Sure, let's go through the step-by-step solution for dividing [tex]\(59,990 \div 280\)[/tex] and writing the remainder as a fraction.
### Step 1: Divide
First, we need to divide 59,990 by 280 to find the quotient and the remainder.
- Quotient: [tex]\(59,990 \div 280 = 214\)[/tex]
- Remainder: [tex]\(59,990 \mod 280 = 70\)[/tex]
So when [tex]\(59,990\)[/tex] is divided by [tex]\(280\)[/tex], the quotient is [tex]\(214\)[/tex] and the remainder is [tex]\(70\)[/tex].
### Step 2: Write the remainder as a fraction
Next, we write the remainder as a fraction over the divisor:
[tex]\[
\frac{\text{remainder}}{\text{divisor}} = \frac{70}{280}
\][/tex]
Simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 70:
[tex]\[
\frac{70 \div 70}{280 \div 70} = \frac{1}{4}
\][/tex]
Therefore, the remainder as a fraction in its simplest form is [tex]\(\frac{1}{4}\)[/tex].
Thus, the division of [tex]\(59,990 \div 280\)[/tex] results in a quotient of [tex]\(214\)[/tex] and a remainder of [tex]\( \frac{1}{4} \)[/tex].
### Estimation using compatible numbers
To estimate using compatible numbers, we can round [tex]\(59,990\)[/tex] to [tex]\(60,000\)[/tex] and [tex]\(280\)[/tex] to [tex]\(300\)[/tex]:
[tex]\[
60,000 \div 300 = 200
\][/tex]
Our estimate, 200, is close to the actual quotient, 214, which indicates that our calculated answer is reasonable.
So, [tex]\(59,990 \div 280 = 214\)[/tex] with a remainder of [tex]\( \frac{1}{4}\)[/tex].
