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If a /4=b /7, what is the value of a/b?
a/4 = b/7
a = (4 b/7)
a/b = 4/7
If a /4=b /7
then 7a = 4b
divide both sides by b
7a/b = 4
divide both sides by 7
a/b = 4/7
To find the value of a/b given that a/4 = b/7, we can set up an equation and solve for the ratio a/b.
Step 1: Start with the given equation a/4 = b/7.
Step 2: Cross multiply the equation. Multiply the numerator of the first fraction with the denominator of the second fraction and vice versa. This gives us 7a = 4b.
Step 3: Divide both sides of the equation by 4 to isolate a. Divide both sides by 4, we have 7a/4 = b.
Step 4: To find a/b, divide both sides of the equation by b. We have (7a/4) / b = 1.
Step 5: Simplify the left side of the equation. (7a/4) / b is the same as (7a/4) * (1/b). The b in the denominator cancels out with the b in the numerator. We are left with 7a/(4b) = 1.
Step 6: Solve for a/b. Multiply both sides of the equation by (4b) to isolate a/b. We have 7a = 4b.
Step 7: Divide both sides of the equation by 7. Divide both sides by 7 to solve for a. We have a = (4b)/7.
Step 8: Substitute the value of a in terms of b back into the equation a/b. We get (4b)/7 divided by b, or (4b)/7b.
Step 9: Simplify the expression. The b in the denominator cancels out with the b in the numerator. We are left with 4/7.
Therefore, the value of a/b is 4/7.