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 HCM (Highest Common Measure), also known as the HCF (Highest Common Factor). This ensures the fraction is in its simplest form.

2/5 = x/15
2*15 / 5 = x
30/5 = x
6 = x

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).