Solve the Decimal Equation: Finding the Missing Number in __ - 0.54 = 1.5

Q: Why do I add 0.54 instead of subtracting it?

Because we use inverse operations to solve equations! Since 0.54 is being subtracted from the unknown number, we must add 0.54 to both sides to cancel it out.

Q: How do I line up the decimals when adding 1.5 + 0.54?

Write $ 1.50 + 0.54 $ so both numbers have the same decimal places. Line up the decimal points vertically: the 5 goes under the 5, and the 4 goes under the 0.

Q: How can I check if 2.04 is really correct?

Substitute it back into the original equation: $ 2.04 - 0.54 $. When you calculate this, you should get exactly 1.5, which matches the right side of the equation!

Q: Why can't I just guess and check with the answer choices?

While that might work sometimes, understanding the method helps you solve any similar problem! Plus, showing your work demonstrates that you truly understand the concept.

Decimal Equations with Addition Inverse

$_{——}-0.54=1.5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find the unknown value together.

00:10 First, we need to isolate the unknown number. Ready?

00:33 Now, let's reduce what's possible! Keep simplifying.

00:54 Use long addition for this part. Take your time.

01:00 Put zeros in the missing places. Almost there!

01:05 Add the numbers, calculate carefully, and substitute the result.

01:14 Place the ones digit, and carry one up if needed.

01:19 Add again, calculate slowly, and substitute one more time.

01:35 And that is how we find the solution! Great job everyone!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$_{——}-0.54=1.5$

Step-by-step solution

We begin by analyzing the equation $\_ - 0.54 = 1.5$ . To find the number that fits in the blank, we follow these steps:

Step 1: Recognize that we need to solve for the blank such that when 0.54 is subtracted, the result is 1.5.
Step 2: Rearrange the equation to solve for the missing number. Thus, we have: $\_ = 1.5 + 0.54$
Step 3: Perform the addition to find: $1.5 + 0.54 = 2.04$

Therefore, the solution to the problem is $2.04$ .

Final Answer

$2.04$

Key Points to Remember

Essential concepts to master this topic

Inverse Operations: Add what was subtracted to isolate the variable
Technique: Rearrange $x - 0.54 = 1.5$ to $x = 1.5 + 0.54$
Check: Substitute back: $2.04 - 0.54 = 1.5$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting instead of adding the decimal
Don't solve $x - 0.54 = 1.5$ by calculating $1.5 - 0.54 = 0.96$ ! This gives the wrong operation and incorrect answer. Always use the inverse operation: if something is subtracted, add it to both sides.

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FAQ

Everything you need to know about this question

Why do I add 0.54 instead of subtracting it?

Because we use inverse operations to solve equations! Since 0.54 is being subtracted from the unknown number, we must add 0.54 to both sides to cancel it out.

How do I line up the decimals when adding 1.5 + 0.54?

Write $1.50 + 0.54$ so both numbers have the same decimal places. Line up the decimal points vertically: the 5 goes under the 5, and the 4 goes under the 0.

What if I get confused about which operation to use?

Think about what's happening to the unknown number! If something is being subtracted from it, you need to add that same amount to both sides to undo the subtraction.

How can I check if 2.04 is really correct?

Substitute it back into the original equation: $2.04 - 0.54$ . When you calculate this, you should get exactly 1.5, which matches the right side of the equation!

Why can't I just guess and check with the answer choices?

While that might work sometimes, understanding the method helps you solve any similar problem! Plus, showing your work demonstrates that you truly understand the concept.

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