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Equivalent fractions
a free lesson with a video

Making equivalent fractions is like splitting all the pieces further into a certain number of new pieces. The visual model for equivalent fractions involves splitting the existing pieces into so many new ones, such as splitting all of them into 4 new pieces. This is shown using the arrow notation with "x4" near the arrows, signifying that the numerator and the denominator get multiplied by 4, because there are now four times as many colored pieces and four times as many pieces in total. Please watch the video to see how to use idea.

Besides the video, please also see this free sample worksheet: Equivalent Fractions worksheet. The worksheet shows the same notation and the same idea as the video and the lesson below. The worksheet is a sample from my book Math Mammoth Fractions 1. The lesson below also explains the same ideas, and is taken from the same book.

This is an important topic. You need to understand equivalent fractions well before learning about adding unlike fractions.

=       These two fractions are equivalent fractions because they picture the same amount. You could say that you get to "eat"  the same amount of "pie" either way. In the second picture  each slice has just been split into two pieces. 1 3 = 2 6

Splitting the pieces The arrows on top and below the equivalent fractions show into how many new pieces each piece was split. = Each slice has been split in two. BEFORE: 3 colored pieces, 4 total AFTER: 6 colored pieces, 8 total × 2 3 4    =    6 8 × 2       =   Each slice has been split into three. BEFORE: 1 colored piece, 3 total AFTER: 3 colored pieces, 9 total × 3         1 3 = 3 9 × 3   =   Each slice has been split into four. The whole number does not change. BEFORE: 1 colored piece, 2 total AFTER: 4 colored pieces, 8 total × 4       1  1 2 =  1 4 8 × 4   =   Each slice has been split in two. BEFORE: 1 colored piece, ___ total AFTER: ___ colored pieces, ___ total × 2         1   =     × 2

When all of the pieces are split the same way, both the number of colored pieces (numerator) and the total number of pieces (denominator) get multiplied by the same number.

1. Connect those fractions that show the same amount. Write the name of each fraction beside it.

1 2

2. Split the pieces and draw the new pieces into the picture. Write down the equivalent
    fractions. If you need help, draw also the "helping arrows" above and below the fractions.

a.  Split each piece in two. = × 2 2 5 =     × 2	b.  Split each piece into three. = × 3 1 2 =     × 3	c.  Split each piece in two. = × 2 2 3 =     × 2
d.  Split each piece in two. =   =	(available in the book)	(available in the book)
g.  Split each piece in two. =   =

3. Write the equivalent fraction. Imagine or draw the helping arrows.
    Note: whole-number parts in a mixed number do not change.

4. Make chains of equivalent fractions according to the model. Look at the patterns formed by
    the denominators, and those formed by the numerators.

= = = a.  1 1 = 2 2 = = 4   =  5    =  6    =       =

b. (available in the book)

= = = c.  1 2 = = =      =  5    =  6    =       =

d. (available in the book)

e. (available in the book)

f.  3 4 =      =      =         =        =        =     =     =

5. First find out how many ways the pieces were split. Then write the missing numerator or denominator.

6. The three number lines have 12th parts, 3rd parts, and 24th parts.

a. Find the fraction that is     equivalent to 2 3  on the     12th parts number line and     on the 24th parts number     line. Mark all three     fractions on the number     lines.       2 3  =        12  =        24

    d. (available in the book)

    e. (available in the book)

Next lesson: adding unlike fractions

The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book.

Math Mammoth Fractions 1 $4.50 A self-teaching printable worktext that teaches fractions and their operations with visual models. You don't need to just memorize fraction rules blindly - learn and understand! The book covers fractions, mixed numbers, equivalent fractions, adding and subtracting like fractions and unlike fractions, adding and subtracting mixed numbers, comparing fractions, and finding a fractional part of a group.