Equivalent fractions (age 9+)

Question 1

A farmer uses three identical fraction strips to compare the same portion of a field. On the first strip the field is divided into 4 equal sections and 1 section is shaded. On the second strip the field is divided into 8 equal sections, and on the third strip it is divided into 12 equal sections. Which list shows the three fractions that correctly represent the same shaded portion on each strip?

Accepted Answer

1/4, 2/8, 3/12

Answer

1/4, 2/8, 4/12

Answer

2/4, 4/8, 6/12

Answer

1/4, 2/7, 3/12

Question 2

Sam has a chocolate bar that is divided into 7 equal squares. He eats 3 of those squares. Afterwards he cuts every square into 4 smaller equal pieces, so the bar now has 28 tiny pieces. Which statement correctly explains why the fraction that shows how much Sam ate (12/28) is equivalent to the original fraction 3/7?

Accepted Answer

Multiplying the numerator and denominator by the same number (4) does not change the size of the whole chocolate bar; it only makes each original piece smaller, so 3/7 = 12/28.

Answer

Since the denominator got bigger, the fraction must become smaller, so we add 1 to the numerator to keep the value the same; thus 3/7 becomes 12/28.

Answer

The fraction stays the same because Sam still ate three original squares, even though we counted the pieces differently; therefore we should keep the numerator as 3 and only change the denominator to 28.

Answer

Because Sam now has 12 tiny pieces out of 28, the numerator grew faster than the denominator, making the fraction larger, but it still represents the same amount he ate.

Question 3

Which explanation correctly tells why the fraction 3/4 is the same as 6/8?

Accepted Answer

Both fractions show the same part of a whole because we multiplied the top and bottom by the same number, so the size of each piece stays the same.

Answer

We multiplied the numerator by 2, so the fraction gets twice as big, making it equal to 6/8.

Answer

Multiplying the denominator makes the whole bigger, so the fraction stays the same.

Answer

Adding 2 to the numerator and denominator changes the fraction to an equivalent one.

Try three questions

Which explanation correctly tells why the fraction 3/4 is the same as 6/8?

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