How to Fill in Missing Numbers for Fractions

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If Mrs. Dale's 6th-grade class can answer 10 quiz questions in five minutes, how many quiz questions can they answer in 14 minutes? Although it might seem trivial, this sort of word problem perfectly illustrates the application of equivalent fractions to find the missing piece in related proportions. There's just one problem: A piece of the puzzle – the answer to how many quiz questions the kids can answer – is missing, but you can use cross multiplication to find it.

TL;DR (Too Long; Didn't Read)

Write down your data as two equivalent fractions, letting x represent the unknown quantity. Multiply the numerator of the first fraction by the denominator of the second fraction, and then multiply the denominator of the first fraction by the numerator of the second fraction. Set the two quantities as equal and solve for x.

1. Designate Numerators and Denominators

2. Before you can cross-multiply to find the missing number, you have to set up the problem using equivalent fractions. Start by designating which data goes in the numerator (top number) of the fraction and which data goes in the denominator (bottom number). For example, you could say that the numerators will represent how many problems the students can solve, while the denominators of the fractions will represent how many minutes they have to do the solving.

3. Write Out the Fractions

4. Now that you've designated which information goes where, write out the fractions and set them as equal to each other. So you'll have 10/5 = x/14. Here, 10/5 is another way of writing that Mrs. Dale's students can solve 10 problems in five minutes, while x/14 is a way of writing that the students can solve an unknown number of problems (represented by the "x") in 14 minutes.

5. Cross-Multiply

6. Multiply the numerator of the first fraction by the denominator of the second fraction. Then multiply the numerator of the second fraction by the denominator of the first fraction. Set the two quantities as equal to each other. To continue the example, you'd have 10 × 14 = 5x.

7. Simplify Where Possible

8. Simplify your equation as much as possible. In this case, you can work out that 10 × 14 = 140 and write the equation as 140 = 5x.

9. Solve for X

10. Keep your eye on the prize: Your ultimate goal is to solve for x and find out what x represents. To continue the example, divide both sides of the equation by 5. This gives you 140 ÷ 5 = 5x ÷ 5. Simplify the fraction, and you have 28 = x. So Mrs. Dale's class can solve 28 problems in 14 minutes.