Question

solving with compatible numbers

use compatible numbers to estimate the quotient.

\\8\frac{1}{6} \div 1\frac{7}{8}\\

the quotient is close to

Explanation:

Identify the given expression

The problem asks us to estimate the quotient of the expression:

$$ 8\frac{1}{6} \div 1\frac{7}{8} $$

Understand compatible numbers

Compatible numbers are numbers that are close in value to the actual numbers but are easy to compute mentally. For division, we want to choose whole numbers that divide evenly.

Estimate each mixed number

Let's look at each mixed number to find close whole numbers:

• For \( 8\frac{1}{6} \), the fraction \(\frac{1}{6}\) is very small, so \( 8\frac{1}{6} \) is very close to \( 8 \).
• For \( 1\frac{7}{8} \), the fraction \(\frac{7}{8}\) is almost a whole, so \( 1\frac{7}{8} \) is very close to \( 2 \).

Check compatibility and divide

The estimated whole numbers are \( 8 \) and \( 2 \). Since \( 8 \) is easily divisible by \( 2 \), these are excellent compatible numbers:

$$ 8 \div 2 = 4 $$

Thus, the quotient is close to \( 4 \).

Answer:

Use compatible numbers to estimate the quotient.

$$ 8\frac{1}{6} \div 1\frac{7}{8} $$

The quotient is close to <blank>4</blank>