Combining like terms
Add the number parts and keep the letter-number.
Pencil money for three days
The shop sold pencils on 3 days. The money was 5c, 3c and 10c rupees, where c is the price of one pencil.
How would you write the total money from pencils as one term?
What this lesson covers
The idea
Like terms are added into a single term by adding their number parts, which is the distributive property.
Pencil money for three days
The shop sold pencils on 3 days. The money was 5c, 3c and 10c rupees, where c is the price of one pencil.
How would you write the total money from pencils as one term?
- 18c
- 18 + c
- It cannot be written as one term
Count the area two ways
The width is the letter-number. Count the area part by part, and all at once. Change the width.
Add the number parts
5c is c added 5 times, 3c is c added 3 times and 10c is c added 10 times. So c is added 5 + 3 + 10 times in all. This is the distributive property of numbers.
5c + 3c + 10c = (5 + 3 + 10)c = 18c
Like terms are added into a single term by adding their number parts, which is the distributive property.
Notes
Like terms are added into a single term by adding their number parts, which is the distributive property: 5c + 3c + 10c = 18c.
Check yourself
5c + 3c + 10c is the same as ?c. What is the number?
Answer: 18
(5 + 3 + 10)c = 18c.
12n − 4n is the same as ?n. What is the number?
Answer: 8
(12 − 4)n = 8n.
What does 4v + 3v simplify to?
9x + x is the same as ?x. What is the number? (x means 1x.)
Answer: 10
(9 + 1)x = 10x.
- 7v — correct. Yes! (4 + 3)v = 7v.
- 12v. That multiplies 4 and 3. Like terms are added: 4 + 3.
- 7. The letter-number stays: 7v.