Add Tenths and Hundredths - 4th Grade Math

1. What is the rule to add $\frac{a}{10}+\frac{b}{100}$ using denominator $ 100 $?

   $\frac{a}{10}+\frac{b}{100}=\frac{10a+b}{100}$. Convert tenths to hundredths by multiplying by 10, then add numerators.

2. Which fraction is equivalent to $\frac{5}{10}$: $\frac{50}{100}$ or $\frac{5}{100}$?

   $\frac{50}{100}$. $\frac{5}{10} \times \frac{10}{10} = \frac{50}{100}$, not $\frac{5}{100}$.

3. What is $\frac{1}{10}+\frac{99}{100}$ written with denominator $ 100 $?

   $\frac{109}{100}$. Convert $\frac{1}{10}$ to $\frac{10}{100}$, then add: $10 + 99 = 109$.

4. What is $\frac{2}{10} + \frac{15}{100}$ written as a fraction with denominator $100$?

   $\frac{35}{100}$. Convert $\frac{2}{10}$ to $\frac{20}{100}$, then add: $20 + 15 = 35$.

5. What is $\frac{9}{10}$ written as a fraction with denominator $ 100 $?

   $\frac{90}{100}$. Multiply numerator and denominator by 10: $9 \times 10 = 90$.

6. What multiplication changes $\frac{n}{10}$ to an equivalent fraction with denominator $100$?

   Multiply by $\frac{10}{10}$. Multiplying by $\frac{10}{10}$ equals 1, preserving the fraction's value.

7. Find and correct the error: $\frac{3}{10} = \frac{3}{100}$.

   Correct: $\frac{3}{10} = \frac{30}{100}$. The numerator must also be multiplied by 10 when converting.

8. Identify the equivalent fraction: Which equals $\frac{4}{10}$, $\frac{40}{100}$ or $\frac{4}{100}$?

   $\frac{40}{100}$. Multiply numerator and denominator by 10: $4 \times 10 = 40$.

9. What is $\frac{6}{10} + \frac{25}{100}$ written as a fraction with denominator $100$?

   $\frac{85}{100}$. Convert $\frac{6}{10}$ to $\frac{60}{100}$, then add: $60 + 25 = 85$.

10. What is $\frac{5}{10} + \frac{40}{100}$ written as a fraction with denominator $100$?

    $\frac{90}{100}$. Convert $\frac{5}{10}$ to $\frac{50}{100}$, then add: $50 + 40 = 90$.

11. What is $\frac{1}{10} + \frac{99}{100}$ written as a fraction with denominator $100$?

    $\frac{109}{100}$. Convert $\frac{1}{10}$ to $\frac{10}{100}$, then add: $10 + 99 = 109$.

12. What is the missing numerator: $\frac{\square}{10}=\frac{20}{100}$?

    $2$. Divide 20 by 10 to find the original numerator in tenths.

13. What is the missing numerator: $\frac{\square}{10}=\frac{80}{100}$?

    $8$. Divide 80 by 10 to find the original numerator in tenths.

14. What is $\frac{4}{10} + \frac{6}{100}$ written as a fraction with denominator $100$?

    $\frac{46}{100}$. Convert $\frac{4}{10}$ to $\frac{40}{100}$, then add: $40 + 6 = 46$.

15. What is $\frac{6}{10}+\frac{7}{100}$ written with denominator $ 100 $?

    $\frac{67}{100}$. Convert $\frac{6}{10}$ to $\frac{60}{100}$, then add: $60 + 7 = 67$.

16. What is the missing numerator: $\frac{6}{10}=\frac{\square}{100}$?

    $60$. Multiply numerator by 10 to convert tenths to hundredths: $6 \times 10 = 60$.

17. What is $\frac{2}{10}+\frac{15}{100}$ written with denominator $100$?

    $\frac{35}{100}$. Convert $\frac{2}{10}$ to $\frac{20}{100}$, then add: $20 + 15 = 35$.

18. What is the equivalent fraction of $\frac{7}{10}$ with denominator $100$?

    $\frac{70}{100}$. Multiply numerator and denominator by 10 to get equivalent fraction.

19. Identify the missing numerator: $\frac{\square}{100} = \frac{8}{10}$.

    $80$. Multiply 8 by 10 to find the equivalent numerator.

20. Identify the missing numerator: $\frac{6}{10} = \frac{\square}{100}$.

    $60$. Multiply 6 by 10 to find the equivalent numerator.

21. What is $\frac{1}{10}$ written as a fraction with denominator $100$?

    $\frac{10}{100}$. Multiply numerator and denominator by 10: $1 \times 10 = 10$.

22. What is the missing numerator: $\frac{4}{10}+\frac{\square}{100}=\frac{55}{100}$?

    $15$. Convert $\frac{4}{10}$ to $\frac{40}{100}$; $55 - 40 = 15$.

23. What is the rule to rewrite $\frac{a}{10}$ as an equivalent fraction with denominator $100$?

    $\frac{a}{10}=\frac{10a}{100}$. Multiply both numerator and denominator by 10 to get equivalent fraction.

24. Find and correct the error: $\frac{5}{10}=\frac{5}{100}$. What is the correct fraction with denominator $ 100 $?

    $\frac{5}{10}=\frac{50}{100}$. Must multiply numerator by 10 when converting tenths to hundredths.

25. What is the equivalent fraction of $\frac{9}{10}$ with denominator $100$?

    $\frac{90}{100}$. Multiply numerator and denominator by 10 to get equivalent fraction.

26. What is $\frac{5}{10}$ written as a fraction with denominator $ 100 $?

    $\frac{50}{100}$. Multiply numerator and denominator by 10: $5 \times 10 = 50$.

27. What is $\frac{3}{10}$ written as a fraction with denominator $100$?

    $\frac{30}{100}$. Multiply numerator and denominator by 10: $3 \times 10 = 30$.

28. What is the missing numerator: $\frac{\square}{10}+\frac{9}{100}=\frac{79}{100}$?

    $7$. Subtract 9 from 79 to get 70, then divide by 10.

29. What is $\frac{9}{10} + \frac{12}{100}$ written as a fraction with denominator $100$?

    $\frac{102}{100}$. Convert $\frac{9}{10}$ to $\frac{90}{100}$, then add: $90 + 12 = 102$.

30. What is $\frac{3}{10}+\frac{4}{100}$ written with denominator $ 100 $?

    $\frac{34}{100}$. Convert $\frac{3}{10}$ to $\frac{30}{100}$, then add: $30 + 4 = 34$.

31. What is $\frac{8}{10} + \frac{3}{100}$ written as a fraction with denominator $100$?

    $\frac{83}{100}$. Convert $\frac{8}{10}$ to $\frac{80}{100}$, then add: $80 + 3 = 83$.

32. What is the first step to add $\frac{a}{10} + \frac{b}{100}$ using denominator $100$?

    Rewrite $\frac{a}{10}$ as $\frac{10a}{100}$. Convert to common denominator 100 before adding fractions.

33. What is $\frac{7}{10}$ written as a fraction with denominator $100$?

    $\frac{70}{100}$. Multiply numerator and denominator by 10: $7 \times 10 = 70$.

34. What is $\frac{7}{10} + \frac{8}{100}$ written as a fraction with denominator $100$?

    $\frac{78}{100}$. Convert $\frac{7}{10}$ to $\frac{70}{100}$, then add: $70 + 8 = 78$.

35. What is $\frac{3}{10} + \frac{4}{100}$ written as a fraction with denominator $100$?

    $\frac{34}{100}$. Convert $\frac{3}{10}$ to $\frac{30}{100}$, then add: $30 + 4 = 34$.

36. What is $\frac{9}{10}+\frac{1}{100}$ written with denominator $ 100 $?

    $\frac{91}{100}$. Convert $\frac{9}{10}$ to $\frac{90}{100}$, then add: $90 + 1 = 91$.

37. What is $\frac{2}{100} + \frac{5}{10}$ written as a fraction with denominator $100$?

    $\frac{52}{100}$. Convert $\frac{5}{10}$ to $\frac{50}{100}$, then add: $2 + 50 = 52$.

38. What is the equivalent fraction of $\frac{3}{10}$ with denominator $100$?

    $\frac{30}{100}$. Multiply numerator and denominator by 10 to get equivalent fraction.

39. What is the equivalent fraction of $\frac{1}{10}$ with denominator $100$?

    $\frac{10}{100}$. Multiply numerator and denominator by 10 to get equivalent fraction.

40. What is $\frac{8}{10} + \frac{30}{100}$ written with denominator $100$?

    $\frac{110}{100}$. Convert $\frac{8}{10}$ to $\frac{80}{100}$, then add: $80 + 30 = 110$.

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