Generate Equivalent Fractions Using Multiplication - 4th Grade Math

1. Identify whether the statement is true: $\frac{3}{4}=\frac{6}{8}$.

   True. $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$ ✓

2. Find the equivalent fraction to $\frac{1}{5}$ by multiplying by $3$.

   $\frac{3}{15}$. Multiply numerator and denominator by $3$: $1 \times 3 = 3$, $5 \times 3 = 15$.

3. What equivalent fraction is made by multiplying $\frac{3}{10}$ by $\frac{5}{5}$?

   $\frac{15}{50}$. Multiplying by $\frac{5}{5} = 1$ gives $\frac{3 \times 5}{10 \times 5} = \frac{15}{50}$.

4. Which fraction is equivalent to $\frac{1}{4}$: $\frac{2}{8}$ or $\frac{3}{8}$?

   $\frac{2}{8}$. $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$, not $\frac{3}{8}$.

5. What is an equivalent fraction to $\frac{3}{10}$ with denominator $50$?

   $\frac{15}{50}$. Multiply both parts by $5$: $3 \times 5 = 15$ and $10 \times 5 = 50$.

6. What is an equivalent fraction to $\frac{5}{6}$ with denominator $18$?

   $\frac{15}{18}$. Multiply both parts by $3$: $5 \times 3 = 15$ and $6 \times 3 = 18$.

7. What multiplication by $n$ does to the number of parts and the size of each part in a model?

   Parts become $n$ times as many; each part becomes $\frac{1}{n}$ the size. Multiplying by $n$ creates more, smaller pieces that total the same amount.

8. What must you do to the numerator if you multiply the denominator by $n$ to keep the value?

   Multiply the numerator by the same $n$. Both parts must be multiplied by the same factor to maintain the ratio.

9. Find the equivalent fraction to $\frac{4}{9}$ by multiplying by $2$.

   $\frac{8}{18}$. Multiply numerator and denominator by $2$: $4 \times 2 = 8$, $9 \times 2 = 18$.

10. Which fraction is equivalent to $\frac{2}{3}$: $\frac{4}{6}$ or $\frac{4}{9}$?

    $\frac{4}{6}$. $\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$; both parts multiplied by $2$.

11. Identify the missing number: $\frac{6}{11}=\frac{?}{33}$.

    $18$. Multiply both parts by $3$: $6 \times 3 = 18$ and $11 \times 3 = 33$.

12. In an area model, if each original part is split into $4$ equal parts, what is $n$?

    $n=4$. The scale factor $n$ equals the number of subdivisions per original part.

13. What equivalent fraction is made by multiplying $\frac{5}{8}$ by $\frac{3}{3}$?

    $\frac{15}{24}$. Multiplying by $\frac{3}{3} = 1$ gives $\frac{5 \times 3}{8 \times 3} = \frac{15}{24}$.

14. Identify the missing number: $\frac{4}{7}=\frac{12}{?}$.

    $21$. Since $12 = 4 \times 3$, multiply denominator $7$ by $3$ to get $21$.

15. Identify the missing numerator: $\frac{3}{5}=\frac{?}{10}$.

    $6$. Multiply both parts by $2$: $3 \times 2 = 6$ and $5 \times 2 = 10$.

16. Find and correct the error: $\frac{2}{5}=\frac{4}{15}$ (numerator doubled only).

    Correct: $\frac{2}{5}=\frac{6}{15}$. Both parts must be multiplied by $3$: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.

17. Identify the equivalent fraction to $\frac{5}{12}$ with numerator $10$.

    $\frac{10}{24}$. Multiply both parts by $2$: $5 \times 2 = 10$ and $12 \times 2 = 24$.

18. Which number must you multiply by to change $\frac{2}{9}$ into $\frac{8}{36}$?

    $4$. Both numerator and denominator are multiplied by $4$: $2 \times 4 = 8$, $9 \times 4 = 36$.

19. What happens to the size of each part when you multiply the denominator by $n$?

    Each part becomes $\frac{1}{n}$ of its previous size. More parts mean each part represents a smaller portion of the whole.

20. Identify the missing number: $\frac{2}{3}=\frac{?}{12}$.

    $8$. Since $12 = 3 \times 4$, multiply numerator $2$ by $4$ to get $8$.

21. What does it mean for two fractions to be equivalent?

    They name the same value or point on a number line. Equivalent fractions represent the same portion of a whole.

22. Find the scale factor $n$ if $\frac{7}{9}=\frac{21}{27}$ is made by multiplying by $n$.

    $n=3$. $21 \div 7 = 3$ and $27 \div 9 = 3$, so both were multiplied by $3$.

23. What does it mean if two fractions are equivalent?

    They represent the same value or same size of the whole. Equivalent fractions are different ways to express the same portion.

24. What is an equivalent fraction to $\frac{7}{8}$ with numerator $21$?

    $\frac{21}{24}$. Multiply both parts by $3$: $7 \times 3 = 21$ and $8 \times 3 = 24$.

25. What is the rule for creating an equivalent fraction by multiplying by $n$?

    $\frac{a}{b}=\frac{n\times a}{n\times b}$ for $n\neq 0$. Multiplying both numerator and denominator by the same number preserves the value.

26. Which statement is correct about multiplying only the numerator by $n$: $\frac{a}{b}\to\frac{n\times a}{b}$?

    It usually changes the value, so it is not equivalent. Both parts must be multiplied by the same number to maintain equivalence.

27. Which fraction is equivalent to $\frac{4}{6}$: $\frac{2}{3}$ or $\frac{3}{4}$?

    $\frac{2}{3}$. $\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$, not $\frac{3}{4}$.

28. Which fraction is equivalent to $\frac{3}{4}$: $\frac{6}{8}$ or $\frac{6}{10}$?

    $\frac{6}{8}$. $\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}$; both parts multiplied by $2$.

29. Identify the missing denominator: $\frac{4}{7}=\frac{12}{?}$.

    $21$. Multiply both parts by $3$: $4 \times 3 = 12$ and $7 \times 3 = 21$.

30. Which fraction is equivalent to $\frac{3}{6}$: $\frac{1}{2}$ or $\frac{2}{3}$?

    $\frac{1}{2}$. $\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$, not $\frac{2}{3}$.

31. What stays the same in a visual model when you change $\frac{a}{b}$ to $\frac{n\times a}{n\times b}$?

    The shaded amount (the fraction's value) stays the same. The total portion represented remains constant despite different part sizes.

32. What happens to the number of equal parts when you multiply the denominator by $n$?

    The whole is divided into $n$ times as many equal parts. Multiplying the denominator creates more divisions of the same whole.

33. Find and correct the error: $\frac{2}{5}=\frac{4}{15}$.

    Correct: $\frac{2}{5}=\frac{6}{15}$. Should multiply both parts by $3$: $2 \times 3 = 6$, not $4$.

34. What is the rule for making an equivalent fraction by multiplying by $n$?

    $\frac{a}{b}=\frac{n\times a}{n\times b}$ for $n\neq 0$. Multiply both numerator and denominator by the same non-zero number.

35. Find the scale factor $n$ if $\frac{2}{5}=\frac{6}{15}$ is made by multiplying by $n$.

    $n=3$. $6 \div 2 = 3$ and $15 \div 5 = 3$, so both were multiplied by $3$.

36. Identify the missing number: $\frac{3}{5}=\frac{?}{10}$.

    $6$. Since $10 = 5 \times 2$, multiply numerator $3$ by $2$ to get $6$.

37. What is an equivalent fraction to $\frac{6}{9}$ in simplest form?

    $\frac{2}{3}$. Divide both numerator and denominator by their GCF of $3$.

38. Identify the missing number: $\frac{9}{10}=\frac{?}{40}$.

    $36$. Multiply both parts by $4$: $9 \times 4 = 36$ and $10 \times 4 = 40$.

39. Identify whether the statement is true: $\frac{2}{3}=\frac{4}{5}$.

    False. $\frac{2}{3} = \frac{4}{6}$, not $\frac{4}{5}$ (different ratios).

40. Which fraction is equivalent to $\frac{6}{9}$: $\frac{12}{18}$ or $\frac{12}{15}$?

    $\frac{12}{18}$. $\frac{6}{9} \times \frac{2}{2} = \frac{12}{18}$; both parts multiplied by $2$.

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