Sure! Let's go through the problem step by step to find out where Ryan made his first mistake.
### Step 1:
Evaluate the original division directly.
[tex]\[ 2,350 \div 5 = 470 \][/tex]
### Step 2:
Break down the original number into parts and divide each part by 5 separately.
[tex]\[ 2,000 \div 5 = 400 \][/tex]
[tex]\[ 300 \div 5 = 60 \][/tex]
[tex]\[ 50 \div 5 = 10 \][/tex]
### Step 3:
Add the results obtained from dividing each part by 5.
[tex]\[ 400 + 60 + 10 = 470 \][/tex]
Now, let's look at Ryan's steps:
1. He correctly divided [tex]\( 2,350 \)[/tex] by [tex]\( 5 \)[/tex] into parts:
[tex]\[ 2,350 \div 5 = (2,000 \div 5) + (300 \div 5) + (50 \div 5) \][/tex]
2. He correctly found:
[tex]\[ 2,000 \div 5 = 400 \][/tex]
[tex]\[ 300 \div 5 = 60 \][/tex]
[tex]\[ 50 \div 5 = 10 \][/tex]
3. However, when he added them together:
[tex]\[ 400 + 60 + 10 \][/tex]
He incorrectly arrived at:
[tex]\[ 461 \][/tex]
From this analysis, we see the error occurred in Ryan's addition step.
Therefore, Ryan's first mistake was in:
(C) Step 3
His error was in summing 400, 60, and 10 incorrectly. The correct sum is 470, not 461.
