Number and Operations>Extending Representations of Division to Fraction Notation(TEKS.Math.6.2.E)
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Texas 6th Grade Math › Number and Operations>Extending Representations of Division to Fraction Notation(TEKS.Math.6.2.E)
Which statement correctly explains the relationship between $7/3$ and $7 \div 3$?
They are different because $7 \div 3$ is 2 remainder 1.
They represent the same number because the fraction bar means division with $7$ as the dividend and $3$ as the divisor.
$7/3$ is the same as $3 \div 7$.
$7/3$ means $7 \times 3$.
Explanation
By definition, $a/b$ represents $a \div b$ (with $b \ne 0$). Here $7/3 = 7 \div 3$; $7$ (the numerator) is the dividend and $3$ (the denominator) is the divisor. Reversing to $3 \div 7$ or changing to multiplication is incorrect.
What does the fraction bar represent in the expression $15/4$?
Subtraction, so $15/4$ means $15 - 4$.
Multiplication, so $15/4$ means $15 \times 4$.
It makes both numbers positive, like absolute value.
Division, so $15/4$ means $15 \div 4$.
Explanation
The fraction bar represents division: $a/b = a \div b$. In $15/4$, $15$ (numerator) is divided by $4$ (denominator). It is not subtraction or multiplication, and it does not act like absolute value.
Which expression is equivalent to $8/5$?
$8 \div 5$
$5 \div 8$
$8 \times 5$
$5 - 8$
Explanation
By definition, $8/5 = 8 \div 5$. The dividend is $8$ and the divisor is $5$. Reversing the order, multiplying, or subtracting are not equivalent.
Which division expression matches the fraction $-9/2$?
$9 \div 2$
$2 \div -9$
$-9 \div 2$
$|9| \div 2$
Explanation
$-9/2$ means $-9 \div 2$: the numerator (dividend) is $-9$, the denominator (divisor) is $2$. Ignoring the negative or taking absolute value is incorrect, and reversing to $2 \div -9$ changes the value.
Which statement about $5/8$ is true?
$5/8$ is the same number as $5 \div 8$.
$5/8$ is the opposite of $8/5$.
$5/8$ equals $8 \div 5$.
$5/8$ equals $-5 \div 8$.
Explanation
Fraction notation represents division: $5/8 = 5 \div 8$ with $5$ as the dividend and $8$ as the divisor. It is not $8 \div 5$, and changing the sign gives a different number. 'Opposite' means negation, while $8/5$ is the reciprocal of $5/8$, not its opposite.