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Arithmetic (all content)

Course: Arithmetic (all content) > Unit 5

Lesson 6: Equivalent fractions 1
Math
Arithmetic (all content)
Fractions
Equivalent fractions 1
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Visualizing equivalent fractions review

Google Classroom
Review equivalent fractions with fraction models and number lines, and try some practice problems.

Equivalent fractions

Fractions are equivalent if they are equal or represent the same amount.

Fraction model

Let's look at an example.
start fraction, 1, divided by, 2, end fraction, equals, start fraction, question mark, divided by, 8, end fraction
First, we can draw start fraction, 1, divided by, 2, end fraction.
A circle divided into two equal parts with one part shaded.
Now, let's divide the same whole into eighths.
A circle divided into eight equal parts. This circle is the same size as the original circle.
How can we shade the whole to show a fraction that is equivalent to start fraction, 1, divided by, 2, end fraction?
The circle that was divided into eight equal parts is shown with four parts shaded. This shows the same area shaded as the circle that was divided into two parts with one part shaded.
We shaded 4 of the 8 sections.
So, start fraction, 1, divided by, 2, end fraction, equals, start fraction, 4, divided by, 8, end fraction.

Number line

Let's visualize another equivalent fraction using a number line.
start fraction, 3, divided by, 5, end fraction, equals, start fraction, question mark, divided by, 10, end fraction
Numbers are equivalent when they are located at the same point on the number line.
First, we can show start fraction, 3, divided by, 5, end fraction on a number line:
A number line that has, moving from left to right, a starting tick mark at 0, 2 unlabeled tick marks, a tick mark at three-fifths, 1 unlabeled tick mark, and a tick mark at 1. There is a blue point at the three-fifths tick mark.
Now, let's divide our number line into tenths and see what fraction is located at the same point as start fraction, 3, divided by, 5, end fraction.
A number line that has, moving from left to right, a starting tick mark at 0, a tick mark at one-tenth, 8 unlabeled tick marks, and a tick mark at 1. There is a blue point 6 tick marks to the right of 0, which is the same point on the number line as the point at three-fifths on the previous number line. Starting at 0, every second tick mark is emphasized.
start fraction, 6, divided by, 10, end fraction and start fraction, 3, divided by, 5, end fraction are located at the same point on the number line.
A number line labeled zero to 1 with tick marks every one-tenth unit. Above the number line, the tick mark at zero is labeled zero, the tick mark at two-tenths is labeled one-fifth, the tick mark at four-tenths is labeled two-fifths, the tick mark at six-tenths is labeled three-fifths, the tick mark at eight-tenths is labeled four-fifths, and the tick mark at 1 is labeled 1. A blue point appears at the tick mark labeled six-tenths and three-fifths.
start fraction, 3, divided by, 5, end fraction, equals, start fraction, 6, divided by, 10, end fraction
Want to learn more about visualizing equivalent fractions? Check out this video.

Practice

Problem 1
  • Current
Complete the equation.
start fraction, 2, divided by, 5, end fraction, equals, start fraction, \bigstar, divided by, 10, end fraction
\bigstar, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
A circle divided into five equal parts with two parts shaded.
The same size circle as above divided into ten equal parts. None of the parts are shaded.

Want to try more problems like this? Check out this exercise.

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