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Factors and multiples Greatest common factor (GCF) Simplifying fractions Prime factors How to write a ratioHere you will learn about simplifying ratios, including how to simplify a ratio and how to write equivalent ratios.
Students will first learn about simplifying ratios as part of ratios and proportions in 6 th grade.
Simplifying ratios is a way of using common factors to divide all the numbers in a ratio until they cannot be divided further.
A simplified ratio is equivalent to a non simplified ratio.
You can use bar modeling to simplify ratios.
For example,
Here are some circles.
Rearrange them into colored bars to show the number of yellow circles and the number of blue circles.
The number of yellow circles is 4, and the number of blue circles is 6. This can be written as the ratio 4:6.
Rearrange these circles into another pattern, where yellow and blue have the same number of complete rows:
The overall ratio is still 4:6, but now you have two rows that show the ratio 2:3. This means that you can split the ratio into 2 groups, and still obtain an equivalent ratio of yellow to blue.
Using bar modeling simplifies the ratio 4:6 to get 2:3.
You can also divide by the greatest common factor or \bf{GCF} to simplify a ratio.
For example,
The ratio of red counters to blue counters is 12:16.
You can simplify the ratio by finding the greatest common factor or \bf{GCF} of each of the numbers in the ratio.
Factors of 12: 1, \, 2, \, 3, \, 4, \, 6, \, 12
Factor of 16: 1, \, 2, \, 4, \, 8, \, 16
The greatest common factor is 4. To simplify the ratio, you divide both sides by 4.
How does this relate to 6 th grade math?
In order to simplify a ratio:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEUse a bar model to simplify the ratio 8:10.
Representing the ratio 8:10 as a bar model, you have…
Where red represents 8 shares and purple represents 10 shares. Thinking about how both 8 and 10 can be grouped equally, they are both divisible by 2 \, - which is also the GCF.
2Divide each part of the ratio by the greatest common factor.
Divide the bar above into two groups with the same amount of red shares and purple shares.
Each bar is the ratio 4:5, which is 8:10 in lowest terms.
Write the ratio 20:32 in lowest terms.
Calculate the greatest common factor of the parts of the ratio.
Factors of 20 = 1, \, 2, \, 4, \, 5, \, 10, \, 20
Factors of 32 = 1, \, 2, \, 4, \, 8, \, 16, \, 32
GCF (20,32) = 4
Divide each part of the ratio by the greatest common factor.
5:8 is in lowest terms.
Write the ratio 21:14 in lowest terms.
Calculate the greatest common factor of the parts of the ratio.
Factors of 21 = 1, \, 3, \, 7, \, 21
Factors of 14 = 1, \, 2, \, 7, \, 14
GCF (21,14) = 7
Divide each part of the ratio by the greatest common factor
3:2 is in lowest terms.
Write the ratio 16:24 in lowest terms.
Calculate the greatest common factor of the parts of the ratio.
Factors of 16 = 1, \, 2, \, 4, \, 8, \, 16
Factors of 24 = 1, \, 2, \, 3, \, 4, \, 6, \, 8, \, 12, \, 24
GCF (16, 24) = 8
Divide each part of the ratio by the greatest common factor.
2:3 is in lowest terms.
Write the ratio 55:95 in lowest terms.
Calculate the greatest common factor of the parts of the ratio.
Factors of 55 = 1, \, 5, \, 11, \, 55
Factors of 95 = 1, \, 5, \, 19, \, 95
GCF (55,95) = 5
Divide each part of the ratio by the greatest common factor.
11:19 is in lowest terms.
Write the ratio 145:212 in lowest terms.
Calculate the greatest common factor of the parts of the ratio.
Factors of 145 = 1, \, 5, \, 29, \, 145
Factors of 212 = 1, \, 2, \, 4, \, 53, \, 106, \, 212
GCF (145,212) = 1
Divide each part of the ratio by the greatest common factor.
Dividing each side by 1 will not change the ratio. The ratio is already in lowest terms.
1) Which bar model shows the ratio 6:10 in lowest terms?
The original ratio 6:10 is shown with 6 blue squares and 10 orange squares.
The greatest common factor is 2, so divide the bar above into two groups with the same amount of blue shares and orange shares.
Each bar is the ratio 3:5, which is 6:10 in lowest terms.
2) Write the ratio 72:24 in lowest terms.
Factors of 24 = 1, \, 2, \, 3, \, 4, \, 6, \, 8, \, 12, \, 24
Factors of 72 = 1, \, 2, \, 3, \, 4, \, 6, \, 8, \, 9, \, 12, \, 18, \, 24, \, 36, \, 72
GCF (24,72) = 24
3) Write the ratio 36:30 in lowest terms.
Factors of 36 = 1, \, 2, \, 3, \, 4, \, 6, \, 9, \, 12, \, 18, \, 36
Factors of 30 = 1, \, 2, \, 3, \, 5, \, 6, \, 10, \, 15, \, 30
GCF (36,30) = 6
4) Write the ratio 28:42 in lowest terms.
Factors of 28 = 1, \, 2, \, 4, \, 7, \, 14, \, 28
Factors of 42 = 1, \, 2, \, 3, \, 6, \, 7, \, 14, \, 21, \, 42
GCF (28,42) = 14
5) Write the ratio 78:91 in lowest terms.
Factors of 78 = 1, \, 2, \, 3, \, 6, \, 13, \, 26, \, 39, \, 78
Factors of 91 = 1, \, 7, \, 13, \, 91
GCF (78,91) = 13
6) Write the ratio 102:81 in lowest terms.
Factors of 102 = 1, \, 2, \, 3, \, 6, \, 17, \, 34, \, 51, \, 102
Factors of 81 = 1, \, 3, \, 9, \, 27, \, 81
GCF(102,81) = 3
Yes, you can write one part of the ratio as the numerator and the other part as the denominator.
This is another name for the greatest common factor (GCF).
Yes, part of a ratio can be a fraction, decimal, mixed number, percentage, or other types of numbers. It can also be algebraic and show a relationship represented by polynomials.
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