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Explain how to estimate the quotient using compatible numbers.

[tex]27 \frac{2}{3} \div 3 \frac{9}{10}[/tex]

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GinnyAnsweridn
To estimate the quotient of [tex]\( 27 \frac{2}{3} \div 3 \frac{9}{10} \)[/tex] using compatible numbers, follow these steps:

1. Convert the Mixed Numbers to Improper Fractions:
- For [tex]\( 27 \frac{2}{3} \)[/tex]:
- The whole number part is [tex]\( 27 \)[/tex].
- The fractional part is [tex]\( \frac{2}{3} \)[/tex].
- Thus, [tex]\( 27 \frac{2}{3} \)[/tex] can be written as [tex]\( 27 + \frac{2}{3} \)[/tex].

- For [tex]\( 3 \frac{9}{10} \)[/tex]:
- The whole number part is [tex]\( 3 \)[/tex].
- The fractional part is [tex]\( \frac{9}{10} \)[/tex].
- Thus, [tex]\( 3 \frac{9}{10} \)[/tex] can be written as [tex]\( 3 + \frac{9}{10} \)[/tex].

2. Sum the Whole and Fractional Parts:
- [tex]\( 27 + \frac{2}{3} \)[/tex] equals approximately [tex]\( 27.6667 \)[/tex].
- [tex]\( 3 + \frac{9}{10} \)[/tex] equals approximately [tex]\( 3.9 \)[/tex].

3. Round Each Number to the Nearest Compatible Whole Number:
- Round [tex]\( 27.6667 \)[/tex] to the nearest whole number, which is [tex]\( 28 \)[/tex].
- Round [tex]\( 3.9 \)[/tex] to the nearest whole number, which is [tex]\( 4 \)[/tex].

4. Divide the Rounded Numbers to Estimate the Quotient:
- [tex]\( 28 \div 4 = 7.0 \)[/tex].

Thus, the estimated quotient of [tex]\( 27 \frac{2}{3} \div 3 \frac{9}{10} \)[/tex] using compatible numbers is [tex]\( 7.0 \)[/tex].
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