Rewrite the given proportions according to the property indi

Joseph Krupa

Joseph Krupa

Answered question

2021-12-13

Rewrite the given proportions according to the property indicated in the table and find out if the ratios in the rewritten proportions are still equal.
  Use the cross multiplication pro perty to verify that ratios are equal. Simplify if necessary. One is done for youOriginal Proportiony3=a44y=3aAlternation Property of the original propertionInverse Property of the original proportionAddition Property of the original proportionSubtraction Property of the original proportionSum Propert of the original proportion

Answer & Explanation

Raymond Foley

Raymond Foley

Beginner2021-12-14Added 39 answers

Step 1
Given
Original proportion
y3=a4
Alternation property : If a:b=c:d, then a:c=b:d, for numbers a, b, c, d
We have, y:3=a:4
Then, by alternation property, we have,
y:a=3:4
Hence,
ya=344y=3a
Step 2
Inverse Property : If a:b=c:d, then b:a=d:c, for numbers a, b, c, d
We have, y:3=a:4
Then, by inverse property, we have,
3:y=4:a
Hence,
3y=4a4y=3a
Jim Hunt

Jim Hunt

Beginner2021-12-15Added 45 answers

Step 1
Solve for a
y3=a4
Multiply both sides of the equation by 12, the least common multiple of 3,4.
4y=3a
Swap sides so that all variable terms are on the left hand side.
3a=4y
Divide both sides by 3
3a3=4y3
Dividing by 3 undoes the multiplication by 3.
a=4y3
Solve for y
y3=a4
Multiply both sides of the equation by 12, the least common multiple of 3,4.
4y=3a
Divide both sides by 4.
4y4=3a4
Dividing by 4 undoes the multiplication by 4.
y=3a4

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