Equivalent Fractions
Find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation.
Read this first
Two fractions can look different. They can still be the same size.
One half and two quarters reach the same place. They are equivalent.
Words you need
- Equivalent
- The same amount, written a different way.
- Half
- One of two equal parts.
- Quarter
- One of four equal parts.
Worked example
e.g. Is 1/2 the same as 3/6?
- Draw a bar cut into 2. Shade 1 part.
- Draw a bar the same size. Cut it into 6. Shade 3 parts.
- Both shaded parts reach the same place.
- So 1/2 and 3/6 are equivalent.
You can also check by multiplying. 1 times 3 is 3. 2 times 3 is 6.
Practice
The pictures fade as you go. By the last few you are on your own.
1Is 1/2 the same as 2/4?with a picture
AnswerYes. They reach the same place.
2Is 1/4 the same as 3/8?with a picture
AnswerNo. 3/8 is a little more.
3Fill the gap: 1/3 = ?/6with a hint
Need a hint?
The bottom doubled, so double the top.
Answer2/6.
4Fill the gap: 2/5 = ?/10with a hint
Need a hint?
The bottom doubled.
Answer4/10.
5Write 1/2 with a bottom number of 8.on your own
Answer4/8.
6Write 4/10 as a decimal.on your own
Answer0.4.
7Is 5/10 the same as 1/2?on your own
AnswerYes. Both are half.
Think about it
1
What do you do to the top when the bottom doubles?
One good answerDouble the top as well, so the amount stays the same.
2
Why does 5/10 equal 0.5?
One good answerTenths are the first decimal column, so 5 tenths is 0.5.
Common mistakes
Adding the same number to top and bottom.
You must multiply, not add. 1/2 is not 2/3.
Drawing bars of different sizes.
The wholes must be the same size or you cannot compare them.