This page is designed to help students, parents, and teachers master the topic of fractions through carefully selected practice questions and step-by-step solutions with explanations. Each solution provides the reasoning behind every step, helping learners build a strong foundation in understanding parts of a whole, equivalent fractions, and ordering.
The questions on this page cover essential topics related to fractions, including:
Question 1: Use fractions to write the part of the whole shape that is shaded?
Explanation: A fraction represents part of a whole, written as \(\dfrac{\text{shaded parts}}{\text{total equal parts}}\). By counting the shaded segments versus total segments in the provided diagram, 3 parts are shaded out of 8 equal total parts.
Therefore, the fraction is \(\dfrac{3}{8}\), making option A correct.
Question 2: Which figure is shaded to show a fraction equal to \(\dfrac{2}{5}\) of its whole?
Explanation: To find a fraction equal to \(\dfrac{2}{5}\), look for a figure divided into 5 equal parts where 2 parts are shaded, or an equivalent fraction where 2 out of every 5 sections are shaded. Figure C correctly displays this proportion.
Therefore, option C is correct.
Question 3: Which two fractions are equivalent?
Explanation: Equivalent fractions represent the exact same value or proportion. If you multiply the numerator and denominator of \(\dfrac{1}{2}\) by 2, you get \(\dfrac{1 \times 2}{2 \times 2} = \dfrac{2}{4}\).
Therefore, \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\) are equivalent, making option B correct.
Question 4: The figures below show that:
Explanation: When numerators are the same, the fraction with the smaller denominator represents larger pieces because the whole is divided into fewer parts. Since fifths are smaller than fourths, \(\dfrac{2}{5}\) is less than \(\dfrac{2}{4}\).
Therefore, \(\dfrac{2}{5} < \dfrac{2}{4}\), making option D correct.
Question 5: Half of half is the same as the fraction:
Explanation: "Half" is written as \(\dfrac{1}{2}\). Finding half of a half means multiplying \(\dfrac{1}{2}\) by \(\dfrac{1}{2}\):
\(\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\)
Therefore, option B is correct.
Question 6: If the fractions \(\dfrac{N}{6}\) and \(\dfrac{2}{3}\) are equivalent, what is the value of \(N\)?
Explanation: To convert the denominator 3 to 6, multiply it by 2. To keep the fraction equivalent, do the same to the numerator:
\(\dfrac{2 \times 2}{3 \times 2} = \dfrac{4}{6}\)
Comparing \(\dfrac{N}{6}\) to \(\dfrac{4}{6}\), we find \(N = 4\). Therefore, option C is correct.
Question 7: Which two figures have shaded parts that represent equivalent fractions?
Explanation: Examining the shaded areas across the multiple choices shows that the figures in option D represent the same proportional shaded area (equivalent fractions).
Therefore, option D is correct.
Question 8: Order from greatest to least: \(\dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{2}, \dfrac{1}{7}\)
Explanation: When unit fractions have a numerator of 1, the fraction with the smallest denominator is the largest value because the whole is divided into fewer pieces. Sorting by size from largest to smallest:
Therefore, the correct order is \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{6}, \dfrac{1}{7}\), making option A correct.
Question 9: What value of \(N\) makes \(\dfrac{N}{3} < \dfrac{1}{2}\) true?
Explanation: Let's test the values of \(N\):
Therefore, \(N = 1\), making option C correct.
Question 10: John, Sarah, Tom and Joane bought 2 pizzas of the same size. John ate \(\dfrac{2}{4}\) of a pizza. Tom, Sarah and Joane each ate \(\dfrac{1}{4}\) of a pizza. How much pizza was left?
Explanation: Calculate the total pizza eaten:
Total eaten = \(\dfrac{2}{4} + \dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4} = \dfrac{5}{4}\) pizzas (or \(1\dfrac{1}{4}\) pizzas).
Since they started with 2 pizzas (\(\dfrac{8}{4}\)), subtract what was eaten:
\(\dfrac{8}{4} - \dfrac{5}{4} = \dfrac{3}{4}\) of a pizza left.
Therefore, option D is correct.