Question

In each pair, tell if the fractions are equal by using cross multiplication.

a. 5/30 and 1/6
b.4/12 and 21/60
c. 17/34 and 41/82
d. 6/9 and 25/36​

Answer 1

a. The fractions are equal.

b. The fractions are not equal

c. The fractions are equal.

d. The fractions are not equal

Explanation:

By definition, equivalent fractions have the same value, but they look different.

In order to verify if two fractions are equivalent, you can use Cross multiplication.

The procedure is: multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

Then:

`a.\ (5)/(30)=(1)/(6)\\\\5*6=1*30\\\\30=30\ (The\ fractions\ are\ equal)`

`b.\ (4)/(12)=(21)/(60)\\\\4*60=21*12\\\\240=252\ (FALSE.\ The\ fractions\ are\ not\ equal)`

`c.\ (17)/(34)=(41)/(82)\\\\17*82=41*34\\\\1394=1394\ (The\ fractions\ are\ equal)`

`d.\ (6)/(9)=(25)/(36)\\\\6*36=25*9\\\\216=225\ (FALSE.\ The\ fractions\ are\ not\ equal)`

Answer 2

a. 5/30 and 1/6 ---> are equal

b.4/12 and 21/60 ---> are not equal

c. 17/34 and 41/82 ---> are equal

d. 6/9 and 25/36​ ---> are not equal

Explanation:

case a) we have 5/30 and 1/6

equate the fractions

`(5)/(30)=(1)/(6)`

using cross multiplication

`(5)(6)=(30)(1)`

`30=30` ----> is true

therefore

The fractions are equal

case b) we have 4/12 and 21/60

equate the fractions

`(4)/(12)=(21)/(60)`

using cross multiplication

`(4)(60)=(21)(12)`

`240=252` ----> is not true

therefore

The fractions are not equal

case c) we have 17/34 and 41/82

equate the fractions

`(17)/(34)=(41)/(82)`

using cross multiplication

`(17)(82)=(41)(34)`

`1,394=1,394` ----> is true

therefore

The fractions are equal

case d) we have 6/9 and 25/36​

equate the fractions

`(6)/(9)=(25)/(36)`

using cross multiplication

`(6)(36)=(25)(9)`

`216=225` ----> is not true

therefore

The fractions are not equal