

9 × 7 + 9 × 3 = 9 × (
 A
+
 B
)   =
 C
 3 7 9 10 90 A B C
EDDIE SAYS
Last question here we go! A = 7 B = 3 C = 9 x 10 = 90 That's another activity achieved, well done!
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started