MATH FOR KIDS

I. Algebra as a Balance Scale

Remember: an equation is like a balanced scale. Whatever operation you perform on one side must also be performed on the other side.

1. Solve each equation.

a) x + 7 = 19
b) x − 8 = 15
c) 3x = 27
d) x ÷ 4 = 9
e) 2x + 5 = 21
f) 4x − 7 = 25
g) 5x + 3 = 2x + 24
h) 3x − 7 = x + 21
i) 6x + 5 = 3x + 29
j) 8x − 12 = 5x + 24

2. Find and correct the mistake.

A student solves:

4x + 7 = 31

4x = 31 + 7

4x = 38

x = 9.5

What did the student do incorrectly? Find the correct value of x.

II. Division Using the Area Model

Split each dividend into parts that are easy to divide.

Example:
52 ÷ 4
= (40 + 12) ÷ 4
= 40 ÷ 4 + 12 ÷ 4
= 10 + 3
= 13

Complete the missing steps.
4568 ÷ 4
= (4000 + _____ + _____) ÷ 4
= _____ + _____ + _____
= __________

III. Algebraic Multiplication and Division

1. Fill in the missing expressions.

a) (2x + 1) × 4 = ________

b) (3x + 2) × 5 = ________

c) (4x − 3) × 2 = ________

d) (12x + 8) ÷ 4 = ________

e) (15x + 10) ÷ 5 = ________

f) (18x − 12) ÷ 6 = ________

2. Fractional and Decimal Results

a) (7x + 2) ÷ 4

b) (6x + 5) ÷ 4

c) (9x + 3) ÷ 6

d) (5x + 7) ÷ 2

IV. A machine multiplies every input by 4 and then adds 4.

a) Write an algebraic expression for the output when the input is 2.
b) Write an algebraic expression for the output when the input is 2x.
c) The output is 52. Find the input.

V. A number is multiplied by 3, and then 7 is subtracted. The result is equal to the number plus 21.

a) Write an equation.

b) Solve the equation.

c) Check your answer.