Year 7 Maths: Write an Equation from Words

Introduction

Hello Year 7! Today we are going to learn how to write an equation from words. This means taking a sentence or phrase and turning it into a mathematical equation. This skill is really important because it helps you solve problems in maths and understand how numbers work together.

Understanding the Basics

An equation is a statement that two things are equal. For example, if we say “five more than a number x,” we can write this as an equation: $$x + 5$$.

Key Rules:

1. Identify Key Words: Look for words that tell you what to do with the numbers, like “add,” “subtract,” “multiply,” or “divide.”
2. Use Symbols: In maths, we use symbols to represent numbers and operations:
   • Addition: +
   • Subtraction: –
   • Multiplication: × or *
   • Division: ÷ or /
3. Variables: Sometimes we use letters like x or y to represent unknown numbers.

Tips and Tricks:

• Underline or Highlight Important Words: This can help you remember which operations to use.
• Practice with Examples: The more you practice, the better you’ll get at translating words into equations.
• Check Your Work: Once you’ve written an equation, read it back to see if it makes sense.

Examples

Let’s look at a few examples:

1. “A number increased by 7”:
   • Here, “increased by” means you will add.
   • So, if we use x for the number, the equation is: $$x + 7$$.
2. “Three times a number”:
   • “Times” means we will multiply.
   • If we use x for the number, the equation is: $$3x$$.
3. “The sum of a number and 4 is 10”:
   • “Sum” means addition.
   • The equation is: $$x + 4 = 10$$.

Practice Questions

Easy Level

1. Four added to a number x.
2. A number y decreased by 5.
3. The product of 6 and a number n.
4. The sum of 3 and a number z.
5. A number plus 10 equals 20.
6. The difference between a number a and 2.
7. A number b multiplied by 4.
8. The total of 8 and a number c.
9. A number d minus 7.
10. The sum of 5 and a number e is 15.
11. A number f divided by 3.
12. Two times a number g.
13. The total of 7 and a number h.
14. A number i decreased by 1.
15. The sum of a number j and 6 equals 12.
16. A number k multiplied by 2.
17. Three less than a number l.
18. A number m increased by 4.
19. The difference between 10 and a number n.
20. The sum of a number o and 9 is 25.

Medium Level

1. Five more than a number x is 13.
2. A number y, decreased by 6, equals 4.
3. The product of 3 and a number n is 21.
4. The sum of a number z and 8 is 20.
5. A number plus 14 is equal to 28.
6. The difference between a number a and 5 is 3.
7. A number b multiplied by 5 equals 35.
8. The total of 6 and a number c is 18.
9. A number d minus 9 equals 1.
10. The sum of 4 and a number e is 10.
11. A number f divided by 2 equals 6.
12. Four times a number g is 28.
13. The total of a number h and 10 is 30.
14. A number i decreased by 3 is equal to 7.
15. The sum of a number j and 7 equals 15.
16. A number k multiplied by 3 equals 15.
17. Eight less than a number l is 4.
18. A number m increased by 10 is equal to 18.
19. The difference between 12 and a number n is 5.
20. The sum of a number o and 11 equals 22.

Hard Level

1. The sum of twice a number x and 4 is 20.
2. A number y, decreased by 12, equals 8.
3. The product of three times a number n and 2 equals 24.
4. The sum of a number z and 15 is equal to three times that number.
5. A number plus 6 equals twice that number.
6. The difference between 5 times a number a and 10 is 15.
7. A number b multiplied by itself equals 36.
8. The total of 7 and a number c is equal to four times that number.
9. A number d minus 4 equals 3 times that number.
10. The sum of a number e and 20 is equal to twice that number.
11. A number f divided by 5 equals 3 more than that number.
12. The difference between a number g and 8 is equal to the sum of 4 and that number.
13. The sum of three times a number h and 2 equals 11.
14. A number i decreased by 6 equals half that number.
15. The product of a number j and 4 is equal to 2 less than that number.
16. A number k added to itself equals 10.
17. The difference between 10 and a number l is equal to double that number.
18. A number m increased by eight equals three times that number.
19. The sum of a number n and 2 multiplied by 3 equals 24.
20. The product of a number o and 5 is equal to the sum of that number and 15.

Answers

Easy Level

1. $$x + 4$$
2. $$y – 5$$
3. $$6n$$
4. $$3 + z$$
5. $$x + 10 = 20$$
6. $$a – 2$$
7. $$4b$$
8. $$8 + c$$
9. $$d – 7$$
10. $$e + 5 = 15$$
11. $$\frac{f}{3}$$
12. $$2g$$
13. $$h + 7$$
14. $$i – 1$$
15. $$j + 6 = 12$$
16. $$2k$$
17. $$l – 3$$
18. $$m + 4$$
19. $$10 – n$$
20. $$o + 9 = 25$$

Medium Level

1. $$x + 5 = 13$$
2. $$y – 6 = 4$$
3. $$3n = 21$$
4. $$z + 8 = 20$$
5. $$x + 14 = 28$$
6. $$a – 5 = 3$$
7. $$5b = 35$$
8. $$6 + c = 18$$
9. $$d – 9 = 1$$
10. $$4 + e = 10$$
11. $$\frac{f}{2} = 6$$
12. $$4g = 28$$
13. $$h + 10 = 30$$
14. $$i – 3 = 7$$
15. $$j + 7 = 15$$
16. $$3k = 15$$
17. $$l – 8 = 4$$
18. $$m + 10 = 18$$
19. $$12 – n = 5$$
20. $$o + 11 = 22$$

Hard Level

1. $$2x + 4 = 20$$
2. $$y – 12 = 8$$
3. $$6n = 24$$
4. $$z + 15 = 3z$$
5. $$x + 6 = 2x$$
6. $$5a – 10 = 15$$
7. $$b^2 = 36$$
8. $$7 + c = 4c$$
9. $$d – 4 = 3d$$
10. $$e + 20 = 2e$$
11. $$\frac{f}{5} = f + 3$$
12. $$g – 8 = 4 + g$$
13. $$3h + 2 = 11$$
14. $$i – 6 = \frac{i}{2}$$
15. $$4j = j + 15$$
16. $$k + k = 10$$
17. $$10 – l = 2l$$
18. $$m + 8 = 3m$$
19. $$3(n + 2) = 24$$
20. $$5o = o + 15$$

I hope this helps you understand how to write equations from words! Keep practicing, and you’ll get even better at it!