Practice HAT questions with answers and explanations.
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The least common multiple of 3 and 4 is 12.
A number divisible by both must therefore be divisible by 12.
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The units digits of powers of 7 cycle as 7, 9, 3, 1.
The fourth power therefore ends in 1.
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Division and multiplication have equal priority and are performed left to right.
So 48 ÷ 6 = 8, and 8 × 3 = 24.
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The greatest common divisor of 18 and 24 is 6.
Dividing both terms by 6 gives 3/4.
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Multiplication is performed before addition.
Thus, 3 × 4 = 12 and 5 + 12 = 17.
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Convert 2/3 to sixths: 2/3 = 4/6.
Then 4/6 + 1/6 = 5/6.
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The operation inside parentheses is completed first.
Then 12 ÷ 3 = 4.
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Convert 1/4 to 2/8.
Then 7/8 - 2/8 = 5/8.
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The multiplicative inverse of a nonzero fraction is its reciprocal.
Interchanging numerator and denominator gives 7/5.
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Multiply numerators and denominators, then simplify.
(3 × 10)/(5 × 9) = 30/45 = 2/3.
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A composite number has more than two positive factors.
The number 4 has factors 1, 2, and 4.
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Dividing by a fraction means multiplying by its reciprocal.
Thus, 4/7 × 3/2 = 12/14 = 6/7.
