Identifying Equivalent Ratios
Equivalent Ratios
Two ratios are equivalent if their cross products are equal. Compare the cross products by cross multiplying: Multiply the denominator of one fraction by the numerator of the other fraction. If the cross products are equal then the ratios are equivalent.
Another Method
Ratios are used in order to find how two or more quantities are related. In order determine whether you have equivalent ratios, you must multiply or divide both sides by the same number.
The first two problems use the first method above whereas the last two problems use the second method above.
Problems #1
Are the following ratios equivalent?
2:3 and 10:12
Step 1
Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second:
2 x 12 = 24
Step 2
Problems #2
Are the following ratios equivalent?
5:25 and 12:60
Step 1
Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second:
5 x 60 = 300
Step 2
Problems #3
Are 10/12 and 35/42 equivalent fractions?
Step 1
Are 7/14 and 32/60 equivalent fractions?
Step 1
Two ratios are equivalent if their cross products are equal. Compare the cross products by cross multiplying: Multiply the denominator of one fraction by the numerator of the other fraction. If the cross products are equal then the ratios are equivalent.
Another Method
Ratios are used in order to find how two or more quantities are related. In order determine whether you have equivalent ratios, you must multiply or divide both sides by the same number.
The first two problems use the first method above whereas the last two problems use the second method above.
Problems #1
Are the following ratios equivalent?
2:3 and 10:12
Step 1
Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second:
2 x 12 = 24
Step 2
Determine the second cross product by multiplying the denominator of the first fraction by the numerator of the second:
3 x 30 = 90
Step 3
Compare the cross products to determine if they are equal:
24 does not equal 30 so 2:3 and 10:12 are not equivalent ratios.
Are the following ratios equivalent?
5:25 and 12:60
Step 1
Determine the cross products by multiplying the numerator of the first fraction by the denominator of the second:
5 x 60 = 300
Step 2
Determine the second cross product by multiplying the denominator of the first fraction by the numerator of the second:
25 x 12 = 300
Step 3
Compare the cross products to determine if they are equal:
300 is equal to 300 so 5:25 and 12:60 are equivalent ratios.
Are 10/12 and 35/42 equivalent fractions?
Step 1
Rewrite the first fraction in it's simplest form by dividing:
Divide 10/12 by 2 in order to rewrite it in it's simplest form: 5/6
Step 2
Rewrite the second fraction in it's simplest form by dividing:
Divide 35/42 by 6 to rewrite it in it's simplest form: 5/6
Step 3
Compare both the simplest form's of both fractions to determine if the two are equivalent:
5/6 is equal to 5/6 therefore 10/12 and 35/42 are equivalent fractions.
Problems #4Divide 10/12 by 2 in order to rewrite it in it's simplest form: 5/6
Step 2
Rewrite the second fraction in it's simplest form by dividing:
Divide 35/42 by 6 to rewrite it in it's simplest form: 5/6
Step 3
Compare both the simplest form's of both fractions to determine if the two are equivalent:
5/6 is equal to 5/6 therefore 10/12 and 35/42 are equivalent fractions.
Are 7/14 and 32/60 equivalent fractions?
Step 1
Rewrite the first fraction in it's simplest form by dividing:
Divide 7/14 by 7 in order to rewrite it in it's simplest form: 1/2
Step 2
Rewrite the second fraction in it's simplest form by dividing:
Divide 32/60 by 4 to rewrite it in it's simplest form: 8/15
Step 3
Compare both the simplest form's of both fractions to determine if the two are equivalent:
1/2 is not equal to 8/15 therefore 7/14 and 32/60 are not equivalent fractions.
Divide 7/14 by 7 in order to rewrite it in it's simplest form: 1/2
Step 2
Rewrite the second fraction in it's simplest form by dividing:
Divide 32/60 by 4 to rewrite it in it's simplest form: 8/15
Step 3
Compare both the simplest form's of both fractions to determine if the two are equivalent:
1/2 is not equal to 8/15 therefore 7/14 and 32/60 are not equivalent fractions.
