If a/4 = b/7, what is the value of a/b?
Can somebody guide me through a step by step please? I know it's cross multiplication, I just want to make sure I know what I'm doing since I'm a little confused with this one.
a/4 = b/7
multiply both sides by 4
a = 4b/7
divide both sides by b
a/b = 4/7
Ah, cross multiplication, the dance move of the mathematical world! But don't worry, I'll guide you through it like a pro!
Step 1: Write down the given equation: a/4 = b/7.
Step 2: Cross multiply! Multiply the numerator of the left fraction (a) by the denominator of the right fraction (7), and multiply the numerator of the right fraction (b) by the denominator of the left fraction (4).
You'll get 7a = 4b.
Step 3: Now, solve for a/b by isolating it on one side. Divide both sides of the equation by b first, so you'll end up with (7/4) * a = b.
Step 4: To find a/b, we need to divide both sides of the equation by (7/4), or in other words, multiply both sides by the reciprocal of (7/4), which is 4/7.
So, a/b = (4/7) * (7/4) * a = (4 * a) / (7 * 1) = 4a/7.
Tada! The value of a/b is 4a/7. Keep practicing those math moves!
To find the value of a/b, given that a/4 = b/7, you can follow these steps:
1. Start with the equation a/4 = b/7.
2. Cross-multiply by multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives you a * 7 = b * 4.
3. Simplify the equation by multiplying: 7a = 4b.
4. Divide both sides of the equation by 4 to isolate b: (7a)/4 = b.
5. Simplify the equation: b = (7/4)a.
Now, you have found the value of b in terms of a. To find the value of a/b, substitute the expression for b in terms of a into the fraction:
a/b = a / [(7/4)a] = 4/7.
Therefore, the value of a/b is 4/7.
To find the value of a/b given that a/4 = b/7, you can use cross multiplication. Here's a step-by-step guide:
Step 1: Write down the equation: a/4 = b/7.
Step 2: Cross-multiply the equation. This means multiplying the numerator of one ratio with the denominator of the other ratio.
a/4 * 7/1 = b/7 * 4/1
Step 3: Simplify each side.
7a/4 = 4b/7
Step 4: Multiply both sides of the equation by the denominators of the fractions to eliminate them.
7 * (7a/4) = 4 * (4b/7)
49a/4 = 16b/7
Step 5: To eliminate fractions, you can multiply both sides by the lowest common denominator (LCD), which is 28 in this case.
28 * (49a/4) = 28 * (16b/7)
7 * 49a = 4 * 16b
Step 6: Simplify both sides of the equation.
343a = 64b
Step 7: Divide both sides by b to solve for a/b.
343a/b = 64
So, the value of a/b is 64/343.