Question 1

What is a fraction? Define numerator and denominator with an example.

Accepted Answer

A fraction is a number that represents parts of a whole when it is divided into equal parts. The numerator is the number above the line that shows how many parts are taken, and the denominator is the number below the line that shows into how many equal parts the whole is divided. For example, in the fraction 1/4, 1 is the numerator and 4 is the denominator. — A fraction represents parts of a whole divided into equal parts. The numerator tells how many parts are taken, and the denominator tells the total equal parts. For example, 1/4 means one part out of four equal parts.

Question 2

Look at a chocolate bar divided into 4 equal parts with one part shaded. Which fraction represents the shaded part?

Accepted Answer

1/4 — The chocolate bar is divided into 4 equal parts, and one part is shaded. The numerator is 1 (shaded part), and the denominator is 4 (total parts), so the fraction is 1/4.

Question 3

Define a proper fraction and give an example.

Accepted Answer

A proper fraction is a fraction where the numerator is less than the denominator, meaning the fraction is less than one. For example, 3/4 is a proper fraction. — Proper fractions have numerators smaller than denominators, so their value is less than one. For example, 3/4 means three parts out of four equal parts, which is less than a whole.

Question 4

Which of the following is an improper fraction?

Accepted Answer

5/3 — An improper fraction has numerator greater than or equal to the denominator. Here, 5/3 has numerator 5 which is greater than denominator 3, so it is improper.

Question 5

Explain what a mixed fraction is and how it can be converted to an improper fraction.

Accepted Answer

A mixed fraction is a combination of a whole number and a proper fraction, such as 2 1/3. It can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing the result over the original denominator. For example, 2 1/3 = (2×3 + 1)/3 = 7/3. — Mixed fractions combine whole numbers and proper fractions. Conversion involves multiplying whole number by denominator, adding numerator, and writing over denominator. Example: 2 1/3 becomes 7/3.

Question 6

Match the following types of fractions with their correct definitions.

Accepted Answer

— Matching tests understanding of fraction types and their definitions.

Question 7

Which of the following fractions are equivalent to 1/2?

Accepted Answer

All of the above — Fractions 2/4, 3/6, and 4/8 all represent the same quantity as 1/2 because they are equivalent fractions obtained by multiplying numerator and denominator of 1/2 by 2, 3, and 4 respectively.

Question 8

Fill in the blank: To find equivalent fractions, multiply or divide both the numerator and denominator of a fraction by the same _____ number.

Accepted Answer

non-zero — Equivalent fractions are found by multiplying or dividing numerator and denominator by the same non-zero number, which does not change the value of the fraction.

Question 9

Using the fraction wall, are the fractions 2/6 and 1/3 equivalent? Explain why.

Accepted Answer

Yes, 2/6 and 1/3 are equivalent fractions because they represent the same part of a whole. When you simplify 2/6 by dividing numerator and denominator by 2, you get 1/3. The fraction wall shows these fractions aligned to the same length. — Equivalent fractions have the same value. 2/6 simplifies to 1/3 by dividing numerator and denominator by 2. The fraction wall visually confirms this equivalence.

Question 10

Compare the fractions 3/7 and 5/7. Which is greater and why?

Accepted Answer

5/7 is greater because denominators are the same and 5 is more than 3 — When denominators are the same, the fraction with the larger numerator is greater. Here, both have denominator 7, and 5 is greater than 3, so 5/7 is greater.

Question 11

Compare the fractions 3/4 and 2/3 using cross multiplication. Which fraction is greater?

Accepted Answer

3/4 is greater — Given: Fractions 3/4 and 2/3
Find: Which fraction is greater
Formula: Cross multiply numerators and denominators
Solution: Step 1: Multiply numerator of first fraction by denominator of second: 3 × 3 = 9
Step 2: Multiply numerator of second fraction by denominator of first: 2 × 4 = 8
Step 3: Compare 9 and 8; since 9 > 8, 3/4 > 2/3
Answer: 3/4 is greater
Note: Cross multiplication helps compare fractions without finding common denominators.

Question 12

Add the fractions $\frac{1}{5}$ and $\frac{2}{5}$. Show the steps.

Accepted Answer

3/5 — Given: Fractions 1/5 and 2/5
Find: Sum of the fractions
Formula: \frac{a}{d} + \frac{b}{d} = \frac{a+b}{d}
Solution: Step 1: Denominators are same (5), so add numerators: 1 + 2 = 3
Step 2: Keep denominator same: 5
Step 3: Sum = 3/5
Answer: 3/5
Note: When denominators are same, add numerators directly.

Question 13

Add $\frac{1}{3}$ and $\frac{1}{4}$. Show the steps and give the answer in simplest form.

Accepted Answer

7/12 — Given: Fractions 1/3 and 1/4
Find: Sum of the fractions
Formula: Find common denominator, then add numerators
Solution: Step 1: Common denominator = 12
Step 2: Convert fractions: 1/3 = 4/12, 1/4 = 3/12
Step 3: Add numerators: 4 + 3 = 7
Step 4: Sum = 7/12
Answer: 7/12
Note: Always simplify if possible; here 7/12 is already in simplest form.

Question 14

Subtract $\frac{3}{5}$ from $\frac{4}{5}$. Show the steps.

Accepted Answer

1/5 — Given: Fractions 4/5 and 3/5
Find: Difference 4/5 - 3/5
Formula: \frac{a}{d} - \frac{b}{d} = \frac{a-b}{d}
Solution: Step 1: Denominators same, subtract numerators: 4 - 3 = 1
Step 2: Denominator remains 5
Step 3: Difference = 1/5
Answer: 1/5
Note: Subtract numerators directly when denominators are same.

Question 15

Subtract $\frac{2}{3}$ from $\frac{3}{4}$. Show the steps and give the answer in simplest form.

Accepted Answer

1/12 — Given: Fractions 3/4 and 2/3
Find: Difference 3/4 - 2/3
Formula: Find common denominator, then subtract numerators
Solution: Step 1: Common denominator = 12
Step 2: Convert fractions: 3/4 = 9/12, 2/3 = 8/12
Step 3: Subtract numerators: 9 - 8 = 1
Step 4: Difference = 1/12
Answer: 1/12
Note: Always simplify if possible; here 1/12 is simplest form.

Fractions

Fractions — Study Notes

Introduction to Fractions

Types of Fractions

Equivalent Fractions

Practice Questions — Fractions

All 10 Chapters in Ganita Prakash