Decomposition and Fraction Equivalence

What is equivalent to 1/5?

• 1/10

• 10/1

• 2/10

• 2/5

Answer explanation

To find an equivalent fraction for 1/5, we can multiply both the numerator and denominator by 2. This gives us 2/10, which is equal to 1/5. The other options do not equal 1/5.

Which fraction is equivalent to 3/4 ?

• 6/8

• 12/15

• 6/15

• 8/12

Answer explanation

To find a fraction equivalent to 3/4, we can multiply both the numerator and denominator by the same number. For 3/4, multiplying by 2 gives us 6/8, which is equivalent. The other options do not simplify to 3/4.

When finding equivalent fractions, we need to multiply or divide:

• Only the numerator

• Only the denominator

• Both the numerator and denominator

• Neither the numerator or denominator

Answer explanation

To find equivalent fractions, you must multiply or divide both the numerator and the denominator by the same non-zero number. This keeps the value of the fraction the same while changing its form.

Are the fractions equivalent?

• Yes, because 8 x 4 = 32

• Yes, because 8 x 4= 32 and 4 + 8 = 12

• No, because 8x4=32 and 4x4=16

Answer explanation

The correct answer is 'No' because 8x4=32 and 4x4=16 show that the fractions are not equivalent. The values produced by these multiplications are different, confirming the fractions do not represent the same quantity.

Fill in the missing number to form an equivalent fraction.

Answer explanation

To form an equivalent fraction, the numerator must be zero if the denominator is also zero. Thus, the missing number is 0, making the fraction 0/x, which is equivalent to 0.

Select ALL the fractions that are equivalent to 1/2.

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• 
• 
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Which numerator makes the fractions equivalent?

• 2

• 4

• 6

• 8

Answer explanation

To find the numerator that makes the fractions equivalent, we can set up a proportion. If we have a fraction with a denominator, multiplying it by 2 gives us an equivalent fraction. Thus, 2 is the correct numerator.

Answer explanation

To find the missing number, set up the proportion: \( \frac{11}{2} = \frac{33}{x} \). Cross-multiply to get \( 11x = 66 \). Solving for \( x \) gives \( x = 6 \). Thus, the missing number is 6.

TRUE or FALSE: Whatever you do to the numerator (top#), you MUST do it to the denominator (bottom#).

• True

• False

Answer explanation

True. In mathematics, if you perform an operation on the numerator of a fraction, you must perform the same operation on the denominator to maintain the value of the fraction.

Answer explanation

To find an equivalent fraction for \( \frac{1}{3} \), multiply both the numerator and denominator by 4: \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \). Thus, the correct answer is \( \frac{4}{12} \).