Equation Solver Challenge Practice Test Worksheets
Equation solver questions test your mental arithmetic and your understanding of how numbers balance. By mastering these multi-step puzzles, you build the speed and accuracy needed for more complex algebra.
For students who can solve simple equations, but lose marks when brackets, balances, and hidden values appear together.
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What Do Find the Value Questions Look Like?
Find the value questions test your mental arithmetic and your understanding of how mathematical expressions balance across an equals sign. The goal is to calculate the known side and work backwards to find the missing factor. Here is a worked example.
Simple Balancing
Question: 9 × 6 + 2 = 7 × ( ______ )
Worked Method
Step 1: Calculate the left side.
9 × 6 = 54
54 + 2 = 56
Step 2: Find the missing factor.
We need 7 × ( ? ) = 56
56 ÷ 7 = 8
Tip: If you know your 7-times table, you'll spot that 7 × 8 = 56 instantly!
Rules to Help You Solve Find the Value Questions
To solve find the value questions like the example above, you need to work systematically through the equation. Keep these three rules in mind:
🔢 Rule 1: Order of Operations
Work out brackets first, then powers (such as 3²). Next, multiply or divide, working from left to right. Finally, add or subtract, working from left to right.
In these examples, start with the left side because it has no missing number.
Example: 9 × 6 + 2 → 54 + 2 = 56.
⚖️ Rule 2: The Balance Rule
The equals sign (=) means both sides must have the same total. If the left side is 56, the right side must also equal 56.
Example: 56 = 7 × ( ______ )
🎯 Rule 3: Work Backwards
Work backwards to find the missing number. For example, if 7 × ? = 56, divide 56 by 7. Put your answer back in the equation to check that both sides match.
Example: 7 × ( ______ ) = 56, so 56 ÷ 7 = 8.
Two More Worked Examples
Here are two more examples showing how to work with larger factors and avoid common addition-order traps.
Larger Values
Question: 7 × 5 + 3 = 2 × ( ______ )
Worked Method
Step 1: Calculate the left side.
7 × 5 = 35
35 + 3 = 38
Step 2: Divide by the factor.
38 ÷ 2 = 19
Tip: Dividing by 2 is the same as halving. Half of 30 is 15, and half of 8 is 4. 15 + 4 = 19.
The Addition Trap
Question: 4 × 4 + 5 = 7 × ( ______ )
Worked Method
Step 1: Follow Order of Operations.
Multiply first: 4 × 4 = 16
Then add: 16 + 5 = 21
Step 2: Solve the right side.
21 ÷ 7 = 3
The Trap: Adding the last two numbers first (4 + 5 = 9) gives 4 × 9 = 36. Here, multiply before adding because there are no brackets around 4 + 5. With brackets, 4 × (4 + 5) would be a different calculation, and you would add first.
