If you are new to the introduction to algebra, then you are at the right place. You can take a look at algebra for Class 6 to polish your concepts for Class 6 Algebra Problems with Solutions . In this article, algebra problems have been solved for you.
Practice makes perfect. You, too, will become an expert in solving algebra after solving the problems in this article. In our previous topic, the link of which is above, the important principles and rules of algebra were explained in a good way. So that Class 6 students do not face any difficulty in solving problems. Now learn to simplify and solve algebra problems with us.
Class 6 Algebra Problems with Solutions containing different Properties
1. Commutative Property
In this property, we know that
In addition:
a+b=b+a
For multiplication:
ab=ba
Here are some questions about Class 6 Algebra Problems with Solutions containg Commutative Property.
1. Show that 8+3=3+8.
Solve:
8+3=3+8
11=11
2nd method:
8+3=3+8
8+3-3=3+8-3
8=8
2. Verify that 12+8=8+12
Solve:
12+8=8+12
20=20
2nd method:
12+8=8+12
12+8-8=8+12-8
12=12
3. Prove that x+5=5+x
Solve:
Let us put x=2
2+5=5+2
7=7
2nd method:
x+5=5+x
x+5-5=5+x-5
x=x
4. Prove that 5+5=5+5
Solve:
5+5=5+5
10=10
2nd method:
5+5=5+5
5+5-5=5+5-5
5=5
5. Verify that p+q=q+p.
Solve:
p+q=q+p
p+q-q=q+p-q
p=p
6. Check whether 7×3=3×7.
Solve:
7×3=3×7
21=21
7×3=3×7
7×3×1/3=3×1/3×7
7=7
7. Verify that 5×y=y×5.
Solve:
5×y=y×5
5y=5y
2nd method:
5×y×1/y=y×1/y×5
5=5
8. Show that x×y=y×x.
Solve:
x×y=y×x
xy=yx=xy
2nd method:
x×y=y×x
x×y×1/y=y×1/y×x
x=x
9. Prove that 1+m=m+1.
Solve:
1+m-m=m-m+1
1=1
10. Check whether 5×4=4×5.
Solve:
5×4=4×5
20=20
2nd method:
5×4=4×5
5×1/5×4=4×5×1/5
4=4
2. Associative Property
In this property,we know that
In addition:
a+(b+c)=(a+b)+c
For multiplication:
a(bc)=(ab)c
Here are some questions about Class 6 Algebra Problems with Solutions containg Associative Property.
1. Verify that (5+6)+7=5+(6+7).
Solve:
(5+6)+7=5+(6+7)
11+7=5+13
18=18
2. Check if (x+4)+5=x+(4+5).
Solve:
(x+4)+5=x+(4+5)
X+4+5=x+9
X+9=x+9
x-x+9=x-x+9
9=9
2nd method:
Let we put x=2,
(x+4)+5=x+(4+5)
(2+4)+5=2+(4+5)
6+5=2+9
11=11
3. Show that (7+6)+x=7+(6+x).
Solve:
(7+6)+x=7+(6+x)
13+x=7+6+x
13+x=13+x
13-13+x=13-13+x
x=x
2nd method:
Let us put x=2,
(7+6)+x=7+(6+x)
(7+6)+2=7+(6+2)
13+2=7+8
15=15
4. Verify that (x+y)+z=x+(y+z).
Solve:
(x+y)+z=x+(y+z)
x+y+z=x+y+z
2nd method:
Let we put x=2,y=1,z=3.
(x+y)+z=x+(y+z)
(2+1)+3=2+(1+3)
3+3=2+4
6=6
5. Verify that (2+1)+3=2+(1+3).
Solve:
(2+1)+3=2+(1+3)
3+3=2+4
6=6
6. Show that (3×2)×2=3×(2×2).
Solve:
(3×2)×2=3×(2×2)
6×2=3×4
12=12
7. Verify that (6×1)×2=6×(1×2).
Solve:
(6×1)×2=6×(1×2)
6×2=6×2
12=12
8. Show that (p×q)×r=p×(q×r).
Solve:
(p×q)×r=p×(q×r)
pq×r=p×qr
pqr=pqr
9. Verify that (5×1)×1=5×(1×1).
Solve:
(5×1)×1=5×(1×1)
5×1=5×1
5=5
10. Verify that (0×1)×1=0×(1×1).
Solve:
(0×1)×1=0×(1×1)
0×1=0×1
0=0
3. Distributive Property
Here are some questions about Class 6 Algebra Problems with Solutions containg Distributive Property.
1. Expand and simplify: 3(2+2).
Solve:
=3(2+2)
=3(4)
=12
2. Expand: 7(x+2).
Solve:
=7(x+2)
=7x+14
3. Show that a(b+c)=ab+ac.
Solve:
a(b+c)=ab+ac
ab+ac=ab+ac
4. Expand: 3(9+x).
Solve:
=3(9+x)
=27+3x
5. Simplify: 2(m+5).
Solve:
=2(m+5)
=2m+10
6. Expand: 2(p+6).
Solve:
=2(p+6)
=2p+12
7. Expand: 6(x+2).
Solve:
=6(x+2)
=6x+12
8. Show that x(y+z)=xy+xz.
Solve:
x(y+z)=xy+xz
xy+xz=xy+xz
9.Simplify: 5(3+k).
Solve:
=5(3+k)
=15+5k
10.Expand: 0(m+n).
Solve:
=0(m+n)
=0m+0n
=0+0
=0
4. Identity Property
In this property;
In addition:
a+0=a
0 is the additive identity.
For multiplication:
a×1=a
1 is the multiplicative identity.
Here are some questions about Class 6 Algebra Problems with Solutions containg Identity Property.
1.Show that 1+0=1.
Solve:
We know that:
a+0=a
Here a=1.
Therefore,
1+0=1
2. Verify that y+0=y.
Solve:
We know that:
a+0=a
Here a=y.
Therefore,
y+0=y
3. Show that p+0=p.
Solve:
We know that:
a+0=a
Here a=p.
Therefore,
p+0=p
4. Show that 5+0=5.
Solve:
We know that:
a+0=a
Here a=5.
Therefore,
5+0=5
5. Show that 15+0=15.
Solve:
We know that:
a+0=a
Here a=15.
Therefore,
15+0=15
6.Show that x×1=x.
Solve:
We know that:
a×1=a
Here a=x.
Therefore,
x×1=x
7.Show that 10×1=10.
Solve:
We know that:
a×1=a
Here a=10.
Therefore,
10×1=10
8. Show that p×1=p.
Solve:
We know that:
a×1=a
Here a=p.
Therefore,
p×1=p
9. Show that 2×1=2.
Solve:
We know that:
a×1=a
Here a=2.
Therefore,
2×1=2
10. Verify that z×1=z.
Solve:
We know that:
a×1=a
Here a=z.
Therefore,
z×1=z
5.Inverse Property
Additive Inverse: For any number a, a +(−a)=0
Multiplicative Inverse: For any nonzero number a, a×1/a=1
Here are some questions about Class 6 Algebra Problems with Solutions containg Inverse Property
1. Show that 5+(−5)=0.
Solve:
We know that:
a+(−a)=0
Here a=5.
Therefore,
5+(−5)=0
2. Verify that (-1)+1=0.
Solve:
We know that:
a+(−a)=0
Here a=1.
Therefore,
−1+1=0
3. Prove that p+(−p)=0.
Solve:
We know that:
a+(−a)=0
Here a=p.
Therefore,
p+(−p)=0
4. Prove that 10+(−10)=0.
Solve:
We know that:
a+(−a)=0
Here a=10.
Therefore,
10+(−10)=0
5. Prove that z+(−z)=0.
Solve:
We know that:
a+(−a)=0
Here a=z.
Therefore,
z+(−z)=0
6. Show that 5×1/5=1.
Solve:
We know that:
a×1/a=1
Here a=5.
Therefore,
5×1/5=1
7. Show that p×1/p=1.
Solve:
We know that:
a×1/a=1
Here a=p.
Therefore,
p×1/p=1
8. Show that 15×1/15=1.
Solve:
We know that:
a×1/a=1
Here a=15.
Therefore,
15×1/15=1
9. Show that z×1/z=1.
Solve:
We know that:
a×1/a=1
Here a=z.
Therefore,
z×1/z=1
10. Show that 3×1/3=1.
Solve:
We know that:
a×1/a=1
Here a=3.
Therefore,
3×1/3=1
Frequently Asked Questions about class 6 algebra problems
1. What is an example of an algebra problem?
An example of an algebra problem is:
Solve for x: 2x+5=10
2. Is algebra problem-solving?
Yes, Algebra is problem-solving.
3. Is algebra easy for students?
Algebra is easy for those who practice its problems and understand its concept
Conclusion about class 6 algebra problems
Algebra shows students how to use the symbols, rules, and properties of mathematics to solve easy-to-understand problems.By practicing different properties such as commutative, associative, distributive, identity, inverse, and zero, students are able to simplify expressions and equations and solve them step by step. Regular practice makes algebra perfect, easier, and builds a strong foundation for students’ higher mathematics.
Now you can practice algebra word problems for class 6 so that your concepts about algebra should be polish further.
