cross-multiply

  1. math_celebrity

    2/3 of a pie is four slices how many slices does the whole pie have

    2/3 of a pie is four slices how many slices does the whole pie have Let s be the number of total slices of pie. We're given: 2s/3 = 4 Cross Multiply: 2s = 3 * 4 2s = 12 Divide each side by 2: 2s/2 = 12/2 s = 6
  2. math_celebrity

    One-half a number is fifty

    The phrase a number means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. One-half a number means we divide x by2: x/2 The word is means equal to. We set x/2 equal to 50 for our algebraic expression x/2 = 50 If the problem asks us to solve for x, we...
  3. math_celebrity

    1/n + 3/5 = 1

    1/n + 3/5 = 1 Subtract 3/5 from each side where 1 = 5/5 1/n + 3/5 - 3/5 = 5/5 - 3/5 1/n = 2/5 Cross multiply: 5 * 1 = 2 * n 2n = 5 Divide each side by 2: n = 5/2 or 2.5
  4. math_celebrity

    1/n + 2/n + 3/n + 4/n = 1

    1/n + 2/n + 3/n + 4/n = 1 10/n = 1 Cross multiply: n * 1 = 10 n = 10
  5. math_celebrity

    1/n^2 = 3/192

    1/n^2 = 3/192 Cross multiply: 192 * 1 = 3 * n^2 3n^2 = 192 Divide each side by 3: 3n^2/3 = 192/3 Cancel the 3's on the left side: n^2 = 64 Take the square root of both sides: n = 8 or -8
  6. math_celebrity

    3n/5 = 1

    3n/5 = 1 Cross multiply: 3n = 5 * 1 3n = 5 Divide each side by 3: 3n/3 = 5/3 n = 5/3
  7. math_celebrity

    n/11 = 11

    n/11 = 11 Cross multiply: n = 11 * 11 n = 121
  8. math_celebrity

    -n/8 = 80

    -n/8 = 80 Cross multiply: -n = 80 * 8 -n = 640 Multiply each side by -1: -1 * -n = -1 * 640 n = -640
  9. math_celebrity

    1/10n = 100

    1/10n = 100 Cross multiply: n = 100 * 10 n = 1000
  10. math_celebrity

    At the 2002 Winter Olympics, Austria won 2 gold medals. This was 1/8 of the total medals Austria won

    At the 2002 Winter Olympics, Austria won 2 gold medals. This was 1/8 of the total medals Austria won. How many did Austria win? Let t be the total medals Austria won. We have: 2 = x/8 Cross multiply, we get: x = 2 * 8 x = 16
  11. math_celebrity

    9 divided by the sum of x and 4 is equal to 6 divided by x minus 4

    9 divided by the sum of x and 4 is equal to 6 divided by x minus 4. Build our two algebraic expressions first: 9 divided by the sum of x and 4 9/(x + 4) 6 divided by x minus 4 6/(x - 4) The phrase is equal to means and equation, so we set the algebraic expressions equal to each other: 9/(x +...
  12. math_celebrity

    Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now

    Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. How many did she start with? Take this in parts Maria starts with b boxes. She buys seven more. So she has b + 7 boxes A week later, half of all her boxes are destroyed in a...
  13. math_celebrity

    Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of

    Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: Benny buys...
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