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Comparing Fractions Using Cross Multiplication

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Basics on the topic Comparing Fractions Using Cross Multiplication

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Cross Multiplication

When we compare fractions, we are determining which one is greater than, less than, or equal to the other.

Cross multiplication is one method used to compare fractions. To compare using cross multiplication: 1)Multiply the denominator of one fraction with the numerator of the other fraction being compared.

2) Compare the products to determine if the fraction is greater than, less than, or equal to the other.

Transcript Comparing Fractions Using Cross Multiplication

Axel and Tank are in the treasure hunt room at the Sunken Ship Funhouse. They get five minutes in the room to find as many treasure chests with the greater amounts of jewels as they can. "This one has two-thirds jewels!" "This one has three-fifths! How do we know which one has more?" In order to collect as many jewels as they can, Axel and Tank will be... Comparing Fractions Using Cross Multiplication. When we compare fractions, we are determining which one is greater than, less than, or equal to the other. Cross multiplication is one method used to compare fractions. To compare using cross multiplication, multiply the denominator of one fraction with the numerator of the other fraction being compared. Then, compare the products to determine if the fraction is greater than, less than, or equal to the other. Let’s use the two-thirds and three-fifths fractions as an example. First, multiply THIS denominator, three, by THIS numerator, three. Three times three is nine. Next, multiply THIS denominator, five, across to THIS numerator, two. Five times two is ten. Now, compare the products. Ten is greater than nine… so two-thirds is GREATER than three-fifths. Why does cross multiplication work when comparing fractions? When we compare fractions with different denominators, we look to make equivalent fractions with the same denominator. We find the least common multiple that each denominator shares and multiplying the numerator by that same number. In the fractions two-thirds and three-fifths, the common denominator is fifteen. Since you multiply three times five to make fifteen, multiply the numerator by five. Two times five is TEN. Five times three is fifteen and three times three equals NINE. Ten-fifteenths is greater than nine-fifteenths...so two-thirds is greater than three-fifths. In cross multiplication, the product of each side of the fraction is the SAME as the numerators created in the equivalent fractions. This method is useful when you are working with fractions with larger numbers or have multiple-step problems to solve. Now, let's help Axel and Tank compare more fractions using cross multiplication. Compare seven-ninths and eight-twelfths. What is nine times eight? Seventy-two. What is twelve times seven? Eighty-four. Is seven-ninths less than, greater than, or equal to eight-twelfths? Seven-ninths is GREATER than eight-twelfths. Compare five-fourteenths and seven-twelfths. Pause the video to solve and press play when you're ready to check the solution. Twelve times five is sixty and fourteen times seven is ninety-eight so, five-fourteenths is LESS than seven-twelfths. Looks like time is running out for Axel and Tank's treasure hunt, so let's review. Remember... when we compare fractions, we are determining which one is greater than, less than, or equal to the other. Cross multiplication is one method used to compare fractions. To solve using cross multiplication, multiply the denominator of one fraction with the numerator of the other fraction across the expression. Then, compare the products to determine which fraction is greater than, less than, or equal to the other. This method is useful when you are working with larger fractions or have a multiple-step problem to solve. "Time's up! How do we get out of here?" "This way!"

Comparing Fractions Using Cross Multiplication exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Comparing Fractions Using Cross Multiplication .
  • Label the picture.

    Hints

    2 x 5 = ? 3 x 3 = ?
    Which answer is greater?

    The symbol < means the left is less than the right.
    The symbol > means the left is greater than the right.
    The symbol = means both the left and right are equal to each other.

    Solution
    • To find which fraction is greater, use cross multiplication with the numerators and denominators.
    • 2 x 5 = 10, and 3 x 3 = 9.
    • 10 is greater than 9, so $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.
  • Complete the steps to compare fractions.

    Hints

    Cross multiply the numerator and denominator to find which fraction is greater, lesser, or equal.

    Shown below is an example.

    $\frac{9}{10}$ ? $\frac{4}{5}$

    In order to find which is greater, first solve for 9 x 5 and 10 x 4 as this cross multiplys the numerators and denominators. Once we have the answers we can compare those numbers.

    The symbol < means the left is less than the right.
    The symbol > means the left is greater than the right.
    The symbol = means both the left and right are equal to each other.

    Solution
    • To find which number is greater, first multiply the numerator of the left fraction with the denominator of the right fraction.
    • Next, multiply the denominator of the left fraction with the numerator of the right fraction.
    • Compare the products of the multiplication equations to find which result is greater.
    • 45 is greater than 40, so $\frac{9}{10}$ is greater than $\frac{4}{5}$.
  • Match the fractions and expressions.

    Hints

    Cross multiply the numerator and denominator to find which fraction is greater than, less than, or equal to.

    Shown below is an example.

    Example:

    • $\frac{4}{9}$ and $\frac{3}{5}$
    • 4 x 5 = 20, 9 x 3 = 18
    • 20 > 18
    • So, $\frac{4}{9}$ > $\frac{3}{5}$

    Solution

    $\frac{9}{10}$ and $\frac{4}{5}$
    9 x 5 = 45
    10 x 4 = 40
    45 < 40

    $\frac{2}{5}$ and $\frac{7}{9}$
    2 x 9 = 18
    7 x 5 = 35
    18 < 35

    $\frac{6}{3}$ and $\frac{4}{9}$
    6 x 9 = 54
    3 x 4 = 12
    54 < 12

    $\frac{2}{10}$ and $\frac{8}{14}$
    2 x 14 = 28
    10 x 8 = 80
    28 < 80

  • Highlight the correct expressions.

    Hints

    Cross multiply the numerator and denominator to find which fraction is greater than, less than, or equal to.

    Shown below is an example.

    The symbol < means the left is less than the right.
    The symbol > means the left is greater than the right.
    The symbol = means both the left and right are equal to each other.

    Solution

    1) 4 x 5 = 20, 6 x 3 = 18. 20 is greater than 18, so $\mathbf{\frac{4}{6}}$ is greater than $\mathbf{\frac{3}{5}}$.
    2) 7 x 10 = 70, 9 x 6 = 54. 70 is greater than 54, so $\mathbf{\frac{7}{9}}$ is greater than $\mathbf{\frac{6}{10}}$.
    3) 2 x 10 = 20, 3 x 8 = 24. 20 is less than 24, so $\mathbf{\frac{2}{3}}$ is less than $\mathbf{\frac{8}{10}}$.
    4) 2 x 10 = 20, 6 x 5 = 30. 20 is less than 30, so $\mathbf{\frac{2}{6}}$ is less than $\mathbf{\frac{5}{10}}$.

  • Compare the fractions.

    Hints

    The symbol < means the left is less than the right.
    The symbol > means the left is greater than the right.
    The symbol = means both the left and right are equal to each other.

    In order to find which fraction is greater than, less than, or equal to, cross multiply the numerator and denominator. Then compare the products.
    In this example, 10 is greater than 9. So, $\mathbf{\frac{2}{3}}$ is greater than $\mathbf{\frac{3}{5}}$.

    Solution
    • $\mathbf{\frac{7}{9}}$ and $\mathbf{\frac{8}{12}}$
    • 7 x 12 = 84
    • 9 x 8 = 72
    • 84 > 72
    • $\mathbf{\frac{7}{9}}$ > $\mathbf{\frac{8}{12}}$
  • Complete the blanks with >, =, or <.

    Hints

    Cross multiply the numerator and denominator to find which fraction is greater, lesser, or equal.

    Example:

    • $\frac{4}{9}$ and $\frac{3}{5}$
    • 4 x 5 = 20, 9 x 3 = 18
    • 20 < 18
    • So, $\frac{4}{9}$ > $\frac{3}{5}$

    Solution

    1) $\frac{5}{11}$ and $\frac{2}{3}$
    5 x 3 = 15
    11 x 2 = 22
    15 < 22
    $\frac{5}{11}$ < $\frac{2}{3}$

    2) $\frac{7}{12}$ and $\frac{6}{7}$
    7 x 7 = 49
    12 x 6 = 72
    49 < 72
    $\frac{7}{12}$ < $\frac{6}{7}$

    3) $\frac{16}{20}$ < $\frac{8}{10}$
    16 x 10 = 160
    20 x 8 = 160
    160 = 160
    $\frac{16}{20}$ = $\frac{8}{10}$

    4) $\frac{13}{15}$ < $\frac{8}{9}$
    13 x 9 = 117
    15 x 8 = 120
    117 < 120
    $\frac{13}{25}$ < $\frac{8}{9}$