If you have already learned algebra for class 6 well and practiced algebra problems, then now you will become capable of solving word problems easily, so let’s start.
Commutative Property (a + b = b + a, a × b = b × a) in Algebra Word Problems for Class 6
Q1. If someone buys two bags and uniforms, and the price of bag and uniform is 1000 and 500, respectively. You should show that the price of the bags or uniforms should be the same whether he buys the first uniform or the bags.
Solution:
Price of one bag=1000
Price of one uniform=500
By commutative property:
2(1000)+2(500)=2(500)+2(1000)
2000+1000=1000+2000
3000=3000
Hence proved.
2. A shopkeeper sells 4 kg of potatoes and 6 kg of tomatoes. You show that the weight of both the fruits is the same, and he wants to place an order.
Solution:
Weight of potatoes =4 kg
Weight of tomatoes = 6 kg
By commutative property:
Weight of potatoes + Weight of tomatoes=Weight of tomatoes+Weight of potatoes
4+6=6+4
10 = 10
3. You have 5 red bags and 12 blue bags. Show that the result of multiplication should be the same even if you change the order.
Solution:
Red bags=5
Blue bags=12
By commutative property:
Red bags × Blue bags = Blue bags × Red bags
5×12=12×5
60=60
4. A girl has 5 balls and 4 bats. Can the order change during multiplication or not?
Solution:
Balls = 5
Bats = 4
By commutative property:
Balls × Bats = Bats × Balls
5 × 4 = 4 × 5
20 = 20
Yes, in the commutative property, we can change the order and it will not change the result.
Hence, it is proved that there is no change if we change the order.
5. Prove that the order change of numbers in addition and multiplication doesn’t affect the result.
Solution:
Let 5 and 2 be any two numbers.
In addition:
5+2=2+5
7=7
In multiplication:
5×2=2×5
10=10
Hence proved.
Associative Property (a + b) + c = a + (b + c) in Algebra Word Problems for Class 6
- There are any three numbers. Show that grouping does not change the result.
Solution:
Let 2, 3, 4 be any three numbers.
By associative property:
In addition:
a + (b + c) = (a + b) + c
2+(3+4)=(2+3)+4
2+7=5+4
9=9
In multiplication:
a (bc) = (ab) c
2(3×4)=(2×3)4
2(12)=6(4)
24=24
2. You have 5 pencils, 2 pens, and 3 erasers. Show that the total number remains the same no matter how you group them.
Solution:
Pencils=5
Pens=2
Erasers=3
Pencils + (Pens + Erasers) = (Pencils + Pens) + Erasers
5+(2+3)=(5+2)+3
5+5=7+3
10=10
3. Show the associative property of multiplication on the numbers 3,6, and 9.
Solution:
By associative property:
In addition:
a + (b + c) = (a + b) + c
3+(6+9)=(3+6)+9
3+15=9+9
18=18
4. There are two bags, and each bag has 1 geometry box, and every geometry box has 5 pens. Use the associative property to find the total number of pens.
Solution:
By associative property:
a (bc) = (ab) c
2(1×5)=(2×1)5
2(5)=2(5)
10=10
5. A shopkeeper has two shops, and each shop has 10 racks, and each rack has 10 shoes. Find total number of shoes by associative property.
Solution:
By associative property:
a (bc) = (ab) c
2(10×10)=(2×10)10
2(100)=20(10)
200=200
Distributive Property (a(b + c) = ab + ac) in Algebra Word Problems for Class 6
- There are three numbers. Show that the distribution does not change the result.
Solution:
Let 2, 3, 4 be any three numbers.
By distributive property:
a (b + c) = (ab + ac)
2(3+4)=((2×3)+(2×4))
2(7)=(6+8)
14=14
2. A boy purchases 5 books and notebooks. The price of the book is Rs 100, and the price of the notebook is Rs 50. Calculate the total by distributive property.
Solution:
By distributive property:
a (b + c) = (ab + ac)
5(100+50)=((5×100)+(5×50))
5(150)=500+250
750=750
3. A shopkeeper sells 5 packs of cold drinks and juices. The price of one pack of cold drinks is 500, and the price of a pack of juices is 400. Find the total.
Solution:
By distributive property:
a (b + c) = (ab + ac)
5(500+400)=((5×500)+(5×400))
5(900)=2500+2000
4500=4500
4. Show that the distribution of numbers gives the same result.
Solution:
Let x, y, and z be any numbers.
By distributive property:
x (y + z) = (xy + xz)
5. Apply the distributive property on 5, 4, 3.
Solution:
By distributive property:
5 (4 + 3) = (5×4 + 5×3)
5(7)=20+15
35=35
Identity Property (a + 0 = a, a × 1 = a) in Algebra Word Problems for Class 6
- There is a number like 5. If you add 0 to it, then it will increase or decrease?
Solution:
Identity Property:
a + 0 = a
5+0=5
Hence, it will remain the same after adding 0.
2. If you have 10 pencils and there is no addition. Then how many pencils do you have?
Solution:
Identity Property:
a + 0 = a
10+0=10
3. You have 7 toys, and there is no addition in your rack. What’s the total of your toys?
Solution:
Identity Property:
a + 0 = a
7+0=7
4. Is there any change in the number after multiplying by 1?
Solution:
Let there be a number 6.
Identity Property:
a×1=a
6×1=6
5. What is the Identity Property in multiplication?
Solution:
Identity Property:
a×1=a
Inverse Property (a + (–a) = 0, a × (1/a) = 1) in Algebra Word Problems for Class 6
- You have 5 candies and you give all to your brother. How much you have?
Solution:
Inverse Property:
a + (–a) = 0
5 + (–5) = 0
5-5=0
2. You have 8 toys and you lost them. Then, how much do you have?
Solution:
Inverse Property:
a + (–a) = 0
8 + (–8) = 0
8-8=0
3. If there is a number and you add its opposite. What’s the result?
Solution:
Let a be any number.
Inverse Property:
a + (–a) = 0
4. If there is a number and you multiply its inverse. What’s the result?
Solution:
Let a is any number and 1/a is its inverse.
Inverse Property:
a × (1/a) = 1
5. State the inverse property.
Solution:
Inverse Property:
a × (1/a) = 1
FAQs on Algebra Word Problems for Class 6 Students
Q1: What is the easiest way to understand algebra word problems for Class 6 students?
The easiest way is to understand concepts of properties and practice daily.
Q2: Why are word problems important in algebra?
It helps students to make concepts clear.
Q3: Which properties of algebra should Class 6 students know?
Commutative, Associative, Distributive, Identity, and Inverse properties.
Q4: Are algebra word problems for Class 6 difficult for beginners?
No, if students first understand the property and then solve step by step, algebra word problems become very easy.
Conclusion on Algebra Word Problems for Class 6
Algebra is not just a game of numbers but it is also about solving real-world problems by using these properties. After learning the Algebra Word Problems for Class 6, the students will be able to grasp algebra and these concepts will be polished more in the higher classes. Practicing these 20 Algebra Word Problems for Class 6 will make algebra easy, full of fun for you and your interest will be generated.
