Explain Effects of Fraction Multiplication - 5th Grade Math
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Which inequality is correct for a positive number $n$ and a fraction $\frac{a}{b}>1$?
Which inequality is correct for a positive number $n$ and a fraction $\frac{a}{b}>1$?
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$n\times\frac{a}{b}>n$. When $\frac{a}{b}>1$, multiplying increases the value.
$n\times\frac{a}{b}>n$. When $\frac{a}{b}>1$, multiplying increases the value.
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What is always true about $n \times 1$ for any number $n$?
What is always true about $n \times 1$ for any number $n$?
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$n\times 1=n$. Multiplying by 1 leaves any number unchanged (identity property).
$n\times 1=n$. Multiplying by 1 leaves any number unchanged (identity property).
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What is always true about $n \times f$ when $n>0$ and $0<f<1$?
What is always true about $n \times f$ when $n>0$ and $0<f<1$?
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$n\times f<n$. Multiplying by a fraction less than 1 always decreases the value.
$n\times f<n$. Multiplying by a fraction less than 1 always decreases the value.
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Identify whether $8\times\frac{9}{10}$ is greater than, less than, or equal to $8$.
Identify whether $8\times\frac{9}{10}$ is greater than, less than, or equal to $8$.
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Less than $8$. Since $\frac{9}{10}<1$, the product is less than 8.
Less than $8$. Since $\frac{9}{10}<1$, the product is less than 8.
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Which number makes $\frac{a}{b}=\frac{a\times n}{b\times n}$ true: $n=0$ or $n\ne 0$?
Which number makes $\frac{a}{b}=\frac{a\times n}{b\times n}$ true: $n=0$ or $n\ne 0$?
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$n\ne 0$. Division by zero is undefined, so $n$ must be nonzero.
$n\ne 0$. Division by zero is undefined, so $n$ must be nonzero.
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Find the missing factor: $\frac{4}{9}=\frac{4\times ?}{9\times ?}=\frac{28}{63}$.
Find the missing factor: $\frac{4}{9}=\frac{4\times ?}{9\times ?}=\frac{28}{63}$.
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$7$. Since $4\times 7=28$ and $9\times 7=63$, the factor is 7.
$7$. Since $4\times 7=28$ and $9\times 7=63$, the factor is 7.
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What is $\frac{7}{8}\times\frac{3}{3}$ written as one equivalent fraction?
What is $\frac{7}{8}\times\frac{3}{3}$ written as one equivalent fraction?
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$\frac{21}{24}$. $\frac{7}{8}\times\frac{3}{3}=\frac{7\times 3}{8\times 3}=\frac{21}{24}$.
$\frac{21}{24}$. $\frac{7}{8}\times\frac{3}{3}=\frac{7\times 3}{8\times 3}=\frac{21}{24}$.
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What is always true about $n \times f$ when $n>0$ and $f>1$?
What is always true about $n \times f$ when $n>0$ and $f>1$?
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$n\times f>n$. Multiplying by a number greater than 1 always increases the value.
$n\times f>n$. Multiplying by a number greater than 1 always increases the value.
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What is $\frac{3}{5}\times\frac{4}{4}$ written as one equivalent fraction?
What is $\frac{3}{5}\times\frac{4}{4}$ written as one equivalent fraction?
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$\frac{12}{20}$. $\frac{3}{5}\times\frac{4}{4}=\frac{3\times 4}{5\times 4}=\frac{12}{20}$.
$\frac{12}{20}$. $\frac{3}{5}\times\frac{4}{4}=\frac{3\times 4}{5\times 4}=\frac{12}{20}$.
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What is the fraction-equivalence rule for any nonzero number $n$?
What is the fraction-equivalence rule for any nonzero number $n$?
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$\frac{a}{b}=\frac{n\times a}{n\times b}$. Multiplying both parts of a fraction by the same number preserves its value.
$\frac{a}{b}=\frac{n\times a}{n\times b}$. Multiplying both parts of a fraction by the same number preserves its value.
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What does it mean if a fraction $\frac{a}{b}$ is between $0$ and $1$?
What does it mean if a fraction $\frac{a}{b}$ is between $0$ and $1$?
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$a<b$ (with $a,b>0$). A fraction is less than 1 when its numerator is smaller than its denominator.
$a<b$ (with $a,b>0$). A fraction is less than 1 when its numerator is smaller than its denominator.
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What does it mean if a fraction $\frac{a}{b}$ is greater than $1$?
What does it mean if a fraction $\frac{a}{b}$ is greater than $1$?
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$a>b$ (with $a,b>0$). A fraction exceeds 1 when its numerator is larger than its denominator.
$a>b$ (with $a,b>0$). A fraction exceeds 1 when its numerator is larger than its denominator.
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Which inequality is correct for a positive number $n$ and a fraction $0<\frac{a}{b}<1$?
Which inequality is correct for a positive number $n$ and a fraction $0<\frac{a}{b}<1$?
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$n\times\frac{a}{b}<n$. When $0<\frac{a}{b}<1$, multiplying decreases the value.
$n\times\frac{a}{b}<n$. When $0<\frac{a}{b}<1$, multiplying decreases the value.
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What is $\frac{5}{6}\times\frac{4}{4}$ written as an equivalent fraction?
What is $\frac{5}{6}\times\frac{4}{4}$ written as an equivalent fraction?
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$\frac{20}{24}$. $\frac{4}{4}=1$, so multiply: $5 \times 4 = 20$ and $6 \times 4 = 24$.
$\frac{20}{24}$. $\frac{4}{4}=1$, so multiply: $5 \times 4 = 20$ and $6 \times 4 = 24$.
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Identify the missing number: $\frac{4}{9}=\frac{4\times n}{9\times n}$; what is $n$ if the new denominator is $45$?
Identify the missing number: $\frac{4}{9}=\frac{4\times n}{9\times n}$; what is $n$ if the new denominator is $45$?
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$n=5$. Since $9×5=45$, we need $n=5$.
$n=5$. Since $9×5=45$, we need $n=5$.
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Identify the missing factor to show $\frac{6}{7}=\frac{18}{21}$ using $\frac{n}{n}$.
Identify the missing factor to show $\frac{6}{7}=\frac{18}{21}$ using $\frac{n}{n}$.
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$n=3$. $\frac{3}{3}$ multiplies both parts: $6×3=18$ and $7×3=21$.
$n=3$. $\frac{3}{3}$ multiplies both parts: $6×3=18$ and $7×3=21$.
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Which option makes the product smaller for $x>0$: multiply by $\frac{9}{10}$ or by $\frac{11}{10}$?
Which option makes the product smaller for $x>0$: multiply by $\frac{9}{10}$ or by $\frac{11}{10}$?
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Multiply by $\frac{9}{10}$. $\frac{9}{10}<1$ while $\frac{11}{10}>1$, so $\frac{9}{10}$ gives a smaller product.
Multiply by $\frac{9}{10}$. $\frac{9}{10}<1$ while $\frac{11}{10}>1$, so $\frac{9}{10}$ gives a smaller product.
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Which option makes the product larger for $x>0$: multiply by $\frac{2}{3}$ or by $\frac{5}{3}$?
Which option makes the product larger for $x>0$: multiply by $\frac{2}{3}$ or by $\frac{5}{3}$?
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Multiply by $\frac{5}{3}$. $\frac{5}{3}>1$ while $\frac{2}{3}<1$, so $\frac{5}{3}$ gives a larger product.
Multiply by $\frac{5}{3}$. $\frac{5}{3}>1$ while $\frac{2}{3}<1$, so $\frac{5}{3}$ gives a larger product.
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What happens to a positive number $x$ when you multiply by a fraction $f$ with $f>1$?
What happens to a positive number $x$ when you multiply by a fraction $f$ with $f>1$?
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The product is greater: $x\times f>x$. Multiplying by a fraction greater than 1 increases the value.
The product is greater: $x\times f>x$. Multiplying by a fraction greater than 1 increases the value.
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What happens to a positive number $x$ when you multiply by a fraction $f$ with $0<f<1$?
What happens to a positive number $x$ when you multiply by a fraction $f$ with $0<f<1$?
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The product is smaller: $x\times f<x$. Multiplying by a fraction between 0 and 1 decreases the value.
The product is smaller: $x\times f<x$. Multiplying by a fraction between 0 and 1 decreases the value.
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