High School

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B. Word problems:

1. In a class of 40 students, \(\frac{3}{8}\) of the students are girls. What fraction of the class are boys?

2. A recipe calls for \(\frac{3}{4}\) cup of flour. If you only have \(\frac{1}{2}\) cup, how much more flour do you need?

3. A baker has \(\frac{3}{5}\) of a bag of flour. She uses \(\frac{1}{2}\) of it to make bread. How much flour does she have left?

C. Simplifying rational numbers:

1. Simplify the following fractions:
(a) \(\frac{36}{54} = \frac{18}{27} = \frac{2}{3}\)
(b) \(\frac{45}{60} = \frac{3}{4}\)
(c) \(\frac{18}{24} = \frac{3}{4}\)

2. Convert the following decimal to a rational number:
(a) 0.75
(b) 1.2
(c) -0.4

Answer :

Let's solve each part of the question step-by-step:

B. Word Problems:

  1. Finding the fraction of boys in the class:

    In a class of 40 students, [tex]\frac{3}{8}[/tex] of the students are girls.

    To find the number of girls, calculate: [tex]40 \times \frac{3}{8} = 15[/tex] girls.

    Therefore, the number of boys is [tex]40 - 15 = 25[/tex] boys.

    The fraction of the class that are boys is [tex]\frac{25}{40}[/tex].

    Simplifying [tex]\frac{25}{40}[/tex]:

    [tex]\frac{25}{40} = \frac{5}{8}[/tex] after dividing both the numerator and the denominator by 5.

  2. Calculating more flour needed for the recipe:

    The recipe requires [tex]\frac{3}{4}[/tex] cup of flour.

    You currently have [tex]\frac{1}{2}[/tex] cup of flour.

    To find how much more flour is needed: [tex]\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4}[/tex].

    Subtracting gives [tex]\frac{1}{4}[/tex] cup more flour is needed.

  3. Determining flour left with the baker:

    The baker has [tex]\frac{3}{5}[/tex] of a bag of flour.

    She uses [tex]\frac{1}{2}[/tex] of it to bake bread.

    To calculate the flour used: [tex]\frac{3}{5} \times \frac{1}{2} = \frac{3}{10}[/tex].

    Flour left: [tex]\frac{3}{5} - \frac{3}{10}[/tex].

    Converting [tex]\frac{3}{5}[/tex] to [tex]\frac{6}{10}[/tex], the subtraction gives [tex]\frac{6}{10} - \frac{3}{10} = \frac{3}{10}[/tex] of a bag of flour left.

C. Simplifying Rational Numbers:

  1. Simplifying fractions:

    a) [tex]\frac{36}{54}[/tex]: Divide both numerator and denominator by 18: [tex]\frac{36 \div 18}{54 \div 18} = \frac{2}{3}[/tex].

    b) [tex]\frac{45}{60}[/tex]: Divide both numerator and denominator by 15: [tex]\frac{45 \div 15}{60 \div 15} = \frac{3}{4}[/tex].

    c) [tex]\frac{18}{24}[/tex]: Divide both numerator and denominator by 6: [tex]\frac{18 \div 6}{24 \div 6} = \frac{3}{4}[/tex].

  2. Converting decimals to rational numbers:

    a) 0.75: This is equivalent to [tex]\frac{75}{100}[/tex], which simplifies to [tex]\frac{3}{4}[/tex] by dividing by 25.

    b) 1.2: This is equivalent to [tex]\frac{12}{10}[/tex], which simplifies to [tex]\frac{6}{5}[/tex] by dividing by 2.

    c) -0.4: This is equivalent to [tex]\frac{-4}{10}[/tex], which simplifies to [tex]\frac{-2}{5}[/tex] by dividing by 2.

I hope this helps! Let me know if you have more questions.

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