Olympiad Test: Fractions - Grade 6 MCQ

To find an equivalent fraction to 13/25, we multiply both the numerator and denominator by the same number or divide them if they share a common factor.

Step-by-step Process:

1. Option A: 65/50
   • Check if 65/50 = 13/25:
   • Simplify 65/50 by dividing both numerator and denominator by their greatest common divisor (5):
   • 65/50 = 13/10
   • This is not equivalent to 13/25.
2. Option B: 26/75
   • Check if 26/75 = 13/25:
   • Simplify 26/75 (cannot be simplified further).
   • Clearly, 26/75 ≠ 13/25.
   • This is not equivalent.
3. Option C: 156/300
   • Check if 156/300 = 13/25:
   • Simplify 156/300 by dividing both numerator and denominator by their greatest common divisor (12):
   • 156/300 = 13/25
   • This is equivalent.
4. Option D: 103/205
   • Check if 103/205 = 13/25:
   • Simplify 103/205 (cannot be simplified further).
   • Clearly, 103/205 ≠ 13/25.
   • This is not equivalent.

Answer: Option C: 156/300

Converting ⁴¹/₁₂ to a Mixed Number

Step 1: Understanding Fraction Terms

• Numerator: The number above the fraction line. For ⁴¹/₁₂, the numerator is 41.
• Denominator: The number below the fraction line. For ⁴¹/₁₂, the denominator is 12.
• Improper Fraction: A fraction where the numerator is greater than the denominator.
• Mixed Number: An improper fraction expressed as a whole number and a proper fraction.

Step 2: Find the Whole Number

Divide the numerator by the denominator:

⁴¹/₁₂ = 3.416666...

The whole number part is 3.

Step 3: Get the New Numerator

To find the new numerator:

1. Multiply the whole number (3) by the denominator (12):
   3 × 12 = 36
2. Subtract this result from the numerator:
   41 - 36 = 5

Step 4: Form the Mixed Fraction

The mixed number is formed by combining the whole number with the new numerator and the original denominator:

Step 5: Simplify the Fraction (if possible)

• Find the GCF (Greatest Common Factor) of the numerator (5) and denominator (12).
• The GCF of 5 and 12 is 1.
• Divide both the numerator and denominator by their GCF:
  ⁵/₁₂ (already in simplest form).

Answer: Option C: 3 ⁵/₁₂

Simplified Form of the Product ¹²/₂₄ × ³⁶/₇₂

Step 1: Simplify Each Fraction

• Simplify ¹²/₂₄:
  • The greatest common factor (GCF) of 12 and 24 is 12.
  • Divide both numerator and denominator by 12:
    ¹²/₂₄ = ¹/₂
• Simplify ³⁶/₇₂:
  • The GCF of 36 and 72 is 36.
  • Divide both numerator and denominator by 36:
    ³⁶/₇₂ = ¹/₂

Step 2: Multiply the Simplified Fractions

Now multiply the two simplified fractions:

Step 3: Verify the Simplified Form

• The numerator (1) and denominator (4) have no common factors other than 1.
• Therefore, ¹/₄ is already in its simplest form.

Answer: Option D: ¹/₄

A proper fraction is a fraction where the numerator (the number above the fraction line) is smaller than the denominator (the number below the fraction line).

Analyzing the options:

1. Option A: 28/13

   • Numerator (28) is greater than the denominator (13).
   • This is an improper fraction.

2. Option B: 11/23

   • Numerator (11) is smaller than the denominator (23).
   • This is a proper fraction.

3. Option C: 16/9

   • Numerator (16) is greater than the denominator (9).
   • This is an improper fraction.

4. Option D: 14/3

   • Numerator (14) is greater than the denominator (3).
   • This is an improper fraction.

Answer: Option B: 11/23

The phrase "five eighteenths" means the fraction where 5 is the numerator (top number) and 18 is the denominator (bottom number).

Analyzing the options:

1. Option A: 15/18

   • This is not the correct representation of five eighteenths.

2. Option B: 18/5

   • This is an improper fraction and represents "eighteen fifths," not five eighteenths.

3. Option C: 5.18

   • This is a decimal number, not a fraction.

4. Option D: 5/18

   • This is the correct fractional representation of "five eighteenths."

Answer: Option D: 5/18

To represent Raju's score as a fraction, use the formula:
Fraction = Marks Scored / Maximum Marks
Maximum marks = 25
Marks scored by Raju = 9 
∴ Raju's score represented as a fraction 
= 9/25

 All fractions have the same numerator. So, the fraction having the smallest denominator is the largest. 

∴ 29/23 is the required largest fraction.

To find out how much 19/20 is greater than 2/20, we subtract 2/20 from 19/20:

So, 19/20 is 17/20 greater than 2/20.

To find the sum of 3/4 + 2/4, first add the numerators:

Since 5/4 has a numerator greater than the denominator, it is an improper fraction.

To convert the mixed fraction into an improper fraction:

1. Multiply the whole number (5) by the denominator (7): 5 × 7 = 35
2. Add the numerator of the fraction (4) to the result: 35 + 4 = 39
3. The improper fraction is 39/7.

Thus, can be expressed as 39/7.

To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF (Highest Common Factor). This ensures the fraction is in its simplest form.

• Start with the equation: 2/5 = x/15.
• Cross-multiply to eliminate the fractions: 2 × 15 = 5 × x.
• Calculate the multiplication: 30 = 5x.
• Divide both sides by 5 to solve for x: x = 30/5.
• Therefore, x equals 6.

Shabana has stitched 21 dresses out of a total of 35 dresses. The fraction of dresses she has stitched is 21/35.

To simplify, divide both the numerator (21) and denominator (35) by their HCF, which is 7:

So, the correct fraction of dresses she has stitched is 3/5.

To determine if a fraction is in its lowest form, we check if the numerator and denominator have any common factors other than 1.

• 15/20: The HCF of 15 and 20 is 5. So, 15/20 can be simplified to 3/4. Thus, it is not in its lowest form.
• 7/5, 13/33, and 27/28 are already in their lowest form because their numerators and denominators have no common factors other than 1.

Given: 3 out of 7 fruits are apples.
Fractional representation: To represent this as a fraction, we take the number of apples (3) as the numerator and the total number of fruits (7) as the denominator.
Writing as a fraction: Therefore, the fractional number for "3 out of 7 of the fruits are apples" is written as 3/7.

To find how much 9/18 is greater than 4/18, subtract 4/18 from 9/18:

So, 9/18 is 5/18 greater than 4/18.

An improper fraction is one where the numerator is greater than or equal to the denominator.

• 7/10 and 7/9 are proper fractions because the numerator is smaller than the denominator.
• 9/7 is an improper fraction because the numerator (9) is greater than the denominator (7).

• Equivalent Fractions: Two fractions are equivalent if their cross multiplications are equal.
• Cross Multiplication: Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa.
• Example: If we have two fractions, a/b and c/d, they are equivalent if ad = bc.
• Proof: Let's consider two fractions, a/b and c/d. Their cross multiplication would be ad and bc.
• If ad = bc: This means that the fractions are equivalent because the cross multiplications are equal.
• If ad ≠ bc: This means that the fractions are not equivalent because the cross multiplications are not equal.

Fractions with the same denominator are called like fractions. For example:

• Examples of like fractions: 2/7, 5/7, 9/7
• Unlike fractions have different denominators: 1/4, 3/8, 5/6
• Unit fractions have numerator as 1: 1/2, 1/3, 1/4
• Improper fractions have numerator greater than or equal to the denominator: 7/5, 9/4

A fraction whose numerator is greater than its denominator is called an improper fraction. For example, 9/7 is an improper fraction because the numerator (9) is greater than the denominator (7).