Question

explain how to estimate the quotient using compatible numbers.

\\27\frac{2}{3} \div 3\frac{9}{10}\\

Explanation:

Identify the given numbers

Using the Fraction Estimation knowledge point
We are given the division expression:

$$ 27\frac{2}{3} \div 3\frac{9}{10} $$

Find compatible numbers

Using the Compatible Numbers knowledge point

$$
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$$

The numbers \(28\) and \(4\) are compatible because \(28\) is easily divisible by \(4\).

Estimate the quotient

Using the Compatible Numbers knowledge point

$$ 28 \div 4 = 7 $$

Answer:

To estimate the quotient of \(27\frac{2}{3} \div 3\frac{9}{10}\) using compatible numbers:

1. Round \(3\frac{9}{10}\) to the nearest whole number, which is \(4\).
2. Find a whole number close to \(27\frac{2}{3}\) that is easily divisible by \(4\). The closest multiple of \(4\) is \(28\).
3. Divide the compatible numbers: \(28 \div 4 = 7\).

The estimated quotient is \(7\).