Solve (1×10.3) + (10.1×4): Decimal Multiplication and Addition

Decimal Operations with Order of Operations

(+1)×(10.3)+(10.1)×(+4)= (+1)\times(10.3)+(10.1)\times(+4)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Let's solve one operation at a time
00:09 1 multiplied by any number always equals the number itself
00:14 Now let's calculate the second multiplication
00:17 Let's break down the number into whole number and remainder
00:20 Let's properly open parentheses and multiply by each factor
00:31 This is the multiplication calculation, let's put it in the exercise
00:36 Let's calculate and solve
00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(+1)×(10.3)+(10.1)×(+4)= (+1)\times(10.3)+(10.1)\times(+4)=

2

Step-by-step solution

Let's solve the exercise by first solving the two multiplication problems, and then combining them:

1×10.3=10.3 1\times10.3=10.3

Now let's break down 10.1 and multiply it by 4 as follows:

(10+0.1)×4= (10+0.1)\times4=

Let's multiply 4 by 10 and then by 0.1:

40+0.4=40.4 40+0.4=40.4

Now we have the exercise:

10.3+40.4= 10.3+40.4=

We'll solve accordingly and get:

50.7 50.7

3

Final Answer

50.7 50.7

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Multiply first, then add according to PEMDAS
  • Technique: Break down 10.1×4 as (10+0.1)×4 = 40+0.4
  • Check: Verify: 1×10.3 + 10.1×4 = 10.3 + 40.4 = 50.7 ✓

Common Mistakes

Avoid these frequent errors
  • Adding before multiplying
    Don't solve left to right like 1+10.3+10.1×4 = wrong answer! This ignores order of operations and gives incorrect results. Always multiply first, then add the products together.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why do I multiply before adding?

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The order of operations (PEMDAS) says multiplication comes before addition. This rule ensures everyone gets the same answer when solving math problems!

How do I multiply decimals like 10.1×4?

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You can break it down: 10.1×4=(10+0.1)×4=40+0.4=40.4 10.1 \times 4 = (10 + 0.1) \times 4 = 40 + 0.4 = 40.4 . Or multiply normally and count decimal places!

What if I get confused with positive and negative signs?

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In this problem, all numbers are positive! (+1) and (+4) are just showing the signs clearly. Positive times positive always equals positive.

Can I solve this problem a different way?

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Yes! You could calculate 10.1×4 10.1 \times 4 first, then 1×10.3 1 \times 10.3 , then add. The order of multiplication doesn't matter, but always multiply before adding.

How do I add decimals like 10.3 + 40.4?

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Line up the decimal points vertically:

  • 10.3
  • +40.4
  • ____
  • 50.7

Add each column from right to left!

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