Q1: What is a mixed number? (a) A number with only a whole number part (b) A number with a whole number and a fraction part (c) A number with only a fraction part (d) A number that is always greater than 10
Solution:
Ans: (b) Explanation: A mixed number is a number that has both a whole number part and a fraction part, like \(2\frac{1}{4}\). Option (a) describes just whole numbers, option (c) describes fractions only, and option (d) is incorrect because mixed numbers can be small, like \(1\frac{1}{2}\).
Q2: Which improper fraction is equal to the mixed number \(3\frac{2}{5}\)? (a) \(\frac{15}{5}\) (b) \(\frac{17}{5}\) (c) \(\frac{12}{5}\) (d) \(\frac{10}{5}\)
Solution:
Ans: (b) Explanation: To convert \(3\frac{2}{5}\) to an improper fraction, multiply the whole number by the denominator and add the numerator: \(3 \times 5 = 15\), then \(15 + 2 = 17\). So the answer is \(\frac{17}{5}\).
Q3: What is \(\frac{11}{4}\) written as a mixed number? (a) \(2\frac{1}{4}\) (b) \(2\frac{3}{4}\) (c) \(3\frac{1}{4}\) (d) \(1\frac{3}{4}\)
Solution:
Ans: (b) Explanation: Divide 11 by 4: \(11 \div 4 = 2\) with a remainder of 3. The whole number is 2, and the remainder becomes the numerator, so \(\frac{11}{4} = 2\frac{3}{4}\).
Q4: Which mixed number is shown by the picture of 2 whole pizzas and \(\frac{1}{3}\) of another pizza? (a) \(2\frac{1}{2}\) (b) \(3\frac{1}{3}\) (c) \(2\frac{1}{3}\) (d) \(1\frac{2}{3}\)
Solution:
Ans: (c) Explanation: The picture shows 2 whole pizzas and \(\frac{1}{3}\) of another pizza, which is written as the mixed number \(2\frac{1}{3}\).
Q5: What is \(1\frac{4}{6}\) in simplest form? (a) \(1\frac{1}{3}\) (b) \(1\frac{2}{3}\) (c) \(1\frac{4}{6}\) (d) \(2\frac{1}{3}\)
Solution:
Ans: (b) Explanation: To simplify \(1\frac{4}{6}\), we need to simplify the fraction part \(\frac{4}{6}\). Both 4 and 6 can be divided by 2: \(\frac{4}{6} = \frac{2}{3}\). So \(1\frac{4}{6} = 1\frac{2}{3}\) in simplest form.
Q6: Which of the following is an improper fraction? (a) \(\frac{3}{5}\) (b) \(\frac{7}{8}\) (c) \(\frac{9}{4}\) (d) \(\frac{2}{9}\)
Solution:
Ans: (c) Explanation: An improper fraction has a numerator that is greater than or equal to the denominator. In \(\frac{9}{4}\), 9 is greater than 4, so it is an improper fraction. The other options have numerators smaller than denominators, making them proper fractions.
Ans: (a) Explanation: Subtract the whole numbers: \(3 - 1 = 2\). Subtract the fractions: \(\frac{5}{8} - \frac{2}{8} = \frac{3}{8}\). So, \(3\frac{5}{8} - 1\frac{2}{8} = 2\frac{3}{8}\).
## Section B: Fill in the Blanks Q9: A mixed number is made up of a __________ and a fraction.
Solution:
Ans: whole number Explanation: A mixed number consists of a whole number part and a fraction part, such as \(4\frac{1}{2}\).
Q10: To convert a mixed number to an improper fraction, multiply the whole number by the __________ and add the numerator.
Solution:
Ans: denominator Explanation: When converting a mixed number like \(2\frac{3}{5}\) to an improper fraction, you multiply the whole number (2) by the denominator (5) to get 10, then add the numerator (3) to get 13, making \(\frac{13}{5}\).
Q11: When the numerator is greater than or equal to the denominator, the fraction is called an __________ fraction.
Solution:
Ans: improper Explanation: An improper fraction has a numerator that is greater than or equal to its denominator, like \(\frac{7}{3}\) or \(\frac{5}{5}\).
Q12: The mixed number \(5\frac{3}{7}\) is equal to the improper fraction __________.
Solution:
Ans: \(\frac{38}{7}\) Explanation: To convert \(5\frac{3}{7}\): multiply \(5 \times 7 = 35\), then add 3 to get \(35 + 3 = 38\). The improper fraction is \(\frac{38}{7}\).
Q13: The improper fraction \(\frac{19}{6}\) is equal to the mixed number __________.
Solution:
Ans: \(3\frac{1}{6}\) Explanation: Divide 19 by 6: \(19 \div 6 = 3\) remainder 1. The whole number is 3, and the remainder 1 becomes the numerator, so \(\frac{19}{6} = 3\frac{1}{6}\).
Q14: When adding mixed numbers with the same denominator, you add the __________ separately from the fractions.
Solution:
Ans: whole numbers Explanation: When adding mixed numbers, add the whole numbers together and the fractions together separately. For example, in \(2\frac{1}{5} + 3\frac{2}{5}\), add \(2 + 3 = 5\) and \(\frac{1}{5} + \frac{2}{5} = \frac{3}{5}\) to get \(5\frac{3}{5}\).
## Section C: Word Problems Q15: Sarah baked \(2\frac{1}{2}\) dozen cookies on Saturday and \(1\frac{1}{2}\) dozen cookies on Sunday. How many dozen cookies did she bake in total?
Solution:
Ans: Add the whole numbers: \(2 + 1 = 3\) Add the fractions: \(\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1\) Combine: \(3 + 1 = 4\) Final Answer: 4 dozen cookies
Q16: Michael ran \(3\frac{3}{4}\) miles on Monday. He ran \(1\frac{1}{4}\) miles on Tuesday. How many more miles did he run on Monday than on Tuesday?
Solution:
Ans: Subtract the whole numbers: \(3 - 1 = 2\) Subtract the fractions: \(\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\) Combine: \(2\frac{2}{4} = 2\frac{1}{2}\) Final Answer: \(2\frac{1}{2}\) miles
Q17: Emma has \(\frac{13}{3}\) cups of flour. Write this amount as a mixed number.
Solution:
Ans: Divide 13 by 3: \(13 \div 3 = 4\) remainder 1 The whole number is 4 and the remainder is 1 The denominator stays 3 Final Answer: \(4\frac{1}{3}\) cups
Q18: A recipe calls for \(2\frac{2}{3}\) cups of sugar. Write this mixed number as an improper fraction.
Solution:
Ans: Multiply the whole number by the denominator: \(2 \times 3 = 6\) Add the numerator: \(6 + 2 = 8\) The denominator stays 3 Final Answer: \(\frac{8}{3}\) cups
Q19: Tom painted \(1\frac{3}{5}\) of a fence in the morning and \(2\frac{1}{5}\) of the fence in the afternoon. How much of the fence did he paint altogether?
Solution:
Ans: Add the whole numbers: \(1 + 2 = 3\) Add the fractions: \(\frac{3}{5} + \frac{1}{5} = \frac{4}{5}\) Combine: \(3\frac{4}{5}\) Final Answer: \(3\frac{4}{5}\) of the fence
Q20: Jenny had \(5\frac{2}{6}\) yards of ribbon. She simplified this measurement. What is \(5\frac{2}{6}\) in simplest form?
Solution:
Ans: Simplify the fraction part: \(\frac{2}{6} = \frac{1}{3}\) (divide both numerator and denominator by 2) The whole number stays 5 Final Answer: \(5\frac{1}{3}\) yards
The document Worksheet (with Solutions): Mixed Numbers is a part of the Grade 4 Course Math Grade 4.
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