Explain Effects of Fraction Multiplication - 5th Grade Math

1. What is $\frac{3}{5}\times\frac{4}{4}$ written as one equivalent fraction?

   $\frac{12}{20}$. $\frac{3}{5}\times\frac{4}{4}=\frac{3\times 4}{5\times 4}=\frac{12}{20}$.

2. Identify whether $\frac{7}{5}$ is greater than $1$, less than $1$, or equal to $1$.

   $\frac{7}{5}>1$. The numerator 7 is greater than the denominator 5.

3. Which statement is true for $x>0$: $x\times\frac{1}{2}$ compared to $x\times\frac{3}{2}$?

   $x\times\frac{1}{2}<x\times\frac{3}{2}$. $\frac{1}{2}<1$ and $\frac{3}{2}>1$, so the left side is smaller.

4. Which inequality is correct for a positive number $n$ and a fraction $0<\frac{a}{b}<1$?

   $n\times\frac{a}{b}<n$. When $0<\frac{a}{b}<1$, multiplying decreases the value.

5. What is the correct comparison: $12\times\frac{4}{4}$ compared to $12$?

   $12\times\frac{4}{4}=12$. Since $\frac{4}{4}=1$, multiplying by 1 gives 12.

6. Identify the value of $n$ that makes $\frac{a}{b}\times\frac{n}{n}$ equal to $\frac{a}{b}$.

   Any $n\ne 0$. Multiplying by $\frac{n}{n}=1$ doesn't change the fraction.

7. What does it mean if a fraction $\frac{a}{b}$ is between $0$ and $1$?

   $a<b$ (with $a,b>0$). A fraction is less than 1 when its numerator is smaller than its denominator.

8. What fraction equals $1$ and can be used to make an equivalent fraction: $\frac{n}{n}=?$

   $\frac{n}{n}=1$ for $n\ne 0$. Any nonzero number divided by itself equals 1.

9. Which option makes the product larger for $x>0$: multiply by $\frac{2}{3}$ or by $\frac{5}{3}$?

   Multiply by $\frac{5}{3}$. $\frac{5}{3}>1$ while $\frac{2}{3}<1$, so $\frac{5}{3}$ gives a larger product.

10. What is always true about $n \times 1$ for any number $n$?

    $n\times 1=n$. Multiplying by 1 leaves any number unchanged (identity property).

11. Identify whether $\frac{3}{8}$ is greater than $1$, less than $1$, or equal to $1$.

    $\frac{3}{8}<1$. The numerator 3 is less than the denominator 8.

12. Identify whether $6\times\frac{5}{4}$ is greater than, less than, or equal to $6$.

    Greater than $6$. Since $\frac{5}{4}>1$, the product exceeds 6.

13. What is the product when any number $x$ is multiplied by $1$?

    $x\times 1=x$. Multiplying by 1 leaves any number unchanged.

14. What is always true about $n \times f$ when $n>0$ and $f>1$?

    $n\times f>n$. Multiplying by a number greater than 1 always increases the value.

15. Which option makes the product smaller for $x>0$: multiply by $\frac{9}{10}$ or by $\frac{11}{10}$?

    Multiply by $\frac{9}{10}$. $\frac{9}{10}<1$ while $\frac{11}{10}>1$, so $\frac{9}{10}$ gives a smaller product.

16. What is $\frac{7}{8}\times\frac{3}{3}$ written as one equivalent fraction?

    $\frac{21}{24}$. $\frac{7}{8}\times\frac{3}{3}=\frac{7\times 3}{8\times 3}=\frac{21}{24}$.

17. What is the value of $\frac{n}{n}$ for any nonzero number $n$?

    $\frac{n}{n}=1$. Any nonzero number divided by itself equals 1.

18. What happens to a positive number $x$ when you multiply by a fraction $f$ with $0<f<1$?

    The product is smaller: $x\times f<x$. Multiplying by a fraction between 0 and 1 decreases the value.

19. What is the equivalent-fraction rule using a nonzero number $n$: $\frac{a}{b}=?$

    $\frac{a}{b}=\frac{n\times a}{n\times b}$ for $n\ne 0$. Multiply both numerator and denominator by the same nonzero number.

20. What is the correct comparison: $9\times\frac{3}{4}$ compared to $9$?

    $9\times\frac{3}{4}<9$. Since $\frac{3}{4}<1$, the product is less than 9.

21. Identify whether $8\times\frac{9}{10}$ is greater than, less than, or equal to $8$.

    Less than $8$. Since $\frac{9}{10}<1$, the product is less than 8.

22. Identify whether $6\times\frac{3}{4}$ is greater than, less than, or equal to $6$.

    Less than $6$. Since $\frac{3}{4}<1$, the product is less than 6.

23. What is always true about $n \times f$ when $n>0$ and $0<f<1$?

    $n\times f<n$. Multiplying by a fraction less than 1 always decreases the value.

24. What is the result of multiplying $\frac{a}{b}$ by $\frac{n}{n}$ for $n\ne 0$?

    $\frac{a}{b}\times\frac{n}{n}=\frac{n\times a}{n\times b}$. Multiplying by $\frac{n}{n}=1$ creates an equivalent fraction.

25. Identify whether $12\times\frac{1}{3}$ is greater than, less than, or equal to $12$.

    Less than $12$. Since $\frac{1}{3}<1$, the product is less than 12.

26. What is the correct comparison for $x>0$: $x\times\frac{9}{8}$ compared to $x$?

    $x\times\frac{9}{8}>x$. Since $\frac{9}{8}>1$, the product is greater than $x$.

27. What is the correct comparison: $9\times\frac{5}{4}$ compared to $9$?

    $9\times\frac{5}{4}>9$. Since $\frac{5}{4}>1$, the product exceeds 9.

28. What happens to a positive number $x$ when you multiply by a fraction $f$ with $f>1$?

    The product is greater: $x\times f>x$. Multiplying by a fraction greater than 1 increases the value.

29. What is the fraction-equivalence rule for any nonzero number $n$?

    $\frac{a}{b}=\frac{n\times a}{n\times b}$. Multiplying both parts of a fraction by the same number preserves its value.

30. Which number makes $\frac{a}{b}=\frac{a\times n}{b\times n}$ true: $n=0$ or $n\ne 0$?

    $n\ne 0$. Division by zero is undefined, so $n$ must be nonzero.

31. What is $\frac{3}{5}\times\frac{7}{7}$ written as an equivalent fraction?

    $\frac{21}{35}$. $\frac{7}{7}=1$, so multiply: $3 \times 7 = 21$ and $5 \times 7 = 35$.

32. Find the missing factor: $\frac{4}{9}=\frac{4\times ?}{9\times ?}=\frac{28}{63}$.

    $7$. Since $4\times 7=28$ and $9\times 7=63$, the factor is 7.

33. Identify whether $15\times\frac{2}{2}$ is greater than, less than, or equal to $15$.

    Equal to $15$. Since $\frac{2}{2}=1$, multiplying by 1 gives 15.

34. What does it mean if a fraction $\frac{a}{b}$ is greater than $1$?

    $a>b$ (with $a,b>0$). A fraction exceeds 1 when its numerator is larger than its denominator.

35. Identify whether $9\times\frac{10}{9}$ is greater than, less than, or equal to $9$.

    Greater than $9$. Since $\frac{10}{9}>1$, the product exceeds 9.

36. Identify the missing number: $\frac{4}{9}=\frac{4\times n}{9\times n}$; what is $n$ if the new denominator is $45$?

    $n=5$. Since $9×5=45$, we need $n=5$.

37. Identify the missing factor to show $\frac{6}{7}=\frac{18}{21}$ using $\frac{n}{n}$.

    $n=3$. $\frac{3}{3}$ multiplies both parts: $6×3=18$ and $7×3=21$.

38. What is the correct comparison for $x>0$: $x\times\frac{8}{9}$ compared to $x$?

    $x\times\frac{8}{9}<x$. Since $\frac{8}{9}<1$, the product is less than $x$.

39. What is $\frac{5}{6}\times\frac{4}{4}$ written as an equivalent fraction?

    $\frac{20}{24}$. $\frac{4}{4}=1$, so multiply: $5 \times 4 = 20$ and $6 \times 4 = 24$.

40. Which inequality is correct for a positive number $n$ and a fraction $\frac{a}{b}>1$?

    $n\times\frac{a}{b}>n$. When $\frac{a}{b}>1$, multiplying increases the value.

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