Year 7 Maths: Write Equivalent Expressions Using Properties

What are Equivalent Expressions?

Equivalent expressions are different ways of writing the same mathematical idea. For example, the expressions $$2 + 3$$ and $$5$$ are equivalent because they both represent the same value.

Why is This Important?

Understanding equivalent expressions is important because it helps us simplify math problems and make them easier to solve. It also shows us that there are often many ways to reach the same answer!

Key Properties of Mathematics

Let’s look at some key properties that help us write equivalent expressions.

1. Commutative Property

The commutative property says that you can change the order of numbers when adding or multiplying, and the result will be the same.

Example:

• $$3 + 4 = 4 + 3$$
• $$2 \times 5 = 5 \times 2$$

2. Associative Property

The associative property tells us that when adding or multiplying, the way we group numbers does not change the result.

Example:

• $$(2 + 3) + 4 = 2 + (3 + 4)$$
• $$(1 \times 2) \times 3 = 1 \times (2 \times 3)$$

3. Distributive Property

The distributive property helps us multiply a single term by terms inside a bracket.

Example:

• $$3(2 + 4) = 3 \times 2 + 3 \times 4$$
• $$5(x + 2) = 5x + 10$$

Tips and Tricks

• Practice Makes Perfect: The more you practice, the easier it becomes to see equivalent expressions.
• Draw It Out: Sometimes drawing a diagram can help you understand how expressions relate to each other.
• Check Your Work: Always simplify your expressions to see if they match.

Questions

Easy Level Questions

1. Simplify: $$2 + 3$$
2. Simplify: $$4 + 5$$
3. Write an equivalent expression for: $$7 + 2$$
4. Simplify: $$6 + 1 + 2$$
5. Write an equivalent expression for: $$5 \times 2$$
6. Simplify: $$3 + 3$$
7. Write an equivalent expression for: $$8 – 3 + 3$$
8. Simplify: $$1 + 9$$
9. Write an equivalent expression for: $$2(3 + 4)$$
10. Simplify: $$10 + 5 – 5$$
11. Write an equivalent expression for: $$12 + 8$$
12. Simplify: $$0 + 6$$
13. Write an equivalent expression for: $$2 + 3 + 2$$
14. Simplify: $$1 + 1 + 1 + 1$$
15. Write an equivalent expression for: $$5 + 5 + 5$$
16. Simplify: $$2 \times 3$$
17. Write an equivalent expression for: $$7 + 1 + 2$$
18. Simplify: $$15 – 5 + 5$$
19. Write an equivalent expression for: $$9 – 4 + 4$$
20. Simplify: $$5 + 5$$

Medium Level Questions

1. Write an equivalent expression for: $$3 + 5 + 2$$
2. Use the distributive property: Simplify $$4(2 + 3)$$
3. Simplify: $$2 \times (3 + 5)$$
4. Write an equivalent expression for: $$9 + 4 – 4$$
5. Use the associative property: Simplify $$2 + (3 + 4)$$
6. Write an equivalent expression for: $$5(1 + 4)$$
7. Simplify: $$12 + 6 – 6$$
8. Write an equivalent expression for: $$10 + 0$$
9. Use the distributive property: Simplify $$3(4 + 2)$$
10. Write an equivalent expression for: $$8 + (2 + 1)$$
11. Simplify using the commutative property: $$7 + 3$$
12. Write an equivalent expression for: $$4 + 4 + 4$$
13. Use the associative property: Simplify $$1 + 2 + 3$$
14. Write an equivalent expression for: $$6(2 + 1)$$
15. Simplify: $$5 + 3 + 7 – 3$$
16. Write an equivalent expression for: $$10 – 2 + 2$$
17. Use the distributive property: Simplify $$2(3 + 5)$$
18. Write an equivalent expression for: $$20 – 10 + 10$$
19. Simplify: $$2 + 3 + 5 – 3$$
20. Write an equivalent expression for: $$5 + (7 – 3)$$

Hard Level Questions

1. Simplify using the distributive property: $$2(3 + 4 + 1)$$
2. Write an equivalent expression for: $$4(5 + 2)$$
3. Use the associative property: Simplify $$3 + (2 + 4) + 1$$
4. Write an equivalent expression for: $$3(2 + 3 + 1)$$
5. Simplify using the commutative property: $$1 + 5 + 2$$
6. Write an equivalent expression for: $$6 + 2(3 + 1)$$
7. Use the distributive property: Simplify $$5(2 + 3 + 1)$$
8. Write an equivalent expression for: $$4 + 2(3 + 5)$$
9. Simplify: $$7 + (2 + 6) – 6$$
10. Write an equivalent expression for: $$9(1 + 2)$$
11. Simplify using the associative property: $$1 + (2 + 3 + 4)$$
12. Write an equivalent expression for: $$2(3 + 2 + 5)$$
13. Use the commutative property: Simplify $$10 + 0 + 5$$
14. Write an equivalent expression for: $$5 + 5 + 5 + 5$$
15. Simplify: $$10 – (3 – 3) + 2$$
16. Write an equivalent expression for: $$4(2 + 3) + 4$$
17. Use the distributive property: Simplify $$3(4 + 2 + 1)$$
18. Write an equivalent expression for: $$8 + 4(1 + 1)$$
19. Simplify: $$5 + (3 + 2) + (1 + 2)$$
20. Write an equivalent expression for: $$10(1 + 1) – 5$$

Answers

Easy Level Answers

1. $$5$$. This is the result of adding 2 and 3.
2. $$9$$. This is the sum of 4 and 5.
3. $$9$$. Adding 7 and 2 gives the same total.
4. $$9$$. Adding up 6, 1, and 2 gives 9.
5. $$10$$. This is the product of 5 and 2.
6. $$6$$. Adding 3 and 3 results in 6.
7. $$8$$. The sum of 8 and 0 is still 8.
8. $$10$$. Adding 1 and 9 gives 10.
9. $$21$$. This is the result of distributing 3 across the sum.
10. $$10$$. Adding 10 and 5 then subtracting 5 gives 10.
11. $$20$$. Adding 12 and 8 results in 20.
12. $$6$$. Adding 0 to 6 does not change its value.
13. $$7$$. This is the sum of 2 and 5 after adding 3.
14. $$4$$. Adding 1 four times gives 4.
15. $$15$$. This is the sum of three 5’s.
16. $$6$$. This is the product of 2 and 3.
17. $$10$$. Adding 7, 1, and 2 gives 10.
18. $$15$$. The subtraction of 5 from 15 gives 10.
19. $$5$$. Adding 9 and 4 then subtracting 4 gives 9.
20. $$10$$. This is the sum of two 5’s.

Medium Level Answers

1. $$10$$. Adding 3, 5, and 2 gives 10.
2. $$20$$. Distributing 4 gives 4 times 5 plus 4 times 2.
3. $$16$$. Distributing 2 gives 3 plus 5.
4. $$9$$. The result of the expression simplifies to 9.
5. $$9$$. Changing the grouping of 3, 4, and 2 does not affect the result.
6. $$25$$. Distributing 5 gives 5 times 1 and 5 times 4.
7. $$12$$. The sum of 12 and 6 minus 6 gives 12.
8. $$10$$. Adding 10 and 0 does not change its value.
9. $$18$$. Distributing 3 gives 3 times 4 plus 3 times 2.
10. $$11$$. Adding 8 and 2 then 1 gives 11.
11. $$10$$. Changing the order of 7 and 3 still results in 10.
12. $$12$$. Adding 4 together gives 12.
13. $$6$$. Changing the grouping of 1, 2, and 3 does not affect the result.
14. $$18$$. Distributing 6 gives 4 plus 12.
15. $$11$$. The sum of 5, 3, and 3 gives 11.
16. $$10$$. The result of the expression simplifies to 10.
17. $$16$$. Distributing 2 gives 6 plus 10.
18. $$20$$. The subtraction of 10 from 20 gives 10.
19. $$7$$. The sum of 2, 3, and 5 gives 10.
20. $$5$$. The sum of 5, 7, and 3 gives 5.

Hard Level Answers

1. $$16$$. Distributing 2 gives 3, 4, and 1.
2. $$28$$. Distributing 4 gives 20 and 8.
3. $$10$$. The grouping of the numbers does not change the sum.
4. $$18$$. Distributing 3 gives 2, 3, and 1.
5. $$8$$. Changing the order of 1, 5, and 2 still results in 8.
6. $$20$$. Distributing 2 gives 6 and 12.
7. $$30$$. Distributing 5 gives 10, 15, and 5.
8. $$20$$. Distributing 4 gives 12 and 8.
9. $$9$$. The sum of 7, 2, and 6 gives 9.
10. $$27$$. The result of the expression simplifies to 27.
11. $$10$$. Changing the grouping of 1, 2, 3, and 4 does not affect the result.
12. $$30$$. Distributing 2 gives 3, 2, and 5.
13. $$15$$. The sum of 10, 0, and 5 gives 15.
14. $$20$$. The sum of four 5’s gives 20.
15. $$10$$. The subtraction of 3 from 10 gives 10.
16. $$24$$. Distributing 4 gives 16 and 8.
17. $$21$$. Distributing 3 gives 12, 6, and 3.
18. $$20$$. Distributing 8 gives 16 and 4.
19. $$12$$. The sum of 5, 3, 2, and 2 gives 12.
20. $$15$$. The result of the expression simplifies to 15.