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

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Convert \( \frac{7}{2} \)into its reciprocal form:

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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