# Worksheet: Fractions With Denominators of 10 and 100
Section A: Multiple Choice Questions
Q1: What fraction is equivalent to \(\frac{7}{10}\)? (a) \(\frac{70}{100}\) (b) \(\frac{7}{100}\) (c) \(\frac{17}{100}\) (d) \(\frac{77}{100}\)
Solution:
Ans: (a) Explanation: To convert tenths to hundredths, multiply both the numerator and denominator by 10. \(\frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100}\). Both fractions represent the same amount.
Q2: Which fraction is greater: \(\frac{3}{10}\) or \(\frac{25}{100}\)? (a) \(\frac{3}{10}\) (b) \(\frac{25}{100}\) (c) They are equal (d) Cannot be determined
Solution:
Ans: (a) Explanation: First, convert \(\frac{3}{10}\) to hundredths: \(\frac{3}{10} = \frac{30}{100}\). Now compare: \(\frac{30}{100}\) is greater than \(\frac{25}{100}\) because 30 > 25. Therefore, \(\frac{3}{10}\) is the greater fraction.
Q3: What is \(\frac{40}{100}\) written in simplest form with a denominator of 10? (a) \(\frac{40}{10}\) (b) \(\frac{4}{10}\) (c) \(\frac{14}{10}\) (d) \(\frac{400}{10}\)
Solution:
Ans: (b) Explanation: To convert hundredths to tenths, divide both the numerator and denominator by 10. \(\frac{40}{100} = \frac{40 \div 10}{100 \div 10} = \frac{4}{10}\). This is the equivalent fraction with a denominator of 10.
Q4: Which decimal is equal to \(\frac{5}{10}\)? (a) 0.05 (b) 0.5 (c) 5.0 (d) 0.50
Solution:
Ans: (b) Explanation: The fraction \(\frac{5}{10}\) means 5 tenths, which equals 0.5 as a decimal. Note: 0.5 and 0.50 represent the same value, but option (b) is the standard form.
Q5: What is the sum of \(\frac{20}{100}\) and \(\frac{30}{100}\)? (a) \(\frac{50}{100}\) (b) \(\frac{50}{200}\) (c) \(\frac{5}{10}\) (d) Both (a) and (c)
Solution:
Ans: (d) Explanation: When adding fractions with the same denominator, add the numerators: \(\frac{20}{100} + \frac{30}{100} = \frac{50}{100}\). Also, \(\frac{50}{100} = \frac{5}{10}\) when simplified. Both (a) and (c) are correct representations of the sum.
Q6: Which fraction is NOT equivalent to \(\frac{6}{10}\)? (a) \(\frac{60}{100}\) (b) \(\frac{66}{100}\) (c) \(\frac{3}{5}\) (d) \(\frac{12}{20}\)
Solution:
Ans: (b) Explanation: Converting \(\frac{6}{10}\) to hundredths: \(\frac{6}{10} = \frac{60}{100}\). Also, \(\frac{6}{10} = \frac{3}{5}\) and \(\frac{12}{20}\) when simplified or multiplied. However, \(\frac{66}{100}\) equals \(\frac{6.6}{10}\), which is not equivalent to \(\frac{6}{10}\).
Q7: What is \(\frac{8}{10}\) plus \(\frac{15}{100}\) expressed as hundredths? (a) \(\frac{23}{100}\) (b) \(\frac{80}{100}\) (c) \(\frac{95}{100}\) (d) \(\frac{23}{10}\)
Solution:
Ans: (c) Explanation: First, convert \(\frac{8}{10}\) to hundredths: \(\frac{8}{10} = \frac{80}{100}\). Now add: \(\frac{80}{100} + \frac{15}{100} = \frac{95}{100}\). The sum is \(\frac{95}{100}\).
Q8: Which statement is true? (a) \(\frac{90}{100} > \frac{9}{10}\) (b) \(\frac{90}{100} <> (c) \(\frac{90}{100} = \frac{9}{10}\) (d) \(\frac{90}{100}\) and \(\frac{9}{10}\) cannot be compared
Solution:
Ans: (c) Explanation: Convert \(\frac{9}{10}\) to hundredths: \(\frac{9}{10} = \frac{90}{100}\). Since both fractions represent the same value, they are equal. \(\frac{90}{100} = \frac{9}{10}\)
Section B: Fill in the Blanks
Q9: To convert a fraction with a denominator of 10 to a fraction with a denominator of 100, you multiply both the numerator and denominator by __________.
Solution:
Ans: 10 Explanation: When converting tenths to hundredths, multiply both parts of the fraction by 10 because \(10 \times 10 = 100\).
Q10: The fraction \(\frac{50}{100}\) is equivalent to \(\frac{5}{__}\).
Solution:
Ans: 10 Explanation: Dividing both the numerator and denominator of \(\frac{50}{100}\) by 10 gives \(\frac{5}{10}\). This is the simplified equivalent fraction.
Q11: The decimal form of \(\frac{75}{100}\) is __________.
Solution:
Ans: 0.75 Explanation: The fraction \(\frac{75}{100}\) means 75 hundredths, which equals 0.75 in decimal form.
Q12: When comparing fractions with denominators of 10 and 100, it is helpful to convert them to have a __________ denominator.
Solution:
Ans: common (or same) Explanation: To compare fractions accurately, converting them to a common denominator makes it easy to see which numerator is greater.
Q13: \(\frac{1}{10}\) is equal to __________ hundredths.
Solution:
Ans: 10 Explanation: Converting \(\frac{1}{10}\) to hundredths: \(\frac{1}{10} = \frac{10}{100}\), which is 10 hundredths.
Q14: The sum of \(\frac{2}{10}\) and \(\frac{3}{10}\) equals \(\frac{__}{10}\).
Solution:
Ans: 5 Explanation: When adding fractions with the same denominator, add the numerators: \(2 + 3 = 5\), so \(\frac{2}{10} + \frac{3}{10} = \frac{5}{10}\).
Section C: Word Problems
Q15: Maria ran \(\frac{3}{10}\) of a mile on Monday and \(\frac{45}{100}\) of a mile on Tuesday. How many miles did she run in total? Express your answer as a fraction with a denominator of 100.
Solution:
Ans: First, convert \(\frac{3}{10}\) to hundredths: \(\frac{3}{10} = \frac{30}{100}\). Now add: \(\frac{30}{100} + \frac{45}{100} = \frac{75}{100}\). Final Answer: \(\frac{75}{100}\) of a mile
Q16: A recipe calls for \(\frac{60}{100}\) cup of sugar. Express this amount as a fraction with a denominator of 10.
Solution:
Ans: Divide both the numerator and denominator by 10: \(\frac{60}{100} = \frac{60 \div 10}{100 \div 10} = \frac{6}{10}\). Final Answer: \(\frac{6}{10}\) cup of sugar
Q17: Jake colored \(\frac{4}{10}\) of a poster, and Emma colored \(\frac{25}{100}\) of the same poster. Who colored more of the poster, and by how much? Express your answer as a fraction with a denominator of 100.
Solution:
Ans: Convert \(\frac{4}{10}\) to hundredths: \(\frac{4}{10} = \frac{40}{100}\). Compare: \(\frac{40}{100}\) and \(\frac{25}{100}\). Jake colored more because \(40 > 25\). Difference: \(\frac{40}{100} - \frac{25}{100} = \frac{15}{100}\). Final Answer: Jake colored more by \(\frac{15}{100}\) of the poster
Q18: A parking lot has 100 spaces. \(\frac{7}{10}\) of the spaces are filled. How many parking spaces are filled?
Solution:
Ans: Convert \(\frac{7}{10}\) to hundredths: \(\frac{7}{10} = \frac{70}{100}\). This means 70 out of 100 spaces are filled. \(\frac{70}{100} \times 100 = 70\) spaces. Final Answer: 70 parking spaces
Q19: Lisa read \(\frac{35}{100}\) of a book on Saturday and \(\frac{2}{10}\) of the book on Sunday. What fraction of the book has she read in total? Express your answer as a fraction with a denominator of 100.
Solution:
Ans: Convert \(\frac{2}{10}\) to hundredths: \(\frac{2}{10} = \frac{20}{100}\). Add: \(\frac{35}{100} + \frac{20}{100} = \frac{55}{100}\). Final Answer: \(\frac{55}{100}\) of the book
Q20: A garden is divided into 100 equal sections. Tomatoes are planted in \(\frac{9}{10}\) of the garden. How many sections have tomatoes?
Solution:
Ans: Convert \(\frac{9}{10}\) to hundredths: \(\frac{9}{10} = \frac{90}{100}\). This means 90 out of 100 sections have tomatoes. \(\frac{90}{100} \times 100 = 90\) sections. Final Answer: 90 sections
The document Worksheet (with Solutions): Fractions With Denominators of 10 and 100 is a part of the Grade 4 Course Math Grade 4.
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