Page 5 - Matematica_Mathematics - Factorul comun_Common factor

Common (“Comun”) refers to something that belongs to several or all of them. We deduce, therefore,
that the common factor is that factor that belongs to all terms of an addition or subtraction.

Practice

2. Highlights the common factor in the examples:

• 8 × 4 − 8 × 3 • 2 × 6 + 2 × 10 • 4 × 6 + 6 × 8 • 9 × 5 − 5 × 2

In the example 3 × 4 + 3 × 7, we notice that we have a sum operation. The first item 3 × 4, and the
second one, 3 × 7. Both have in common factor 3. So, 3 is the common factor of this operation. In solving it
we will say that “we take out common factor on 3” (“scoatem factor comun pe 3”) or “we give common factor
on 3” („dăm factor comun pe 3”). The rest of the terms we will write in parenthesis and sum them up, because
we have not forgotten that we started from a sum operation.

3 × 4 + 3 × 7 = 3 × (4 + 7)

In the example 6 × 7 – 7 × 4, we give common
factor on 7 and between the other factors we will perform
the subtraction operation.

6 × 7 – 7 × 4 = 7 × (6 – 4)

We can give common factor in a multi-term operation.

5 × 7 + 8 × 5 – 5 × 5 + 10 × 5 = 5 × (7 + 8 – 5 + 10)

Practice

3. Calculate the results of the exercises by the common factor method.

• 5×8−8×4=

• 7×6+7×4=

• 34×10+86×10–10×20=