   # Compare fractions practice

Comparing fractions is an important concept in the understanding of fractions. Our program helps to train this skill.  ## Practice comparing fractions to 1, 1/2. Recognize simple equivalent fractions.

During practicing, students master the basic fraction comparing skill. They learn equivalent fractions, how to compare fractions to 1 and 1/2. In case of the wrong answer, Math Skill Builder will show the explanation.  ## Compare fractions by using benchmarks and other strategies.

The ability to use benchmarks instead of the method that involve LCM is pretty helpful for success in math.

### Benchmarking to 1 strategy.

We need to compare
 10 11
and
 7 6
 10 11
 7 6
 0 1
Use the benchmarking to 1 strategy. Notice that one of the fractions is less than 1, and the other is greater than 1.
 10 11
<1
and
 7 6
>1
, then
 10 11
<
 7 6

### Benchmarking to 1/2 strategy

We need to compare
 6 11
and
 4 10
 6 11
 4 10
 0 1
Use the benchmarking to 1/2 strategy. Notice that one of the fractions is less than 1/2, and the other is greater than 1/2.
 6 11
>
 1 2
and
 4 10
<
 1 2
, then
 6 11
>
 4 10

### Residual thinking strategy.

We need to compare
 5 6
and
 7 8
 5 6
 7 8
 0 1
Use the residual thinking strategy. Notice that one of the fractions is "closer" to 1 then the other.
5/6 needs 1/6 to make 1 and 7/8 needs 1/8 to make 1.
1/8 is smaller, so 7/8 is "closer" to 1 and greater than 5/6.
 1 6
>
 1 8
, so
 5 6
<
 7 8

### Fractions with the same numerators.

We need to compare
 7 12
and
 7 9
 7 12
 7 9
 0 1
If the numerators are the same, the larger fraction is the one with smaller denominator.
12>9, so
 7 12
<
 7 9

### Fractions with the same denominators.

We need to compare
 3 11
and
 10 11
 3 11
 10 11
 0 1
If the denominators are the same, the larger fraction is the one with greater numerator.
3<10, so
 3 11
<
 10 11  ## Comparing fractions by making the numerator or denominator the same.

If it is impossible to compare fractions by benchmarks and other strategies, students have to use more complicated methods. This training helps them to learn how to compare fractions by making numerators or denominators the same and then use already learned skills.

### Comparing fractions by making the numerator the same.

We need to compare
 3 7
and
 9 22
 3 7
(
 9 21
)
 9 22
 0 1
Make both of the numerators the same.
Notice that 3x3=9. Multiply the numerator and denominator by 3 to make the numerators the same, and then compare the fractions.
 3 x 3 7 x 3
=
 9 21
,
 9 21
>
 9 22
, so
 3 7
>
 9 22

### Comparing fractions by making the denominator the same.

We need to compare
 26 30
and
 5 6
 26 30
 5 6
(
 25 30
)
 0 1
Make both of the denominators the same.
Notice that 6x5=30. Multiply the numerator and denominator by 5 to make the denominators the same, and then compare the fractions.
 5 x 5 6 x 5
=
 25 30
,
 26 30
>
 25 30
, so
 26 30
>
 5 6

## Progress report

The report shows the learning progress in percentage (0% - not learned, 100% - learned perfectly).
There are three levels of the report.

### Short report

Compare to 1, 1/2: 76%
Compare by using benchmarks: 96%
Compare by making numerators, denominators the same: 60%

### Normal and detail report

Compare to 1, 1/2
Compare to 187%
Equivalent to 1/297%
Compare to 1/245%
Compare by using benchmarks
Benchmark to 1 strategy100%
Benchmark to 1/2 strategy91%
Closer to 1 strategy98%
Compare by making numerators,
denominators the same
Compare fractions with the same numerator100%
Compare fractions with the same denominator80%
Make both of the numerators the same35%
Make both of the denominators the same25%