Fractions Operations MCQ Test — Class 7 CBSE

Solution:

A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).

For example, 1/2, 3/4, and 5/7 are all proper fractions because their numerators are less than their denominators.

Options A describes an improper fraction, B describes a fraction equal to 1, and D describes an undefined expression.

Solution:

To add or subtract fractions with different denominators, you must first find a common denominator, which is usually the Least Common Multiple (LCM) of the denominators.

Ravi incorrectly added the numerators and denominators directly without finding a common denominator.

The correct way to add 1/3 and 1/2 is to find the LCM of 3 and 2, which is 6. Then, convert the fractions: 1/3 = 2/6 and 1/2 = 3/6. Finally, add: 2/6 + 3/6 = 5/6.

Solution:

To find the remaining pizza, subtract the amount eaten from the initial amount: 5/6 - 1/3.

Find a common denominator for 6 and 3. The LCM is 6. Convert 1/3 to an equivalent fraction with denominator 6: 1/3 = (1 × 2) / (3 × 2) = 2/6.

Now, subtract the fractions: 5/6 - 2/6 = (5 - 2)/6 = 3/6.

Simplify the result: 3/6 = 1/2.

Solution:

The chocolate bar has 3 equal rows, so 2 shaded rows represent 2/3 of the total rows.

The chocolate bar has 4 equal columns, so 3 shaded columns represent 3/4 of the total columns.

When you find the region that is double-shaded, you are essentially finding a fraction 'of' a fraction, which corresponds to multiplication.

Therefore, the double-shaded region represents the product 2/3 × 3/4.

Solution:

Division is defined as the inverse operation of multiplication. When we divide a number 'a' by a number 'b', it is equivalent to asking how many times 'b' fits into 'a'.

Multiplying by the reciprocal of a fraction is the method used to perform this inverse operation for fractions.

For example, a/b ÷ c/d = a/b × d/c. This effectively 'undoes' the division by c/d.

Solution:

The phrase '3/4 of 12' means to multiply 3/4 by 12.

Multiply the fraction by the whole number: — (3/4) × 12

To calculate, multiply the numerator by the whole number and keep the denominator, then simplify: — (3 × 12) / 4 = 36 / 4

Simplify the result: — 36 / 4 = 9

Solution:

To compare 3/5 and 2/3 using cross-multiplication, multiply the numerator of the first fraction by the denominator of the second, and vice-versa.

First product: 3 (numerator of 3/5) × 3 (denominator of 2/3) = 9.

Second product: 2 (numerator of 2/3) × 5 (denominator of 3/5) = 10.

Since 9 < 10, it means the first fraction is less than the second fraction. So, 3/5 < 2/3.

Solution:

Let the unknown fraction be 'x'. The problem can be written as an equation: 2/7 + x = 5/7.

To find 'x', subtract 2/7 from 5/7:

Since the denominators are already the same, simply subtract the numerators: — x = 5/7 - 2/7 = (5 - 2)/7

Calculate the result: — x = 3/7

Solution:

Adding mixed numbers by separating the whole and fractional parts is a clear and organized method.

First, add the whole numbers: 2 + 1 = 3.

Next, add the fractional parts: 1/4 + 1/2. Find a common denominator (LCM of 4 and 2 is 4). 1/4 + 2/4 = 3/4.

Combine the results: 3 + 3/4 = 3 3/4. This method is often preferred for its clarity, especially when fractional sums result in improper fractions that need to be converted.

Solution:

To find the number of pieces, divide the total length of the ribbon by the length of each piece: — Number of pieces = Total length ÷ Length of one piece = 7/8 ÷ 1/4

To divide by a fraction, multiply by its reciprocal. The reciprocal of 1/4 is 4/1 (or 4). — 7/8 × 4/1

Multiply the fractions: — (7 × 4) / (8 × 1) = 28 / 8

Simplify the improper fraction by dividing the numerator by the denominator: — 28 ÷ 8 = 3 with a remainder of 4. So, 3 4/8, which simplifies to 3 1/2 or 3.5.