Multi-Step Operations - ISEE Upper Level: Quantitative Reasoning
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What is the value of $\frac{3}{7}\div\frac{6}{7}+\frac{1}{4}$?
What is the value of $\frac{3}{7}\div\frac{6}{7}+\frac{1}{4}$?
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$\frac{3}{4}$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{4}$.
$\frac{3}{4}$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{4}$.
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What is the value of $\frac{1}{2}\times\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{1}{8}$?
What is the value of $\frac{1}{2}\times\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{1}{8}$?
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$\frac{5}{8}$. Parentheses require addition first, then multiplication by $\frac{1}{2}$, followed by adding $\frac{1}{8}$.
$\frac{5}{8}$. Parentheses require addition first, then multiplication by $\frac{1}{2}$, followed by adding $\frac{1}{8}$.
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What is the value of $(18-6)\times(2+5)$?
What is the value of $(18-6)\times(2+5)$?
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$84$. Parentheses dictate subtraction and addition first, then multiplication of the results.
$84$. Parentheses dictate subtraction and addition first, then multiplication of the results.
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What is the value of $\left(\frac{2}{3}\right)\times\left(\frac{9}{4}\right)-\frac{1}{2}$?
What is the value of $\left(\frac{2}{3}\right)\times\left(\frac{9}{4}\right)-\frac{1}{2}$?
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$1$. Multiplication of fractions precedes subtraction, so compute $\frac{2}{3} \times \frac{9}{4}$ first, then subtract $\frac{1}{2}$.
$1$. Multiplication of fractions precedes subtraction, so compute $\frac{2}{3} \times \frac{9}{4}$ first, then subtract $\frac{1}{2}$.
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What is the value of $\frac{7}{10}+\frac{3}{5}-\frac{1}{2}$?
What is the value of $\frac{7}{10}+\frac{3}{5}-\frac{1}{2}$?
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$\frac{4}{5}$. Convert to tenths and perform addition followed by subtraction from left to right.
$\frac{4}{5}$. Convert to tenths and perform addition followed by subtraction from left to right.
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What is the value of $\left(\frac{3}{8}\right)\div\left(\frac{1}{4}\right)+\frac{1}{2}$?
What is the value of $\left(\frac{3}{8}\right)\div\left(\frac{1}{4}\right)+\frac{1}{2}$?
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$2$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{2}$.
$2$. Division of fractions is multiplication by the reciprocal, performed before adding $\frac{1}{2}$.
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What is the value of $\left(\frac{5}{2}-\frac{1}{4}\right)\div\frac{3}{2}$?
What is the value of $\left(\frac{5}{2}-\frac{1}{4}\right)\div\frac{3}{2}$?
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$\frac{3}{2}$. Parentheses require subtraction first, then divide the result by $\frac{3}{2}$ via multiplication by its reciprocal.
$\frac{3}{2}$. Parentheses require subtraction first, then divide the result by $\frac{3}{2}$ via multiplication by its reciprocal.
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What is the value of $\frac{5}{6}-\frac{1}{3}+\frac{1}{2}$?
What is the value of $\frac{5}{6}-\frac{1}{3}+\frac{1}{2}$?
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$1$. Convert fractions to a common denominator of 6, then subtract and add from left to right.
$1$. Convert fractions to a common denominator of 6, then subtract and add from left to right.
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What is the value of $\frac{9-3}{2}+\frac{8}{4}$?
What is the value of $\frac{9-3}{2}+\frac{8}{4}$?
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$5$. Numerator subtraction precedes division, then add the result of the second division.
$5$. Numerator subtraction precedes division, then add the result of the second division.
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What is the value of $\left(\frac{1}{3}+\frac{1}{6}\right)\times12$?
What is the value of $\left(\frac{1}{3}+\frac{1}{6}\right)\times12$?
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$6$. Parentheses require addition of fractions first, then multiplication by 12.
$6$. Parentheses require addition of fractions first, then multiplication by 12.
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What is the value of $\frac{2}{5}\text{ of }50+\frac{1}{2}\text{ of }20$?
What is the value of $\frac{2}{5}\text{ of }50+\frac{1}{2}\text{ of }20$?
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$30$. 'Of' indicates multiplication, so compute each product separately and add the results.
$30$. 'Of' indicates multiplication, so compute each product separately and add the results.
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