The problem asks us to determine whether the result of a division problem is greater than or less than the number being divided. If the result is greater, we write a triangle in the bracket. If the result is less, we write a circle in the bracket. We are given three division problems: (8) $4 \div \frac{2}{9}$ (9) $\frac{1}{2} \div \frac{6}{7}$ (10) $\frac{8}{5} \div \frac{5}{3}$

ArithmeticDivisionFractionsComparison
2025/7/3

1. Problem Description

The problem asks us to determine whether the result of a division problem is greater than or less than the number being divided. If the result is greater, we write a triangle in the bracket. If the result is less, we write a circle in the bracket.
We are given three division problems:
(8) 4÷294 \div \frac{2}{9}
(9) 12÷67\frac{1}{2} \div \frac{6}{7}
(10) 85÷53\frac{8}{5} \div \frac{5}{3}

2. Solution Steps

The rule for dividing by a fraction is to multiply by the reciprocal of the fraction.
(8) 4÷29=4×92=4×92=362=184 \div \frac{2}{9} = 4 \times \frac{9}{2} = \frac{4 \times 9}{2} = \frac{36}{2} = 18. Since 18>418 > 4, the result is greater than the number being divided. Write a triangle.
(9) 12÷67=12×76=1×72×6=712\frac{1}{2} \div \frac{6}{7} = \frac{1}{2} \times \frac{7}{6} = \frac{1 \times 7}{2 \times 6} = \frac{7}{12}. Since 712<12\frac{7}{12} < \frac{1}{2}, the result is less than the number being divided. Write a circle.
(10) 85÷53=85×35=8×35×5=2425\frac{8}{5} \div \frac{5}{3} = \frac{8}{5} \times \frac{3}{5} = \frac{8 \times 3}{5 \times 5} = \frac{24}{25}. Since 2425<85\frac{24}{25} < \frac{8}{5}, the result is less than the number being divided. Write a circle.

3. Final Answer

(8) 4÷294 \div \frac{2}{9} [\triangle]
(9) 12÷67\frac{1}{2} \div \frac{6}{7} [\bigcirc]
(10) 85÷53\frac{8}{5} \div \frac{5}{3} [\bigcirc]

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