How To Cross Multiply To Find X

Download Article

Cross multiplying is a way to solve an equation that involves a variable as function of two fractions set equal to each other. The variable is a placeholder for an unknown number or quantity, and cross-multiplying reduces the proportion to i simple equation, allowing yous to solve for the variable in question. Cantankerous multiplying is particularly useful when you're trying to solve a ratio. Here's how to do it:

i

Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction. Allow'due south say you're working with the equation ii/x = 10/13. Now, multiply 2 * 13. 2 * 13 = 26.^[1]
2

Multiply the numerator of the right-paw fraction by the denominator of the left-hand fraction. Now multiply x by 10. x * 10 = 10x. Yous can cross multiply in this direction first; it really doesn't matter equally long as you lot multiply both numerators by the denominators diagonal from them.^[ii]

Ad
3
Set the two products equal to each other. Merely set 26 equal to 10x. 26 = 10x. It doesn't affair which number you list beginning; since they're equal, you can swap them from one side of the equation to the other with impunity, equally long as you treat each term equally a whole.^[iii]
- And so, if you're trying to solve 2/x = x/13 for x, you'd have 2 * 13 = x * 10, or 26 = 10x.
4

Solve for the variable. Now that you're working with 26 = 10x, you lot tin start by finding a common denominator and dividing both 26 and 10 by a number that divides evenly into both numbers. Since they are both even, y'all can divide them past ii; 26/2 = 13 and 10/two = 5. You're left with 13 = 5x. At present, to isolate 10, divide both sides of the equation by 5. So, 13/5 = 5x/v, or 13/5 = ten. If y'all'd like the answer in decimal form, you can outset by dividing both sides of the equation by x to go 26/10 = 10x/10, or 2.half dozen = 10.^[4]

Advertisement

ane

Multiply the numerator of the left-hand fraction past the denominator of the right-mitt fraction. ^[5] Let'south say you're working with the following equation: (x + iii)/2 = (x + 1)/4. Multiply (x + 3) by iv to get 4(x +3). Distribute the 4 to go 4x + 12.
2

Multiply the numerator of the right-hand fraction by the denominator of the left-manus fraction. ^{[half dozen]} Repeat the process on the other side. (x +1) x 2 = 2(x +ane). Distribute the 2 and you get 2x + 2.
3
Set up the 2 products equal to each other and combine the similar terms. Now, you'll have 4x + 12 = 2x + 2. Combine the 10 terms and the constant terms on opposite sides of the equation.
- So, combine 4x and 2x by subtracting 2x from both sides. Subtracting 2x from 2x on the correct side will get out you with 0. On the left side, 4x - 2x = 2x, so you lot have 2x remaining.
- At present, combine 12 and 2 by subtracting 12 from both sides of the equation. Subtract 12 from 12 on the left and y'all'll have 0, and subtract 12 from 2 on the correct side to become 2-12 = -10.
- Yous're left with 2x = -x.
4

Solve. All y'all accept to exercise is divide both sides of the equation by 2. 2x/2 = -ten/2 = x = -5. After cantankerous multiplying, y'all have found that x = -5. Y'all can go back and check your work by plugging in -5 for x to make certain that both sides of the equation are equal. They are. If yous plug -v back into the original equation, you'll go -ane = -1.

Advertisement

Add New Question

Question

How would I solve xxx% of 65

Multiply 65 past 0.3. (You could think of it equally multiplying 65 by 10% by merely moving the decimal point to the left one digit to get six.5 and and so multiplying by 3 to become 30% of 65.)
Question

One solar day 176 people visited a small art museum. The ratio of members to nonmembers that day was 5 to eleven. How many people who visited the museum that day were nonmembers?

Add together together the two numbers in the ratio: 5 + 11 = 16. Divide that sum into the total number of visitors: 176 ÷ 16 = 11. Multiply that caliber by the ratio number representing the non-members (xi): (11)(11) = 121 non-members. (If yous wanted to find the number of members, you'd multiply eleven by the 5 in the ratio: (11)(5) = 55 members.)
Question

What fractions do non piece of work?

The higher up technique works with all fractions. Some fractions are only more than complicated than others, as in Method 2 higher up.
Question

How practise I multiply 8 by three/4 ?

Multiply the whole number past the numerator, and go on the aforementioned denominator. Reduce the fraction if possible. (Another mode of looking at it is to catechumen the 8 to the fraction viii/1, then create a new fraction by multiplying the 2 numerators together to go the new numerator, and multiplying the ii denominators together to get the new denominator, which volition be the aforementioned every bit the old denominator. Reduce if possible.)
Question

How practise I do it if there is = afterwards the two fractions?

Cross-multiplying works only when one fraction is gear up equal to the other. In other words, the "equals" sign must appear between the two fractions.
Question

60% of 145 is what?

Multiply 145 by 0.vi.
Question

I'm stuck so bad on x/2 - 2/3 = 2x/3. Any aid?

Multiply both sides of the equation past half dozen, considering 6 is the lowest common denominator of the equation (because two times 3 is half dozen). That turns the equation into this: 3x - iv = 4x. Subtract 3x from both sides of the equation, then that -4 = ten.
Question

What is the solution of 19/38 = 10/19?

First reduce xix/38 to one/ii. So 1/two = ten/19. Then cantankerous-multiply: (1)(xix) = (2)(x). So nineteen = 2x, and x = 19/ii, or 9½.
Question

How do I work out x/i x 2500/24 x 1/60?

Multiply the three numerators together to get the final numerator. Do the same with the denominators. Reduce if necessary.
Question

How to I solve k+1 over k-12 equals 4/3?

(k + one) / (thou - 12) = four/3. Cross-multiply: (grand + 1)(3) = (m - 12)(4). And so (3k + 3) = (4k - 48). Subtract 3k from both sides, and add 48 to both sides: 51 = thousand.

Show more answers

Inquire a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Video

Note that if you substituted a different number (say, v) in the same proportion, you'd have 2/v = x/13. Even if yous multiply the left-side equation by 5/v once again, you get 10/25 = ten/13, which is conspicuously wrong. The latter case signals that you lot made an error in your cross-multiplication technique.
You lot can check your work by substituting the issue you got directly into the original proportion. If the proportion simplifies down to a valid argument, such as 1 = 1, your work was right. If the proportion simplifies downward to an invalid statement, such as 0 = 1, you made an error. For example, substituting two.6 into the proportion gives yous two/(2.6) = ten/13. Multiply the left-side proportion by 5/five and you have 10/thirteen = 10/13, a valid statement that cancels downward to 1 = 1. And then 2.6 is correct.

Thank you for submitting a tip for review!

About This Article

Article Summary X

To cross multiply, first by multiplying the numerator of the left-mitt fraction by the denominator of the right-hand fraction. Then, multiply the numerator of the right-paw fraction by the denominator of the left-hand fraction. Next, set up the two products equal to each other. Finally, solve for the variable. To learn how to cross multiply with 2 of the same variable, roll down!

Did this summary help you?

Thanks to all authors for creating a page that has been read 639,960 times.