Divide [tex]$59,990 \div 280$[/tex]. Write the remainder as a fraction.

Step 1: Divide.
[tex]$
59,990 \div 280
$[/tex]

Step 2: Write the remainder as a fraction.
[tex]$
\frac{\text{remainder}}{\text{divisor}} = \frac{}{280}
$[/tex]
Write the remainder over the divisor.

[tex]$
\frac{70}{280} = \square
$[/tex]

Simplify.

Compare your estimate with the quotient.

Since the estimate is close, the answer is reasonable.

So, [tex]$59,990 \div 280 = \qquad$[/tex]



Answer :

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].